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Showman et al.: The Global Atmospheric Circulation of Saturn 11.1 INTRODUCTION
The Global Atmospheric Circulation of Saturn
Adam P. Showman, Andrew P. Ingersoll, Richard Achterberg, and Yohai Kaspi
Over the past decade, the Cassini spacecraft has provided an unprecedented observationalrecord of the atmosphere of Saturn, which in many ways now surpasses Jupiter as thebest-observed giant planet. These observations, along with data from the Voyager spacecraftand Earth-based telescopes, demonstrate that Saturn, like Jupiter, has an atmospheric circulationdominated by zonal (east-west) jet streams, including a broad, fast eastward equatorial jet andnumerous weaker jets at higher latitudes. Imaging from Voyager, Cassini, and groundbasedtelescopes also document a wide range of tropospheric features, including vortices, waves,turbulence, and moist convective storms. At large scales, the clouds, ammonia gas, andother chemical tracers exhibit a zonally banded pattern whose relationships to the zonal jetsremains poorly understood. Infrared observations constrain the stratospheric thermal structureand allow the derivation of stratospheric temperatures; these exhibit not only the expectedseasonal changes but a wealth of variations that are likely dynamical in origin and highlightdynamical coupling between the stratosphere and the underlying troposphere. In parallel tothese observational developments, significant advances in theory and modeling have occurredover the past decade, especially regarding the dynamics of zonal jets, and we survey these newdevelopments in the context of both Jupiter and Saturn. Highly idealized two-dimensionalmodels illuminate the dynamics that give rise to zonal jets in rapidly rotating atmospheresstirred by convection or other processes, while more realistic three-dimensional models of theatmosphere and interior are starting to identify the particular conditions under which Jupiter-and Saturn-like flows—including the fast equatorial superrotation, multiple jets at higherlatitudes, storms, and vortices—can occur. Future data analysis and models have the potentialto greatly increase our understanding over the next decade.
11.1. Introduction1
The dynamics of Jupiter and Saturn have long been the2
subject of fascination. Although Galileo trained the tele-3
scope on both objects starting in 1610, the pace of at-4
mospheric discoveries over subsequent centuries was far5
slower for Saturn than for Jupiter because of the fact that6
Saturn is dimmer, smaller in Earth’s sky, and more muted in7
its cloud-albedo contrasts. The first description of Jupiter’s8
zonal banding occurred in 1630. Cassini and others dis-9
covered short and long-lived spots, the equatorial current,10
and other atmospheric features on Jupiter starting in the lat-11
ter decades of the 1600s, and ever more refined observa-12
tions have continued episodically since then (e.g., Rogers13
1995). In contrast, early observations of Saturn could not14
make out features on the planet’s surface, instead empha-15
sizing the discovery of Saturn’s moons and the nature of its16
rings (van Helden 1984). Cassini reported an equatorial belt17
on Saturn in 1676, and hints of non-zonal atmospheric fea-18
tures appeared a century later in the 1790s, but it took until19
the latter decades of the 1800s before spots could reliably20
be observed on Saturn (van Helden 1984). This disparity21
in pace of discovery between Jupiter and Saturn continued22
through the twentieth century, and even over the last few23
decades, the relative difficulty of observing Saturn relative24
to Jupiter means that Saturn has received much less atten-25
tion than its sister planet. Yet the Cassini mission, in or-26
bit around Saturn since 2004, has revolutionized the quality27
and quantity of observational constraints, which now rival 1
or exceed those available for Jupiter. This for the first time 2
places Saturn at the forefront of understanding giant planets 3
as a class. 4
The atmospheric circulations on Saturn and Jupiter are 5
dominated by numerous fast east-west (zonal) jet streams, 6
which interact with a wealth of vortices, waves, turbu- 7
lent filamentary structures, convective storms, and other 8
features in poorly understood ways. The jet profiles ex- 9
hibit qualitative similarities—on both planets, there exists 10
a broad, fast prograde (eastward) equatorial jet and numer- 11
ous narrower, weaker jets at higher latitudes. Nevertheless, 12
the zonal jets are considerably broader, faster, and fewer 13
in number on Saturn than Jupiter—peak wind speeds reach 14
∼500 m s−1 on the former but never exceed 200 m s−1 on 15
the latter. Both planets exhibit cloud banding that is modu- 16
lated by the zonal jets and, at large scales, is far more zon- 17
ally symmetric than the cloud pattern on Earth. Yet the de- 18
tailed relationship of the cloud-band structure to the zonal- 19
jet structure differs considerably between Jupiter and Sat- 20
urn. Moreover, despite the existence of many dozens of 21
vortices on both planets, Saturn lacks prominent large vor- 22
tices like Jupiter’s Gread Red Spot and White Oval. These 23
differences remain poorly understood. As case studies in 24
similarities and differences, comparative investigations of 25
the two planets therefore have great potential for insights. 26
Motivations for studying the atmospheric dynamics of 27
Jupiter and Saturn are several. Our understanding of Earth’s 28
1
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
circulation is well developed (see, e.g., Vallis 2006), but1
necessarily confined to the specific conditions relevant to2
Earth. The giant planets illustrate how an atmosphere’s cir-3
culation operates when there is no planetary surface, when4
the incident solar energy flux is weak (∼2 W m−2 on Saturn5
versus 240 W m−2 for Earth), when the energy flux trans-6
ported through the interior is comparable to the energy flux7
absorbed from the Sun, and when the background gas com-8
prises hydrogen rather than high-molecular-weight species9
like N2 or O2 (which, among other things, promotes larger10
atmospheric scale heights on Jupiter and Saturn than on11
Earth and implies that, opposite to the situation on Earth,12
moist air is denser than dry air at a given temperature and13
pressure). Moreover, as they lack many of the complexities14
of the Earth system, the giant planets serve as ideal lab-15
oratories for testing and understanding fundamental issues16
in geophysical fluid dynamics (GFD) such as the dynamics17
of zonal jets, vortices, and stratified turbulence. The gi-18
ant planets are dynamic and exhibit meteorological and cli-19
matic changes on timescales ranging from minutes to cen-20
turies. Most of the phenomena that are richly characterized21
in the observational record remain poorly understood; con-22
tinued observations, theory, and modeling will be necessary23
to understand even some of the zeroth-order aspects of the24
circulation. Finally, Saturn and Jupiter can serve as a proto-25
type for helping to understand the behavior of the numerous26
brown dwarfs and giant planets that are being discovered27
outside the solar system.28
The primary goal of this chapter is to survey observa-29
tions and theory of Saturn’s atmospheric dynamics near30
the close of the Cassini mission. Our scope is Saturn’s31
global atmospheric circulation, emphasizing the thermal32
and dynamical structure of the large-scale zonal jets, vor-33
tices, turbulence, and interior structure. We summarize the34
current dynamical state of Saturn—emphasizing observa-35
tions but including dynamical interpretation and analysis36
where appropriate—beginning with the troposphere (Sec-37
tion 11.2), followed by the stratosphere (Section 11.3). In38
Section 11.4, we summarize Saturn’s dynamics, beginning39
with basic balance arguments for jet structure, and proceed-40
ing to a summary of models for the formation of the zonal41
jets. Anticipating the Grand Finale stage of the Cassini Mis-42
sion, we end with a brief discussion of constraints provided43
by gravity data on the deep jet structure. Our review fol-44
lows the prior reviews of Ingersoll et al. (1984) and Del45
Genio et al. (2009), who summarized the state of knowl-46
edge after the Voyager flyby and nominal Cassini missions,47
respectively. It also complements other reviews of Jupiter48
and the giant planets generally, including Ingersoll (1990),49
Marcus (1993) Dowling (1995a), Ingersoll et al. (2004), and50
Vasavada and Showman (2005). Reviews of Saturn’s poles,51
stratospheric thermal structure, and convective storms can52
be found in the chapters by Sayanagi et al., Fletcher et al.,53
and Sanchez-Lavega et al. in this volume.54
11.2. Observations of the Troposphere 1
On Saturn the winds blow primarily east-west and are or- 2
ganized into alternating jet streams, each peaking at its par- 3
ticular latitude. At large scales, the cloud structure is zon- 4
ally banded—to a much stronger degree than on Earth—but 5
also contains numerous vortices, waves, storms, and various 6
cloud features at small scales (Figure 11.1). Viewed from a 7
non-rotating reference frame, cloud features near the equa- 8
tor exhibit periods of about 10 h 10 min. At latitudes of 9
35–40 in each hemisphere, the recurrence period is about 10
10 h 40 min, and at higher latitude the periods vary within 11
this range up to the pole. 12
These observations indicate that rotation plays a crucial 13
role in the atmospheric dynamics of Saturn. The importance 14
of rotation can be characterized using the Rossby number, 15
which is the ratio of the advection force to the Coriolis force 16
in the horizontal momentum equation. The advection force 17
per mass has characteristic magnitude U2/L, and the hor- 18
izontal Coriolis force per mass has characteristic magni- 19
tude fU , where U is the characteristic wind speed, L is 20
the characteristic horizontal length scale of the circulation 21
(e.g., the jet width), f = 2Ω sinφ is the Coriolis parameter, 22
Ω is the planetary rotation rate (2π over the rotation pe- 23
riod), and φ is latitude. Thus, the Rossby number is given 24
byRo = U/fL. The cloud measurements described above 25
suggest a characteristic rotation period of order 10.5 hours, 26
with zonal speed differences between the cloud bands of 27
typically ∼100 m s−1 (Figure 11.1 and 11.2). Inserting ap- 28
propriate values of f ≈ 2 × 10−4 s−1, U ≈ 100 m s−1, 29
and L ≈ 107 m (relevant to Saturn’s zonal jets), we ob- 30
tain Ro ≈ 0.05. Thus, on Saturn—as well as on Jupiter, 31
Uranus, Neptune, and Earth’s atmosphere and oceans— 32
the large-scale circulation exhibits small Rossby number. 33
This estimate implies that, for the large-scale flows on the 34
giant planets, advective forces are weak compared to the 35
Coriolis force. Since the pressure-gradient force is the 36
only other significant force in the horizontal momentum 37
equation, the smallness of Ro implies that the dominant 38
balance in the horizontal momentum equation is between 39
the Coriolis force and the pressure-gradient force—called 40
geostrophic balance (see, e.g., Holton and Hakim 2013, 41
Chapter 2). 42
Although the observed differential rotation is evidence 43
of wind, we do not know the precise wind speeds relative 44
to the planetary interior—simply because Saturn’s interior 45
rotation rate is not well determined. The other giant planets 46
have internally generated magnetic fields that are tilted with 47
respect to the rotation axis, and those fields are presumably 48
locked to the electrically conducting fluid interiors, at least 49
on time scales of years to decades, so the daily wobble of 50
the field gives us a good estimate of the internal rotation pe- 51
riod. Saturn has an internal field as well, but it is not tilted. 52
Thus far, the instruments on Cassini and other spacecraft 53
have been unable to detect a wobble and therefore unable to 54
provide an exact period from which to measure the winds. 55
Voyager flew past Saturn in 1980 and measured magnetic 56
2
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
the absorbing gas. In MT3, high-altitude features appearbright against the dark background of absorbing gas.Saturn’s appearance in UV3 will expose any ultraviolet-absorbing aerosols and is strongly affected by gas scatter-ing. In UV3, high-altitude features that absorb UV lightappear dark against a bright background, since there is lessgas above them to scatter light toward the spacecraft. Thesuite of filters is expected to reveal features at pressurelevels between tens and hundreds of mbar.[22] The CB2 map contains more fine-scale structure than
the others in Figures 5a and 5b, such as the internal structureof larger vortices, the presence smaller vortices and patchyclouds, and the convective storm and its associated clouds.In images using filters sensitive to higher features, thecontrast between major latitude bands increases, but thereis less fine-scale detail. However, when MT images areviewed at full spatial resolution, the bands are found tocontain extended cloud filaments that bend and fold due tointeractions between jets, or between jets and vortices. Ingeneral, there are no major features (e.g., vortices) that areunique to the higher-sounding wavelengths. An importantexception occurs near the equator, where there is relativelysharp detail in MT2 and MT3 (and inverted in brightness in
UV3) that is distinct from cloud textures within CB2 at thesame location. The presence of distinct and different cloudmorphologies in the CB2 and MT2 images allowed thedirect measurements of vertical wind shear reported inPorco et al. [2005]. The convective storm is not visible inMT2, MT3, or UV3, suggesting that it does not penetratebeyond the deeper levels sensed.[23] Saturn’s banding is correlated with the profile of
zonal winds, but not in a way that obviously implies the‘‘belt/zone’’ model, in which bright anticyclonic regions(zones) signify the upwelling branches of meridional circu-lations and clear cyclonic regions (belts) are sites ofsubsidence [Smith et al., 1981]. Figures 5a and 5b showthat narrow bands with less cloud/haze scattering occur justsouthward (i.e., on the cyclonic sides) of the eastward jetmaxima at 49.5!S, 60.5!S, and 74.5!S. The two broadregions in between these eastward jets are relatively uniformin brightness, despite the change in sign of vorticity acrossthe westward jet. The region in between the eastward jets at33!S and 49.5!S conforms more to the belt/zone model,with more scattering from anticyclonic latitudes and lessfrom cyclonic. The band just south of 60.5!S is unusuallybright in BL1 and UV3, suggesting low aerosol opacity andenhanced Rayleigh scattering. Finally, the polar spot is darkat all wavelengths except UV3, where it is absent.
4. Vortices
[24] We have analyzed the characteristics and behavior ofvortices by measuring their sizes, shapes, and spatial distri-bution on the HRMs and monitoring their evolution on theAMs.Avortexwas noted if it was present in three consecutiveAMs or in both HRMs. There were many small, shorter-livedfeatures, but these could not be distinguished from imageartifacts. We manually measured the center location, east-west extent, and north-south extent of each vortex using adisplay tool that allows zooming and adjustment of brightnessand contrast. We estimate the uncertainty in the centerlocation to be <2 pixels based on frame-to-frame repeatabilityand repeated measurements on the same frame. Our approachto determining the center location is similar to that of Li et al.[2004]. For symmetric vortices, we estimated the center pixel;for asymmetric vortices, we estimated the centroid of the areaof greatest contrast.
4.1. Number and Size Frequency Distribution
[25] The number of vortices counted in the AMs in-creased with time, primarily as a result of the threefoldincrease in spatial resolution as the spacecraft approachedSaturn. Even the final AMs contain only !65 vortices,compared to 138 in the HRMs. The size frequency distri-butions in Figure 6 suggest that the population of vorticeswith east-west diameters <1000 km cannot accurately becounted in the final AM. Therefore the AMs cannot revealhow the total number of vortices over all sizes varied withtime. However, a comparison of the AM and HRM histo-grams suggests that the number of mid to large vorticesevolved but remained similar between the two observations.
4.2. Vortex Characteristics
[26] We have attempted to classify vortices into familiesbased on their brightness and morphology at 750 nm (CB2
Figure 5b. Similar to Figure 5a, but maps were con-structed from images acquired using the three ISS filterscentered in progressively stronger CH4 absorption bands:(top) MT1 (619 nm), (middle) MT2 (727 nm), and (bottom)MT3 (889 nm).
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ring of bright cloud material at 88.8!S. The dark spot isreminiscent of the infrared hot spot described by Orton andYanamandra-Fisher [2005]. The polar cloud ring is slightlyoff center from the pole (not due to viewing geometry) andcontains a small segment of arc with increased width.
[17] We measured the latitudinal profile of zonal wind bytracking the displacement of cloud features on the pair ofHRMs. The time separation is 10 hours 30 min, giving aprecision of 1.4 m s!1 for a displacement of one map pixel atthe equator. The combination of errors due to image naviga-tion, feature tracking, and foreshortening at higher latitudes isestimated to be <20 pixels (consistent with the low dispersionof the measurements shown below). Features were identifiedand tracked by eye using custom IDL software that blinks themapped images on a monitor and allows the user to fine-tunetiepoint locations on a pair of static zoom windows. Trackedfeatures include discrete clouds and long-livedmorphologicalfeatures (e.g., kinks) within cloud bands or streaks. Vortices,diffuse clouds/hazes, and features that exhibited nonzonalmotionswere avoided in order to derive the ambient flowwiththe highest accuracy. At any given location, cloud featuresappear to translate with a single wind speed; no evidence ofmultilevel cloud decks or vertical wind shear was found in theCB2 images.[18] Figure 4 shows a total of 458 wind measurements,
including 347 on the HRMs from our study and 111 on the
Figure 2. Polar stereographic projection of Saturn’s south-ern hemisphere on 18 September 2004, during Cassini’s firstrevolution of the planet. Themap shown here is the first of theHRM pair used for polar wind measurements. The spatialresolution of the raw 750-nm images is"50 km pixel!1 in theimage plane. Data within 10! latitude of the pole are takenfrom a single mapped image.
Figure 3. Profile of Saturn’s zonal winds measured onCassini images overlain on a segment of the cylindrical mapshown in Figure 1.
Figure 4. Plot of the 458 Cassini zonal wind measure-ments from this study and Porco et al. [2005]. The thinsolid curve has been manually fit to the Cassini points.Voyager (thick shaded curve) [Sanchez-Lavega et al., 2000]and HST (dashed curve) [Sanchez-Lavega et al., 2002]profiles are shown for comparison. The box near the polebounds the velocities of features on a circumpolar cloudring "3! in diameter.
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Fig. 11.1.— Cassini images of Saturn’s southern hemisphere. Left: A cylindrical projection mosaic comprised of CassiniISS images using the MT2 filter, centered in a methane absorption band at 727 nm wavelength and showing the equatorto ∼85S latitude and 180–360W longitude. The image is overlain with the zonal-wind profile obtained from cloudtracking (plotted such that 0 m s−1 in System III is at the center of the panel). Right: Polar stereographic projection ofCassini ISS images in the CB2 filter, which is centered at 750 nm, in the continuum between methane absorption bands.From Vasavada et al. (2006).
Fig. 11.2.— Mean zonal wind profile for the 2004–2009 time period. The black curve is from clear filters that sense cloudsin the 350–700 mbar pressure range. The red curve is from methane band filters that sense clouds in the 60–250 mbarpressure range. From Garcıa-Melendo et al. (2011).
fields, radio emissions, and modulations of the charged par-1
ticle distribution around the planet that pointed to a period2
that was close to the longest periods determined by tracking3
clouds in the atmosphere. Accordingly, the System III rota-4
tion period of 10 h 39 min 24 s was chosen as the reference5
frame from which to measure the longitudes and drift rates6
of phenomena on Saturn (Desch and Kaiser 1981). This 1
longitude system is the official standard, even though the 2
electromagnetic phenomena on which it was based have not 3
kept pace but have wandered in ways that are uncharacter- 4
istic of the planet’s interior. In recent years, several authors 5
have attempted to obtain improved estimates of the interior 6
3
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
rotation period. Anderson and Schubert (2007) and Read1
et al. (2009b) used theoretical arguments combined with the2
observed wind field to suggest rotation periods that are 5–3
6 minutes shorter than the System III period, and Helled4
et al. (2015) used the measured low-order gravitational co-5
efficients and the shape of the planet to suggest a rotation6
period of 10 h 32 min 45 s± 46 s. If these estimates are cor-7
rect, then the winds measured relative to the interior would8
be shifted westward (by a latitude-dependent value) relative9
to those plotted in Figure 11.2.10
On an oblate planet like Saturn, where the rotational flat-11
tening (1 − Rp/Re) is 9.8%, where Rp and Re are the po-12
lar and equatorial radii, there are two ways to define the13
latitude. Planetocentric latitude φpc is the angle of a line14
from the center of the planet relative to the equatorial plane.15
Planetographic latitude φpg is the angle of the local verti-16
cal relative to the equatorial plane. If we approximate the17
planet’s shape, e.g., on a constant-pressure surface, as an el-18
lipse rotated about its short axis, then the relation between19
φpg and φpc is tanφpg = (Re/Rp)2 tanφpc. Thus |φpg|20
is always greater than |φpc| except at the poles and equator,21
where they are equal. Both kinds of latitude are used in the22
literature and this review.23
11.2.1. Zonal Velocity24
Figure 11.2, from Garcıa-Melendo et al. (2011), shows25
the zonal mean zonal wind as a function of planetocentric26
latitude, measured in the System III reference frame. The27
curves are time averages from 2004 to 2009, but at high and28
mid latitudes the variations from year to year are generally29
less than the uncertainty of the measurement, which falls in30
the range 5 to 9 m s−1, depending on the latitude. Depar-31
tures from the zonal mean—the eddies—do not show up on32
this figure. They have been averaged out, but at least on a33
large scale the eddy winds are small.34
The two curves in Figure 11.2 refer to different alti-35
tudes. In both cases the winds are obtained by tracking36
small clouds in images separated by one Saturn rotation pe-37
riod. The black curve uses images in the CB2 and CB338
filters, centered at 752 and 959 nm, where the main sources39
of opacity are the clouds themselves. Generally this band-40
pass senses clouds at the 350–700 mbar pressure range, but41
clouds outside this range may show up at certain times and42
places. The red curve uses images in the MT2 and MT343
filters, centered at 727 and 890 nm, where methane, one44
of the well-mixed gases in the atmosphere, limits the depth45
one can see. Thus the red curve shows the motion of clouds46
and haze at the 60–250 mbar pressure range, depending on47
latitude. This range spans the tropopause—the temperature48
minimum where the pressure scale height (the e-folding49
scale) is of order 30 km, so the clouds contributing to the50
red curve are ∼40 km higher than those contributing to the51
black curve.52
One notable feature of the zonal wind profile is the high53
speed in the equatorial band—at least 360 m s−1 faster than54
the minimum speeds at higher latitudes. These differential55
speeds are two times larger than those on Jupiter and are 1
7–8 times larger than the difference between the easterlies 2
and westerlies on Earth. Nevertheless, they are comparable 3
to the speed differential on Uranus, and less than that on 4
Neptune. These differences are not well understood. 5
The four high-latitude eastward jets, separated by four 6
high-latitude westward jets (eastward jet minima) in each 7
hemisphere are another notable feature. Both in terms of 8
their speeds and their numbers, these jets are more like 9
Jupiter’s jets, although the latter are somewhat more numer- 10
ous and somewhat less speedy. Away from the equator, the 11
winds are remarkably steady in time and remarkably con- 12
stant in altitude. There is a general tendency for the profiles 13
at the zonal jet minima to be more rounded than the pro- 14
files at the zonal jet maxima, which are sharper. The zonal 15
wind must go to zero at the pole, and Figure 11.2 hints at 16
the extremely rapid drop in winds speed within one degree 17
of the south pole. This is the south polar vortex, like the eye 18
of a hurricane, with 150 m s−1 winds circling around the 19
pole at −89 latitude (Dyudina et al. 2008; O’Neill et al. 20
2015, 2016). The circulation direction is cyclonic, meaning 21
that it is in the same direction that the planet is rotating as 22
seen looking down from above. In the southern hemisphere 23
a cyclonic vortex is clockwise. A cyclonic vortex exists 24
at the north pole as well (Antunano et al. 2015), although 25
Figure 11.2 doesn’t show it because the north pole was in 26
darkness when the data were taken. Hurricanes on Earth 27
are also cyclonic, although they form in the subtropics and 28
drift around, unlike the polar vortices on Saturn (Dyudina 29
et al. 2008). See the chapter by Sayanagi et al. on polar 30
phenomena. 31
The final notable feature is the vertical variation near the 32
equator. From 10 to 25 in each hemisphere, the wind is 33
slightly stronger at the higher altitude. From 2 to 10, the 34
high-altitude winds are weaker, and within the narrow jet 35
inside ±2, the high-altitude winds are stronger. The equa- 36
torial winds are also variable in time. Garcıa-Melendo et al. 37
(2011) point out that the equatorial winds were 450 m s−1 38
at the time of the Voyager encounters in 1980 and 1981 39
(Sanchez-Lavega et al. 2000), and ranged up to 420 m s−1 40
as measured by Hubble in 1990 (Barnet et al. 1992). Garcıa- 41
Melendo et al. (2011) conclude that there was a real slow- 42
down of the wind speed at the equator. Nevertheless, Choi 43
et al. (2009) showed by tracking features in 5-µm images 44
from Cassini VIMS—which sense as deep as ∼2 bars— 45
that the near-equatorial winds reach speeds of ∼450 m s−1, 46
similar to the Voyager wind measurements. This suggests 47
that any real slowdown in the winds may have been con- 48
fined to the lower-pressure levels of the upper troposphere 49
(significantly above the level where VIMS 5-µm images 50
sense). Moreover, a stratospheric oscillation in temperature 51
has been observed from Earth-based telescopes since 1980 52
(Orton et al. 2008) and implies an oscillation in the winds 53
via the thermal-wind equation (see Section 11.3), which 54
may have some connection to the oscillation in equatorial 55
jet speeds seen in Figure 11.2. 56
4
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
11.2.2. Clouds and Temperatures1
The clouds that we see in the clear filters CB2 and CB32
are thought to be crystals of ammonia. From spectroscopic3
observations, we know that ammonia vapor is close to sat-4
uration at these levels, so it is likely that ammonia is con-5
densing. Solid particles do not give as clear a spectroscopic6
signature as the vapor, so it is difficult to say what other sub-7
stances are present in the cloud particles. What condenses8
below the ammonia cloud base depends on composition and9
temperature, and both are uncertain. One must rely on mod-10
els based on plausible assumptions, which we now describe.11
Figure 11.3, from Atreya (2006), is a cartoon showing12
a possible cloud structure for Saturn for three different as-13
sumptions about the mixing ratios of condensable gases rel-14
ative to hydrogen and helium, which are the major con-15
stituents. One takes the ratios O/H, N/H, S/H, and Ar/H16
on the Sun, determined spectroscopically, and multiplies17
(enriches) them all by a single factor, either 1, 5, or 10.18
Then one allows the reactive elements to combine with hy-19
drogen to form H2O, NH3, and H2S. The Ar and He stay20
in atomic form, and the remaining hydrogen becomes H2.21
Even with 10-fold enrichment, the minor constituents make22
up less than 2% of the molecules in the gas. One assumes23
Fig. 11.3.— Cloud structure for 1, 5, and 10-fold enrich-ment of H2O, NH3, and H2S relative to solar composition.An enrichment factor of 1 means taking the solar elemen-tal ratios of O/H, N/H, and S/H and allowing the mixtureto cool to planetary temperatures. Higher enrichment fac-tors are applied uniformly to all elements relative to hydro-gen and helium. Even with an enrichment factor of 10, thenumber of H2 + He molecules in the gas is still more than98%. From Atreya (2006), calculated using updated solarcomposition data from Grevesse et al. (2005).
the atmosphere is convecting up to the tops of the ammo- 1
nia clouds, which means temperature T and pressure p fol- 2
low an adiabat—a moist adiabat in this case to take into 3
account the latent heat released when the vapors condense. 4
The particular adiabat is chosen to match the observed T 5
and p at the top of the clouds, which is about as deep as 6
we can see with remote sensing instruments. In the fig- 7
ure the clouds are labeled and color-coded by their com- 8
position, and T , p values are given along the sides. For a 9
rising parcel, the less volatile substance, water, condenses 10
out first—at higher temperatures, and the more volatile sub- 11
stance, ammonia, condenses out last—at lower tempera- 12
tures. The location of cloud base is fairly certain provided 13
the composition is known. The cloud density is much less 14
certain, since it assumes that none of the condensate falls 15
out of the cloud and none is carried upward from where 16
it condenses. Despite these uncertainties, the three-cloud 17
structure is generally accepted. Enrichment factors up to 10 18
times the solar abundances are supported by the C/H ratio 19
implied by the methane abundance (Fletcher et al., 2009, 20
2012). Methane, which doesn’t condense at Saturn atmo- 21
spheric temperatures, is easier to measure above the clouds 22
by remote sensing and is therefore a good measure for the 23
planet as a whole. 24
Temperature profiles obtained from radio occultations 25
and infrared spectra are shown in Figure 11.4. They show 26
that the temperature is close to an adiabat below the 300- 27
400 mbar level, presumably indicating that convection is 28
occurring, but becomes sigificantly stratified at higher lev- 29
els (Li et al. 2013). The two techniques agree reasonably 30
well, and can only sense to levels near∼1 bar, below which 31
we have few observational constraints. The temperatures 32
are fairly steady deeper than the ∼300-mbar level, but ex- 33
hibit greater spatial and temporal variations in the strato- 34
sphere. 35
11.2.3. Inferences From Dynamical Balance 36
Given the observations of zonal winds at cloud level and 37
temperatures in the overlying layers, basic dynamical argu- 38
ments can be used to infer the zonal winds above the cloud 39
deck. On planets that rotate rapidly, with small Rossby 40
number, there exists a dynamical link between winds and 41
temperatures. Specifically, combining geostrophic bal- 42
ance, hydrostatic equilibrium, and the ideal-gas law leads to 43
the thermal-wind equation for a shallow atmosphere (e.g., 44
Holton and Hakim 2013, p. 82). In the meridional direction, 45
this reads: 46
∂u
∂ log p=R
f
(∂T
∂y
)p
(11.1)
where u is the zonal wind, p is pressure, R is the specific 47
gas constant, f = 2Ω sinφ is the Coriolis parameter, Ω is 48
the planetary rotation rate, φ is latitude, T is temperature, 49
y is northward distance, and the derivative on the righthand 50
side is taken at constant pressure. This equation can only 51
be applied away from the equator since geostrophy breaks 52
down at the equator. The equation implies that, away from 53
5
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
Temperature (K) Temperature (K)
Fig. 11.4.— Temperature profiles (abscissa, in K) versus pressure, measured by Voyager and Cassini by two differentmethods. The nadir observations use upwelling thermal radiation to infer temperature as a function of pressure. Theoccultations use the spacecraft’s radio signal passing tangentially through the atmosphere to infer density, from whichtemperature and pressure are derived. The profiles are close to adiabatic below the 300 mbar level. From Li et al. (2013).
the equator, vertical gradients of the zonal wind are pro-1
portional to meridional temperature gradients. Given the2
known winds at the cloud level from cloud tracking (Fig-3
ure 11.2), and given observations of temperature and its4
meridional gradient in the layers above the clouds, we can5
therefore integrate Equation (11.1) to estimate the zonal6
winds above the clouds.7
The top panel of Figure 11.5, from Read et al. (2009a),8
shows temperatures derived from Composite Infrared Spec-9
trometer (CIRS) observations from Cassini (Fletcher et al.10
2007, 2008), with an interpolation between 6 and 35 mbar11
where the Cassini CIRS instrument has no spectral sensi-12
tivity. The axes are latitude and log-pressure, with pressure13
increasing downwards. The contours show that the temper-14
ature increases upward above the 80 mbar level. The lower15
panel of Figure 11.5 depicts the zonal-mean zonal wind16
inferred for Saturn’s upper troposphere and lower strato-17
sphere by integrating the thermal-wind equation (11.1). The18
integration adopts as a lower boundary condition the zonal-19
mean zonal winds obtained from visually tracking clouds20
in the 350-700 mbar pressure range. At pressures greater21
than several mbar, the temperatures are correlated with the 1
winds such that the equatorward flanks of eastward jets— 2
the anticyclonic regions—are colder than the surrounding 3
regions (on an isobar), and the poleward flanks of eastward 4
jets—the cyclonic regions—are warmer than the surround- 5
ing regions. Given the thermal-wind equation, this correla- 6
tion implies that the change of zonal wind with altitude is 7
opposite to the direction of the wind—the winds are decay- 8
ing with altitude. Figure 11.5 indicates that they decay to 9
an average speed of about 40 m s−1, which is the average 10
speed of the stratosphere at the 1-2 mbar level. 11
This result is not new, but it has not been fully explained. 12
The IRIS instrument on Voyager observed the same corre- 13
lation of thermal gradients with the zonal jets during the 14
encounters with Jupiter (e.g., Conrath and Pirraglia 1983; 15
Gierasch et al. 1986). The problem is that there is no obvi- 16
ous radiative or thermodynamic heat source that would pro- 17
duce temperature gradients that correlate with the jets. The 18
IRIS team therefore proposed a mechanical origin. They 19
postulated that, in the upper troposphere above the clouds, 20
the net zonal acceleration due to eddies acts as a drag force 21
6
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
in the opposite direction from the zonal jets. Such a zonal1
eddy force would—in statistical steady state—be balanced2
by the Coriolis force acting on the meridional wind. In other3
words, the postulated eddy accelerations would induce a4
meridional circulation.5
Specifically, this force balance predicts that, for the Cori-6
olis acceleration to balance the eddy acceleration, the re-7
sulting meridional circulation would be poleward across8
eastward jets and equatorward across westward jets.1 This9
configuration implies that the meridional flow converges on10
the poleward flank of eastward jets, leading to downward11
1For poleward motion, the Coriolis force induces an eastward acceleration,whereas for equatorward motion, it induces a westward acceleration. Ifthere were an eastward jet with a westward eddy-induced acceleration, theCoriolis force must be eastward in order to balance the eddy acceleration.This implies a poleward meridional flow. Likewise, if there were a west-ward jet with an eastward eddy acceleration, the Coriolis force must bewestward to achieve steady state. This implies equatorward meridionalflow.Showman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE
Pres
sure
(mba
r)Pr
essu
re(m
bar)
Fig. 11.5.— Top: Saturn’s zonal-mean temperature versus latitude and pressure from Cassini CIRS observations takenin 2004-2006, during Saturn’s northern spring. Analysis is from Fletcher et al. (2007). Note the temperature minimumaround 80 mbar and the increase in temperatures toward the south pole at all levels above the 6-mbar level. The instrumentis not sensitive to the regions from 6–35 mbar and the temperatures have been interpolated across this pressure range.Bottom: Zonal-mean zonal winds versus latitude and pressure obtained by integrating the thermal-wind equation using thetemperature structure in the top panel, and assuming the zonal winds at 500 mbar correspond to the cloud-tracked windprofile. From Read et al. (2009a).
fied (specific entropy increases with altitude), the down-682
welling advects high-entropy air downward from above,683
leading to warmer temperature on constant-pressure sur-684
faces. Similarly, the meridional flow diverges on the685
equatorward flank of eastward jets, leading to upward686
motion, which advects low-entropy air from below and687
produces cooler temperatures on constant-pressure sur-688
faces. In other words, this scenario explains the temper-689
ature anomalies observed by Voyager and Cassini, and in690
thermal-wind balance, the resulting zonal jets must decay691
with altitude. Note that the poleward flank of eastward jets692
exhibit cyclonic vorticity and the equatorward flanks of693
eastward jets exhibit anticyclonic vorticity. Based mostly694
on differences in Jupiter’s cloud colors and morphology,695
the amateur astronomers called the cyclonic and anticy-696
clonic regions belts and zones, respectively. With a west-697
ward eddy acceleration on the zonal jets, the belts are re-698
gions of downwelling and the zones are regions of up-699
welling.700
3.4. Chemical Tracers701
Although one cannot measure upwelling and down-702
welling directly—the velocities are too small—one can703
detect these motions using chemical tracers. If a substance704
is removed from the air at high altitudes, either by con-705
densation or by chemical reactions, then finding it above706
that altitude means that it was brought there by an updraft.707
Conversely, if a substance is severely depleted at some lo-708
cation, then those parcels were probably brought there by709
a downdraft. If one knows the rate of the chemical reac-710
tion, one can often estimate the speed of the updraft or711
downdraft.712
Figure 11.6, from Fletcher et al. (2011), shows some713
of the tracers of vertical motion. The data are from the714
Cassini VIMS instrument and are from spectra in the 4.6–715
5.1 µm atmospheric window. A window is where the gases716
of the atmosphere are especially transparent, and photons717
in this spectral range are sampling the 1–3 bar pressure re-718
gion. Clouds are the main source of opacity, and the solid719
and dotted curves are from two different models of the720
clouds. Ammonia (upper right graph) is generally abun-721
dant at low altitude and is depleted by precipitation at high722
10
Fig. 11.5.— Top: Saturn’s zonal-mean temperature ver-sus latitude and pressure from Cassini CIRS nadir-viewingobservations taken in 2004-2006, during Saturn’s northernspring. Analysis is from Fletcher et al. (2007). Note thetemperature minimum around 80 mbar and the increase intemperatures toward the south pole at all levels above the6-mbar level. The instrument is not sensitive to the regionsfrom 6–35 mbar and the temperatures have been interpo-lated across this pressure range. Bottom: Zonal-mean zonalwinds (in Voyager System III) versus latitude and pressureobtained by integrating the thermal-wind equation using thetemperature structure in the top panel, and assuming thezonal winds at 500 mbar correspond to the cloud-trackedwind profile. Warm colors represent eastward wind, andcool colors represent weaker and/or westward wind. FromRead et al. (2009a).
motion.2 Because the upper troposphere is stably strati- 1
fied (specific entropy increases with altitude), the down- 2
welling advects high-entropy air downward from above, 3
leading to warmer temperature on constant-pressure sur- 4
faces. Similarly, the meridional flow diverges on the equa- 5
torward flank of eastward jets, leading to upward motion, 6
which advects low-entropy air from below and produces 7
cooler temperatures on constant-pressure surfaces. In other 8
words, this scenario explains the temperature anomalies ob- 9
served by Voyager and Cassini, and in thermal-wind bal- 10
ance, the resulting zonal jets must decay with altitude. Note 11
that the poleward flank of eastward jets exhibit cyclonic 12
vorticity and the equatorward flanks of eastward jets ex- 13
hibit anticyclonic vorticity. Based mostly on differences 14
in Jupiter’s cloud colors and morphology, the amateur as- 15
tronomers called the cyclonic and anticyclonic regions belts 16
and zones, respectively. With a westward eddy acceleration 17
on the zonal jets, the belts are regions of downwelling and 18
the zones are regions of upwelling. 19
11.2.4. Chemical Tracers 20
Although one cannot measure upwelling and down- 21
welling directly—the velocities are too small—one can de- 22
tect these motions using chemical tracers. If a substance 23
is removed from the air at high altitudes, either by con- 24
densation or by chemical reactions, then finding it above 25
that altitude means that it was brought there by an updraft. 26
Conversely, if a substance is severely depleted below the al- 27
titude where the chemical reactions are occurring, then the 28
depleted air was probably brought there by a downdraft. If 29
one knows the rate of the chemical reaction, one can often 30
estimate the speed of the updraft or downdraft. 31
Figure 11.6, from Fletcher et al. (2011), shows some of 32
the tracers of vertical motion. The data are from the Cassini 33
VIMS instrument and are from spectra in the 4.6–5.1µm 34
atmospheric window. A window is where the gases of the 35
atmosphere are especially transparent, and photons in this 36
spectral range are sampling the 1–3 bar pressure region. 37
Clouds are the main source of opacity, and the solid and 38
dotted curves are from two different models of the clouds. 39
Ammonia (upper right graph) is generally abundant at low 40
altitude and is depleted by precipitation at high altitude. 41
Abundant ammonia usually means it was brought there by 42
an updraft. Thus the updrafts have high ammonia and the 43
downdrafts have low ammonia. Thus the spike at |φ| < 8, 44
where φ is the latitude, is a sign of upwelling at the equator. 45
Similarly the troughs at 8 < |φ| < 20 are a sign of down- 46
2In principle, mass conservation requires that a meridional convergence bebalanced by a vertical divergence of the flow. Thus, one could theoreti-cally imagine that a meridional convergence could be balanced either byupward motion above the convergence level, or by downward motion be-low the convegence level (or a combination). Because of the strong stablestratification in the stratosphere, the magnitude of the upward flow abovethe convergence level should be limited, and thus we expect a significantdegree of downward motion below the convergence level. Analogous ar-guments lead to the conclusion that upward motion should occur belowlocations of meridional flow divergence.
7
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
Fig. 11.6.— Tracers of vertical motion. The graphs are derived from 5-µm spectra obtained by the Cassini VIMS instru-ment, which senses thermal emission from the 1–3 bar pressure range. The solid and dotted curves employ two differentassumptions about cloud opacity. Although the optical depth of the deep cloud is relatively constant, the cloud base pres-sure is lower (cloud height is greater), which is suggestive of equatorial upwelling. The higher NH3 mole fraction out tolatitudes of ±8 is suggestive of upwelling, and the troughs at ±(8− 20) are suggestive of downwelling. The AsH3 molefraction shows a distribution that is almost opposite to that of NH3, which is not fully understood. One possible explanationis that the pattern of upwelling and downwelling reverses at some level and the two gases are reflecting that reversal. FromFletcher et al. (2011).
welling. The broad downwelling in the cyclonic regions on1
either side of the equator is consistent with the expected2
convergence of meridional flow into a region with an east-3
ward jet on the equatorward side and a westward jet on the4
poleward side.5
Figure 11.7, from Janssen et al. (2013), tells a similar6
story. The data show thermal emission at 2.2-cm wave-7
length, in the microwave region, and were taken by the8
Cassini radar instrument acting as a radiometer. Ammonia9
vapor is the main source of opacity at this wavelength—10
clouds are unimportant—so the bright areas are places of11
reduced ammonia abundance, which allows radiation from12
the warmer, deeper levels to escape into space. The de-13
pleted bands within ±10 of the equator are evidence of14
downwelling. The black band on the equator is an image of15
Saturn’s rings, which are colder than the planet. The dotted16
line gives the time of ring plane crossing, and the dashed17
line gives the time of the closest approach of the spacecraft18
to the planet. As the spacecraft moved in and out of the ring19
plane, which it did on July 24, 2010, the rings covered a20
part of the opposite hemisphere, affording a brief look at the21
equator. The equator itself is not so bright, and is consistent22
with ammonia abundance near the saturation value, as it is23
over most of the planet outside the subtropical (±10) band.24
Within that band, the ammonia must be depleted down to 1
1.5 bars to fit the high brightness temperatures (Laraia et al. 2
2013). 3
The distribution of NH3 on Saturn resembles the distri- 4
bution of H2O on Earth. On both planets there is rising in 5
the tropics and sinking in the subtropics, although on Earth 6
the subtropics extend further out, to ±30. On Earth the 7
circulation is called the Hadley cell, and the band of ris- 8
ing motion at the equator is called the Intertropical Conver- 9
gence Zone (ITCZ), a feature of which are the high cumu- 10
lus clouds associated with deep convection. The clouds of 11
Saturn show a similar pattern (lower left of Figure 11.6) in 12
which the base pressure of the deep cloud is less, indicat- 13
ing displacement to higher altitude. However the Hadley 14
cell analogy may be misleading, because Earth has equato- 15
rial easterlies (westward winds) and Saturn has equatorial 16
westerlies (eastward winds). The eddy sources and the con- 17
figuration of zonal accelerations they induce may therefore 18
differ significantly between the two planets. 19
Gases other than ammonia tell a somewhat different 20
story, and the differences are not fully understood. Fig- 21
ure 11.6 shows that the latitude distribution of arsine, AsH3 22
is almost the opposite of the NH3 distribution. Arsine has 23
a dip at the equator and broad peaks on either side of the 24
8
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
Fig. 7 with a value ranging over about ±0.5%. Errors in the removalof gain as well as sidelobe signal variations using the quiescent-band averages will lead to errors as well, which we judge to be rel-atively small by examining the time dependence of these averagesin Fig. 8. Conservatively, we expect an absolute uncertainty better
than 2%, or a brightness temperature uncertainty less than 3 K.Large-scale systematic errors are smaller, perhaps as much as 1 Kfrom equator to pole as discussed above, and <1 K elsewhereSmall-scale errors are consistent with the white noise of the indi-vidual measurements, !0.1 K.
Fig. 9. Final cylindrical maps of Saturn from the five observation campaigns. The absolutely calibrated maps are shown in the five panels as residuals from a model thatassumes ammonia to be fully saturated in the cloud-forming region. The dashed and dotted lines indicate periapsis and ring plane crossings, respectively (there were noobservations made exactly at ring plane crossing for the 2005 and 2011 maps). Planetographic latitudes are indicated by black ticks on the vertical scales, planetocentric bywhite. The unobserved portions of the maps are shaded to the equivalent brightness for the fully saturated model, so that, except for the ring blockage around the equator, themaps indicate that the ammonia cloud region is everywhere unsaturated. Orbital characteristics and mapping details are given in Tables 2 and 3, and uncertainties andcaveats concerning the maps are given in the text.
M.A. Janssen et al. / Icarus 226 (2013) 522–535 531
Fig. 7 with a value ranging over about ±0.5%. Errors in the removalof gain as well as sidelobe signal variations using the quiescent-band averages will lead to errors as well, which we judge to be rel-atively small by examining the time dependence of these averagesin Fig. 8. Conservatively, we expect an absolute uncertainty better
than 2%, or a brightness temperature uncertainty less than 3 K.Large-scale systematic errors are smaller, perhaps as much as 1 Kfrom equator to pole as discussed above, and <1 K elsewhereSmall-scale errors are consistent with the white noise of the indi-vidual measurements, !0.1 K.
Fig. 9. Final cylindrical maps of Saturn from the five observation campaigns. The absolutely calibrated maps are shown in the five panels as residuals from a model thatassumes ammonia to be fully saturated in the cloud-forming region. The dashed and dotted lines indicate periapsis and ring plane crossings, respectively (there were noobservations made exactly at ring plane crossing for the 2005 and 2011 maps). Planetographic latitudes are indicated by black ticks on the vertical scales, planetocentric bywhite. The unobserved portions of the maps are shaded to the equivalent brightness for the fully saturated model, so that, except for the ring blockage around the equator, themaps indicate that the ammonia cloud region is everywhere unsaturated. Orbital characteristics and mapping details are given in Tables 2 and 3, and uncertainties andcaveats concerning the maps are given in the text.
M.A. Janssen et al. / Icarus 226 (2013) 522–535 531
Fig. 7 with a value ranging over about ±0.5%. Errors in the removalof gain as well as sidelobe signal variations using the quiescent-band averages will lead to errors as well, which we judge to be rel-atively small by examining the time dependence of these averagesin Fig. 8. Conservatively, we expect an absolute uncertainty better
than 2%, or a brightness temperature uncertainty less than 3 K.Large-scale systematic errors are smaller, perhaps as much as 1 Kfrom equator to pole as discussed above, and <1 K elsewhereSmall-scale errors are consistent with the white noise of the indi-vidual measurements, !0.1 K.
Fig. 9. Final cylindrical maps of Saturn from the five observation campaigns. The absolutely calibrated maps are shown in the five panels as residuals from a model thatassumes ammonia to be fully saturated in the cloud-forming region. The dashed and dotted lines indicate periapsis and ring plane crossings, respectively (there were noobservations made exactly at ring plane crossing for the 2005 and 2011 maps). Planetographic latitudes are indicated by black ticks on the vertical scales, planetocentric bywhite. The unobserved portions of the maps are shaded to the equivalent brightness for the fully saturated model, so that, except for the ring blockage around the equator, themaps indicate that the ammonia cloud region is everywhere unsaturated. Orbital characteristics and mapping details are given in Tables 2 and 3, and uncertainties andcaveats concerning the maps are given in the text.
M.A. Janssen et al. / Icarus 226 (2013) 522–535 531
Fig. 11.7.— Thermal emission at 2.2-cm wavelength obtained by the Cassini radar instrument operating as a radiometer.The black band at the equator is the rings, which are low emitters because they are cold. Gaseous NH3 blocks the radiationfrom warmer, deeper levels and emits at colder levels, so regions that are depleted in NH3 appear bright. Latitudes out to±10 appear to be depleted in NH3, which implies downwelling. Although difficult to see due to blockage by the rings,the equator itself is dark, implying upwelling. The great northern storm is visible in the March 20, 2011 map at 30-40
planetographic latitude and 0-180 west longitude. A smaller storm is visible at −45 latitude and 330 west longitude.Both storms show NH3 depletion. From Janssen et al. (2013).
equator out to ±20. One of the cloud models shows an1
extension of the peak to a latitude of −30, but the other2
model does not. The distribution of phosphine, PH3 (not3
shown), is a lot like that of arsine. Degeneracies between4
the retrievals of the cloud properties and the abundances of5
trace species like AsH3 can occur (e.g Giles et al. 2017),6
so the AsH3 results shown in Figure 11.6 should perhaps7
be viewed as tentative until more analysis has been per-8
formed; nevertheless, the different cloud models explored9
by Fletcher et al. (2011) all pointed toward an equatorial dip10
in AsH3 relative to the surrouding latitudes, suggesting that11
it should be taken seriously. Both arsine and phosphine are 1
in chemical equilibrium at much deeper levels than those 2
probed in the 4.6–5.1µm data, and they are destroyed by 3
photolysis at high altitudes. That they don’t show the same 4
patterns as NH3 has interesting implications. 5
Fletcher et al. (2011) discuss the possibility of stacked 6
meridional circulation cells, the top one with rising air at 7
the equator, as in Earth’s Hadley circulation, and the bot- 8
tom one—the reverse cell—with sinking at the equator. The 9
NH3 cloud base is around 1.5 bars, as shown in Figure 11.3, 10
so its mixing ratio should be large up to that level in an up- 11
9
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
draft. Above that level it loses ammonia by condensation.1
A downdraft could carry ammonia-depleted air down be-2
low the 1.5-bar level until it eventually mixes with air from3
the planet’s interior. Thus the NH3 distribution shown in4
Figure 11.6 is consistent with an Earth-like Hadley cell ex-5
tending down at least to the ∼2-bar level. The AsH3 dis-6
tribution is consistent with a reverse Hadley cell since its7
chemical transformations are taking place at much deeper8
levels. The base pressure of the deep cloud, shown in the9
lower left panel of Figure 11.6, is about 2.0 bars at the equa-10
tor and 2.8 bars on either side of the equator. This could be11
interpreted in two ways. If the cloud particles are NH4SH or12
H2O, and have been carried up from deeper levels, then the13
higher altitude (lower base pressure) at the equator would14
signify an updraft. However, if the cloud base pressure were15
entirely dependent on the abundance of a condensing gas,16
then the lower base pressure would signify a lower abun-17
dance of the condensing gas and hence a downdraft. The18
latter would be consistent with a reverse cell, with sinking19
motion at the equator. Note however that the upper cell is20
consistent with a meridional circulation that is driven by21
an eddy acceleration acting in the opposite direction as the22
zonal winds in the upper troposphere. The lower meridional23
cell would seem to require forces that accelerate the zonal24
winds, and such forces do exist, as we now describe.25
11.2.5. Eddies And The Momentum Budget26
The above analysis takes the zonal winds at cloud top27
(Figure 11.2) as given. The eddy-induced acceleration op-28
posing the jet direction was postulated to account for the29
wind’s decay with height above the cloud-top level. In con-30
trast, observations demonstrate that at the cloud level, ed-31
dies transport momentum that acts to drive the jets. Here32
we describe these observations and their interpretation.33
By themselves, the zonal-mean of the eddy winds aver-34
age out to zero, but the eddies can have a net effect when35
the northward and eastward components act together. Con-36
sider a latitude band with an eastward jet to the north and37
a westward jet to the south. The eddy winds, with compo-38
nents u′ and v′, induce motion of air parcels north and south39
in the space between the two jets. (Here, as before, u is the40
zonal wind, and v is the meridional wind; primes denote41
deviations from the zonal average.) But if the parcels going42
north have more eastward momentum than the parcels go-43
ing south, there will be a net transfer of momentum to the44
north. This would add to the eastward momentum of the45
eastward jet and it would subtract it from the westward jet,46
speeding up each jet in its respective direction.47
Such a hypothesis is testable if one has good measure-48
ments of the eddy velocities. Parcels moving north (v′ > 0)49
would also be moving east (u′ > 0), and parcels mov-50
ing south (v′ < 0) would also be moving west (u′ < 0).51
In both cases the parcel trajectories would be tilted along52
a northeast-southwest line, and the measured eddy winds53
would have u′v′ > 0, where the overbar denotes the zonal54
mean. The eddy-momentum flux is ρu′v′, where ρ is the55
density. The eddy-momentum flux is a stress, and it has 1
units of force per unit area. A positive tilt (u′v′ > 0) im- 2
plies a northward transport of eastward momentum by the 3
eddies. A tilt the other way (u′v′ < 0) would represent 4
a negative eddy-momentum flux—a northward transport of 5
westward momentum by the eddies. In either case, if u′v′ 6
and ∂u/∂y have the same sign, where u is the mean zonal 7
wind and y is the northward coordinate, then the eddies are 8
adding momentum to the zonal jets. 9
Figure 11.8, from Del Genio and Barbara (2012), shows 10
the sign of the correlation. At almost all latitudes, u′v′ and 11
∂u/∂y have the same sign. Both quantities are positive 12
at latitudes 50-57N, 33-42N, 10-25S, 28-35S, and 45-48S. 13
Both quantities are negative at latitudes 42-50N, 10-33N, 14
35-40S, and 48-52S. The data are noisy because the eddy 15
winds are weak—only a few m s−1, but the data clearly 16
indicate that Saturn’s eddies are acting as a force that ac- 17
celerates the zonal jets. Both Voyager and Cassini observed 18
similar behavior at Jupiter (Beebe et al. 1980; Ingersoll et al. 19
1981; Salyk et al. 2006). 20
This sounds like negative viscosity, and indeed that term 21
was used to describe such phenomena, which are observed 22
not only in Earth’s atmosphere but also the oceans, the Sun, 23
and laboratory experiments (Starr 1968). However, using 24
an eddy viscosity to relate a local stress like ρu′v′ to a lo- 25
cal rate of strain like ∂u/∂y is often a meaningless exer- 26
cise (Phillips 1969). Energy transfer from smaller to larger 27
scales does not violate any thermodynamic principle, and 28
an eddy-momentum transfer that generates a shear flow— 29
zonal jets—can arise naturally through the interaction of 30
turbulence with the planetary rotation. Since the eddies are 31
putting energy into the zonal flow, they must have their own 32
source of energy. That could come from below, as inter- 33
nal heat powers convection currents that rise into the cloud 34
layer. Or it could come from the sides, as lateral tempera- 35
ture gradients release their potential energy into a longitudi- 36
nally varying wave in a process called baroclinic instability 37
(e.g., Vallis 2006; Holton and Hakim 2013). 38
This eddy force at cloud level, which acts to acceler- 39
ate the zonal jets, is opposite in sign to that postulated in 40
the upper troposphere that tends to decelerate the jets, and 41
it has the opposite effect on the meridional overturning. 42
This reversal in sign of the eddy acceleration with height 43
could lead to stacked meridional circulation cells, the eddy- 44
momentum forces that oppose the jets driving the upper cell 45
and the eddy-momentum forces that accelerate the jets driv- 46
ing the lower cell. Neither of these meridional cells how- 47
ever, is like the Earth’s Hadley circulation (see Vallis 2006 48
or Schneider 2006 for reviews). On Earth, the eddy acceler- 49
ations in the subtropics are westward, whereas the eddy ac- 50
celerations occurring within Saturn’s equatorial jet are east- 51
ward, leading to eddies driving a reverse meridional cell on 52
Saturn. The direct circulation cell on Saturn, which seems 53
to start at ∼2 bars and extend into the stratosphere (Fig- 54
ure 11.5), is driven by an eddy acceleration opposing the 55
zonal jets, which is opposite to the eddy momentum force 56
at deeper levels. 57
10
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
ument. This is some random text to see the proportions ofthe figures in the double column document. This is some ran-dom text to see the proportions of the figures in the doublecolumn document. This is some random text to see the pro-portions of the figures in the double column document. Thisis some random text to see the proportions of the figures inthe double column document. This is some random text tosee the proportions of the figures in the double column docu-ment. This is some random text to see the proportions of thefigures in the double column document. This is some randomtext to see the proportions of the figures in the double columndocument. This is some random text to see the proportionsof the figures in the double column document. This is somerandom text to see the proportions of the figures in the doublecolumn document. This is some random text to see the pro-portions of the figures in the double column document. Thisis some random text to see the proportions of the figures inthe double column document. This is some random text tosee the proportions of the figures in the double column docu-ment. This is some random text to see the proportions of thefigures in the double column document. This is some randomtext to see the proportions of the figures in the double columndocument.
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u0v0 uFigure 4: fig. 11.15
5
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u0v0 uFigure 4: fig. 11.15
5
Fig. 11.8.— Eddy momentum transport and zonal winds. The left panel shows the mean zonal wind profile u obtained bytracking individual cloud features. The right panel shows the number of measured wind vectors in each 1 bin of latitude.The middle panel shows the covariance u′v′ between the eastward eddy wind u′ and the northward eddy wind v′, where aneddy is defined as the residual after the mean zonal wind has been subtracted off. Multiplied by the density, this covarianceis the eddy momentum transport—the northward transport of eastward momentum by the eddies. This transport tends tohave the same sign as ∂u/∂y, where y is the northward coordinate, which indicates that the eddies are putting energy intothe mean zonal wind and not the reverse. From Del Genio and Barbara (2012).
The eddy-momentum flux driving the jets at cloud level1
has been observed directly on Jupiter and Saturn (Beebe2
et al. 1980; Ingersoll et al. 1981; Salyk et al. 2006; Del Ge-3
nio and Barbara 2012). In contrast, there is no direct ob-4
servational confirmation of the eddy acceleration above the5
clouds that is postulated to oppose the jets. The term eddy6
includes all motions that remain after the zonal mean has7
been subtracted off—waves, vortices, convective plumes8
and any other non-axisymmetric component of the motion.9
Evidence for the eddy force opposing the jets comes from10
the decay of the zonal winds with height as inferred from11
temperature gradients (Figure 11.5). Evidence for a reverse12
meridional circulation cell comes from the AsH3 and PH313
distributions, but further evidence comes from the distribu-14
tion of lightning, as we discuss below.15
11.2.6. Lightning And Moist Convection16
Lightning is evidence of moist convection. The violent17
updrafts in a thunderstorm are a crucial element for electri-18
cal charge separation, which occurs when large ice particles 1
fall through upwelling air that contains small liquid droplets 2
(Uman 2001; MacGorman and Rust 1998). The charg- 3
ing mechanism is not well understood, but three phases of 4
water—solid, liquid, and vapor—in the cloud at once seem 5
to be necessary. On giant planets, with their three-tiered 6
structure (Figure 11.3), it is not immediately clear which 7
cloud produces the lightning (Yair et al. 2008). For a solar 8
composition atmosphere, the mole fractions of H2O, NH3, 9
and H2S, in units of 10−4 are 9.7, 1.3, and 0.29, respectively 10
(these values depend on the abundance of helium, which is 11
poorly known; here we have used the latest He/H2 estimate 12
from Sromovsky et al. 2016). For Saturn, enrichment by 13
a factor of 10 is likely (Fletcher et al. 2009; Fletcher et al. 14
2012), and uniform enrichment would raise all these num- 15
bers by the same factor. Thus on the basis of abundance 16
alone, water is the condensable gas most likely to produce 17
lightning. Also, water is the only gas where the tempera- 18
tures and abundances allow three phases to exist at the same 19
11
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
level in the atmosphere. For Saturn the triple point of water1
occurs at a pressure of about 10 bars (Figure 11.3). This2
number depends on the temperature profile, but is relatively3
independent of the enrichment factor. Increasing the lat-4
ter mostly affects the depth of the liquid cloud, extending5
it down to p = 20 bars and T = 330 K for 10 times solar6
abundances.7
Figure 11.9, from Dyudina et al. (2013), shows the8
brightness distribution of a typical lightning flash as seen9
from the Cassini spacecraft. Every pixel in the vicinity of10
the flash is plotted as a function of its horizontal distance11
from the flash center. This removes the effects of foreshort-12
ening and shows that the flashes are roughly circular. The13
half width at half maximum (HWHM) of the brightness dis-14
tribution is about 100 km, and that is related to the depth of15
the lightning relative to the tops of the clouds—the level16
where the photons emerge. That depth is approximately17
equal to 1.5 times the HWHM. Cloud parameters—both18
their height and their scattering properties—create a large19
uncertainty. Dyudina et al. (2013) estimate that the tops20
are probably NH3 or NH4SH clouds at depths exceeding21
Fig. 11.9.— Spatial distribution of brightness of two light-ning flashes vs. distance from the flash center. The distri-butions would appear circular if viewed from directly over-head. The half width at half maximum, defined as the ra-dius where the brightness is half of the central brightness,is about 100 km. From these data, scattering models indi-cate that the vertical distance from the lightning source tothe top of the clouds where the photons are detected is inthe range 125–250 km. The data are consistent with a light-ning source in the water cloud (Figure 11.3). From Dyudinaet al. (2013).
1.2 bars, in which case the lighting is in the water cloud. 1
Nighttime imaging of Jupiter by the Galileo spacecraft 2
showed that lightning is concentrated in the belts (Little 3
et al. 1999; Gierasch et al. 2000), and that was a surprise. 4
The traditional view, which was based on Voyager observa- 5
tions of the upper troposphere (Gierasch et al. 1986), was 6
that the belts are regions of descent and the zones are re- 7
gions of ascent, for several reasons: The zones exhibit a 8
thick, bright, relatively uniform cloud deck, whereas the 9
belts exhibit patchier, generally thinner clouds. The ammo- 10
nia mixing ratios at and above the clouds are small in the 11
belts and large in the zones, signifying descent and ascent, 12
respectively. The belts are warm, signifying high-entropy 13
air brought down from above, and the zones are relatively 14
cold. Lighting therefore seemed unlikely in the belts, since 15
moist convection requires moist air brought in from below. 16
This led Ingersoll et al. (2000) to postulate that perhaps the 17
belts have upwelling at the base of the cloud and down- 18
welling at the tops. This amounted to a pair of meridional 19
circulation cells turning in opposite directions, one on top 20
of the other. Showman and de Pater (2005) showed that 21
this stacked-cell scenario also best explains the deep am- 22
monia abundances from 1–5 bars, which indicates that belts 23
and zones are both depleted in ammonia relative to the pre- 24
sumed deeper atmosphere. According to this new picture, 25
the traditional view was not wrong, but it was based only on 26
the properties of the upper circulation cell. Lightning and 27
ammonia had provided a view to deeper levels, at least on 28
Jupiter. The data for Saturn are less clear, partly because 29
lightning is such a rare event on that planet. 30
Figure 11.10, from Dyudina et al. (2007), shows light- 31
Fig. 11.10.— Lightning activity during the first two yearsof the Cassini orbital mission. The top panel shows signalsdetected by the RPWS instrument, which is on all the timeand is sensitive to lightning all over the planet. The lowerpanel shows when storm clouds were seen by the Cassiniimaging system. Both panels show that there was no light-ning for 445 days from the end of 2004 to the beginning of2006. For comparison, there are ∼2000 lightning storms atany given moment on Earth. From Dyudina et al. (2007).
12
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE
ning intensity over a 2-year period from 2004 to 2006 as1
recorded by the Radio and Plasma Wave Science (RPWS)2
instrument on Cassini. The RPWS is a radio receiver and3
spectrometer, and it is “on” all the time. The figure shows4
that there was lighting activity on days 200–270 in 2004,5
then a 445-day gap with no lightning, followed by activ-6
ity on days 350–385 in 2005. Only one storm was active7
during each of the two periods, and it might have been the8
same storm, as indicated by the drift rate in longitude shown9
on the bottom part of the figure. The storm was located at10
−35 planetocentric latitude, at the center of the westward11
jet shown in Figure 11.2. This latitude band became known12
as “storm alley” during the first few years of the Cassini13
mission. The storm was a multi-armed complex, 2000 km14
in diameter, which spawned smaller spots at a rate of one15
every 1–2 days. These drifted off to the west relative to the16
central complex. The smaller spots began with high, thick17
clouds that dissipated in the first day, leaving a dark spot18
that consisted either of a hole in the clouds or else a deep19
cloud with a low reflectivity (Dyudina et al. 2007). The20
small bright spot in the lower left corner of Figure 11.7, the21
image taken on March 20, 2011, is also at−35 latitude. Its22
brightness at 2.2-cm wavelength indicates that it is a region23
of low abundance of ammonia vapor, which is consistent24
with a hole in the clouds. The latitude band at the center of25
the westward jet at−35 seems to have been active over the26
10+ years of the Cassini orbital mission.27
During the Cassini mission, the northern hemisphere did28
not have a lightning storm until December 5, 2010, when29
the RPWS suddenly started detecting lightning signals and30
the imaging system detected a new cloud at 35 latitude. As31
in the southern hemisphere, the latitude of the storm coin-32
cided with the center of a westward jet (Figure 11.2). How-33
ever the northern storm was a different beast from those in34
storm alley. Its head remained the most active part, but by35
late January its tail had spread around the planet to the east36
and was encountering the head from the west (Fischer et al.37
2011; Sanchez-Lavega et al. 2011). The tail was depleted in38
ammonia, as seen in the March 20, 2011 map at 2.2 cm (Fig-39
ure 11.7). The head spawned a series of large anticyclonic40
vortices, 10,000 km in north-south dimension, which also41
drifted to the east, but more slowly than the debris in the42
tail. When the first of these—also the largest—encountered43
the head in June 2011, the head broke up and essentially44
ceased to exist (Sanchez-Lavega et al. 2012; Sayanagi et al.45
2013). The chapter by Sanchez-Lavega et al. in this book is46
devoted to the giant storm, and we will only discuss a few47
features that are especially relevant to this dynamics chap-48
ter.49
Figure 11.11, from Achterberg et al. (2014), shows50
changes from 2009 to 2011, before and after the storm,51
using infrared data from the Cassini CIRS instrument. Fig-52
ures 11.11a and 11.11b show that the storm warmed the53
latitude band from 30–45. The warming also showed up54
as an increase in the emitted power at that latitude (Li et al.55
2015). Figures 11.11c and 11.11d show evidence of gas56
having been brought up from the level of the water cloud, as57
inferred from the relative abundance of the two states of the 1
H2 molecule. The observed warming made ∂T/∂y more 2
negative on the north side of the disturbed band and more 3
positive on the south side. The thermal-wind equation then 4
says there should have been an increase in ∂u/∂z on the 5
north side and a decrease on the south side. If we are seeing 6
the tops of the clouds, and if u is constant underneath, we 7
should see an increase in u to the north and a decrease to 8
the south, and that is what was observed (Sayanagi et al. 9
2013). 10
Lightning on Jupiter was seen mostly in the belts, which 11
are the regions of cyclonic shear (Little et al. 1999; Gierasch 12
et al. 2000). Lightning on Saturn was seen near the cen- 13
ters of the westward jets, which have cyclonic shear on the 14
equatorward side and anticyclonic shear on the poleward 15
side. Thus the two planets appear to be different. However, 16
Dyudina et al. (2013) noted that within the giant storm there 17
were small regions of cyclonic shear, and they were where 18
the lightning occurred. The giant storm consisted of an anti- 19
cyclonic head with a chain of large anticyclones stretching 20
off to the east, each one rolling in a clockwise direction. 21
The narrow regions where they came close together were 22
cyclonic. A cyclonic region has low pressure at the cen- 23
ter, with the inward pressure gradient force balancing the 24
outward Coriolis force. In a terrestrial hurricane, this leads 25
to convergent flow in the boundary layer, where friction at 26
the ocean surface slows the wind and weakens the Corio- 27
lis force, leading to an unbalanced pressure gradient force 28
acting inward. The inward flow picks up moisture from the 29
ocean surface, leading to intense moist convection around 30
the center. One might think that the same process is hap- 31
pening on the giant planets, since moist convection occurs 32
in the cyclonic regions. But how this might work without 33
an ocean, or a physical surface against which friction can 34
occur, is unclear. The deep atmosphere below the clouds 35
would have to provide a frictional force on the cloud layer 36
that leads to convergence. If the flow below the clouds were 37
sufficiently turbulent, with large vertical stresses, it might 38
do the job. But that theory needs to be worked out. 39
11.2.7. Stability Of the Zonal Jets 40
The cloud-top zonal jets on Jupiter and Saturn are re- 41
markably constant in time. Their positions and wind speeds 42
haven’t changed much over 100 years, although small dif- 43
ferences between Voyager and Cassini were observed, espe- 44
cially at the equator (Peek 1958; Porco et al. 2003; Vasavada 45
et al. 2006; Li et al. 2013; Garcıa-Melendo et al. 2011). This 46
remarkable constancy motivates a consideration of the ex- 47
tent to which the jets are dynamically stable. The definition 48
of a stable flow is one in which infinitesimal perturbations 49
cannot grow in amplitude. There exist a class of theorems 50
that provide information on jet stability for the idealized 51
case of zonally symmetric jets, with no forcing or damping, 52
and several of these have been evaluated for Saturn. 53
Most stability theorems are cast in terms of the poten- 54
tial vorticity (PV), which, for the case of a single-layer, 55
13
Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHEREShowman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE
Fig. 11.11.— Saturn in the infrared before (2009) and after (2011) the great northern storm of 2010-2011. The data werecollected by the Cassini CIRS instrument and are sensitive to the 300-mbar level. The top two panels show that the stormwarmed the latitude band from 30–45 by 3 K. The bottom two panels show that the warming was due to air rising fromthe water cloud (Figure 11.3), as inferred from a change between the two states, ortho and para, of the H2 molecule. FromAchterberg et al. (2014).
3.7. Stability of the zonal jets1095
The zonal jets on Jupiter and Saturn are remarkably1096
constant in time. Their positions and wind speeds haven’t1097
changed much over 100 years, although small differences1098
between Voyager and Cassini were observed, especially1099
at the equator (Peek 1958; Porco et al. 2003; Vasavada1100
et al. 2006; Li et al. 2013; Garcıa-Melendo et al. 2011).1101
The definition of a stable flow is one in which infinitesi-1102
mal perturbations cannot grow in amplitude. For zonal jets1103
on rotating planets, an important quantity is the potential1104
vorticity (PV). It is a conserved dynamical tracer of the1105
motion—“conserved” because its value does not change1106
under certain common conditions—no viscosity, no heat1107
exchange, and no mixing as the parcel moves around, and1108
“dynamical” because it is computed from dynamical vari-1109
ables like wind and temperature. An inert gas is an exam-1110
ple of a passive tracer. It is conserved but not dynamical.1111
There are many ways to compute PV, depending on1112
what approximations, if any, are used for the equations1113
of motion. The rigorous form is Ertel’s potential vorticity1114
(Vallis 2006)1115
PVErtel =1
(2 + r v) · rS (9)
Here S is specific entropy, another conserved tracer pro-1116
vided the fluid is moving adiabatically, i.e., without ex-1117
changing heat with its surroundings or dissipating ki-1118
netic energy. Conservation of PV requires both of these1119
conditions—no heat exchange and no dissipation. Notice1120
that PV is a scalar although it is constructed from vectors,1121
and it is a local quantity that is associated with individual1122
fluid elements. For approximate equations of motion like1123
the Boussinesq, anelastic, and quasi-geostrophic equations1124
there are approximate forms of PV, but it is still a con-1125
served tracer. The single-layer, shallow water version is1126
PV = + f
h(10)
where = k · (r v). Here is the vertical compo-1127
nent of vorticity—twice the angular velocity due to the1128
motion relative to the rotating planet, and f is the verti-1129
cal component due to the planet’s rotation. Thus is the1130
relative vorticity, f is the planetary vorticity, and + f is1131
the absolute vorticity. In this shallow-water form, h is the1132
depth of the fluid. The inverse dependence on h reflects1133
the fact that stretching along the rotation axis (increasing1134
h) causes a contraction toward the axis and a decrease in1135
the moment of inertia, causing the parcel to spin faster1136
and + f to increase. The PV of the parcel is conserved1137
because the numerator and denominator change together.1138
Note that, for a stratified, three-dimensional atmosphere,1139
the Ertel version (9) can be written in the form (10) if one1140
uses the component of vorticity that is perpendicular to1141
surfaces of constant specific entropy, and if one treats h as1142
a differential mass per unit area between surfaces of con-1143
stant specific entropy.1144
17
Showman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE
Fig. 11.11.— Saturn in the infrared before (2009) and after (2011) the great northern storm of 2010-2011. The data werecollected by the Cassini CIRS instrument and are sensitive to the 300-mbar level. The top two panels show that the stormwarmed the latitude band from 30–45 by 3 K. The bottom two panels show that the warming was due to air rising fromthe water cloud (Figure 11.3), as inferred from a change between the two states, ortho and para, of the H2 molecule. FromAchterberg et al. (2014).
3.7. Stability of the zonal jets1095
The zonal jets on Jupiter and Saturn are remarkably1096
constant in time. Their positions and wind speeds haven’t1097
changed much over 100 years, although small differences1098
between Voyager and Cassini were observed, especially1099
at the equator (Peek 1958; Porco et al. 2003; Vasavada1100
et al. 2006; Li et al. 2013; Garcıa-Melendo et al. 2011).1101
The definition of a stable flow is one in which infinitesi-1102
mal perturbations cannot grow in amplitude. For zonal jets1103
on rotating planets, an important quantity is the potential1104
vorticity (PV). It is a conserved dynamical tracer of the1105
motion—“conserved” because its value does not change1106
under certain common conditions—no viscosity, no heat1107
exchange, and no mixing as the parcel moves around, and1108
“dynamical” because it is computed from dynamical vari-1109
ables like wind and temperature. An inert gas is an exam-1110
ple of a passive tracer. It is conserved but not dynamical.1111
There are many ways to compute PV, depending on1112
what approximations, if any, are used for the equations1113
of motion. The rigorous form is Ertel’s potential vorticity1114
(Vallis 2006)1115
PVErtel =1
(2 + r v) · rS (9)
Here S is specific entropy, another conserved tracer pro-1116
vided the fluid is moving adiabatically, i.e., without ex-1117
changing heat with its surroundings or dissipating ki-1118
netic energy. Conservation of PV requires both of these1119
conditions—no heat exchange and no dissipation. Notice1120
that PV is a scalar although it is constructed from vectors,1121
and it is a local quantity that is associated with individual1122
fluid elements. For approximate equations of motion like1123
the Boussinesq, anelastic, and quasi-geostrophic equations1124
there are approximate forms of PV, but it is still a con-1125
served tracer. The single-layer, shallow water version is1126
PV = + f
h(10)
where = k · (r v). Here is the vertical compo-1127
nent of vorticity—twice the angular velocity due to the1128
motion relative to the rotating planet, and f is the verti-1129
cal component due to the planet’s rotation. Thus is the1130
relative vorticity, f is the planetary vorticity, and + f is1131
the absolute vorticity. In this shallow-water form, h is the1132
depth of the fluid. The inverse dependence on h reflects1133
the fact that stretching along the rotation axis (increasing1134
h) causes a contraction toward the axis and a decrease in1135
the moment of inertia, causing the parcel to spin faster1136
and + f to increase. The PV of the parcel is conserved1137
because the numerator and denominator change together.1138
Note that, for a stratified, three-dimensional atmosphere,1139
the Ertel version (9) can be written in the form (10) if one1140
uses the component of vorticity that is perpendicular to1141
surfaces of constant specific entropy, and if one treats h as1142
a differential mass per unit area between surfaces of con-1143
stant specific entropy.1144
17
Showman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE
Fig. 11.11.— Saturn in the infrared before (2009) and after (2011) the great northern storm of 2010-2011. The data werecollected by the Cassini CIRS instrument and are sensitive to the 300-mbar level. The top two panels show that the stormwarmed the latitude band from 30–45 by 3 K. The bottom two panels show that the warming was due to air rising fromthe water cloud (Figure 11.3), as inferred from a change between the two states, ortho and para, of the H2 molecule. FromAchterberg et al. (2014).
3.7. Stability of the zonal jets1095
The zonal jets on Jupiter and Saturn are remarkably1096
constant in time. Their positions and wind speeds haven’t1097
changed much over 100 years, although small differences1098
between Voyager and Cassini were observed, especially1099
at the equator (Peek 1958; Porco et al. 2003; Vasavada1100
et al. 2006; Li et al. 2013; Garcıa-Melendo et al. 2011).1101
The definition of a stable flow is one in which infinitesi-1102
mal perturbations cannot grow in amplitude. For zonal jets1103
on rotating planets, an important quantity is the potential1104
vorticity (PV). It is a conserved dynamical tracer of the1105
motion—“conserved” because its value does not change1106
under certain common conditions—no viscosity, no heat1107
exchange, and no mixing as the parcel moves around, and1108
“dynamical” because it is computed from dynamical vari-1109
ables like wind and temperature. An inert gas is an exam-1110
ple of a passive tracer. It is conserved but not dynamical.1111
There are many ways to compute PV, depending on1112
what approximations, if any, are used for the equations1113
of motion. The rigorous form is Ertel’s potential vorticity1114
(Vallis 2006)1115
PVErtel =1
(2 + r v) · rS (9)
Here S is specific entropy, another conserved tracer pro-1116
vided the fluid is moving adiabatically, i.e., without ex-1117
changing heat with its surroundings or dissipating ki-1118
netic energy. Conservation of PV requires both of these1119
conditions—no heat exchange and no dissipation. Notice1120
that PV is a scalar although it is constructed from vectors,1121
and it is a local quantity that is associated with individual1122
fluid elements. For approximate equations of motion like1123
the Boussinesq, anelastic, and quasi-geostrophic equations1124
there are approximate forms of PV, but it is still a con-1125
served tracer. The single-layer, shallow water version is1126
PV = + f
h(10)
where = k · (r v). Here is the vertical compo-1127
nent of vorticity—twice the angular velocity due to the1128
motion relative to the rotating planet, and f is the verti-1129
cal component due to the planet’s rotation. Thus is the1130
relative vorticity, f is the planetary vorticity, and + f is1131
the absolute vorticity. In this shallow-water form, h is the1132
depth of the fluid. The inverse dependence on h reflects1133
the fact that stretching along the rotation axis (increasing1134
h) causes a contraction toward the axis and a decrease in1135
the moment of inertia, causing the parcel to spin faster1136
and + f to increase. The PV of the parcel is conserved1137
because the numerator and denominator change together.1138
Note that, for a stratified, three-dimensional atmosphere,1139
the Ertel version (9) can be written in the form (10) if one1140
uses the component of vorticity that is perpendicular to1141
surfaces of constant specific entropy, and if one treats h as1142
a differential mass per unit area between surfaces of con-1143
stant specific entropy.1144
17
Fig. 11.11.— Saturn in the infrared before (2009) and after (2011) the great northern storm of 2010-2011. The data werecollected by the Cassini CIRS instrument and are sensitive to the ∼300-mbar level. The right panels show that the stormwarmed the latitude band from 30–45 by ∼3 K. The left panels show that the warming was due to air rising from depthsnear the water cloud (Figure 11.3). The equilibrium ratio of the two states of the H2 molecule, ortho and para, dependson temperature. At depth, the expected para fraction is smaller, whereas at the cloud tops, it is larger. The conversionbetween the two states occurs on relatively long timescales. Thus, the sudden emergence of a zonal band of air with lowpara fraction—as seen in panel (d)—suggests that this air was transported from depth, but that there has not yet beensufficient time for the para fraction of this air to relax into the larger para fraction associated with equilibrium at the coldtemperatures of the cloud tops. From Achterberg et al. (2014).
shallow-water flow is1
PV =ζ + f
h(11.2)
where ζ = k · (∇×v) is the relative vorticity, v is the fluid2
velocity, and k is the vertical unit vector. In this shallow-3
water form, h is the depth of the fluid. Under friction-4
less, adiabiatic conditions, the PV is a materially conserved5
quantity (e.g. Vallis 2006). The inverse dependence on h6
reflects the fact that stretching along the rotation axis of the7
fluid parcel (thereby increasing h) causes a contraction to-8
ward the parcel’s rotation axis and a decrease in the mo-9
ment of inertia, causing the parcel to spin faster and ζ + f10
to increase. The PV of the parcel is conserved because the11
numerator and denominator change together. Note that, for12
a stratified, three-dimensional atmosphere, the PV can also13
be written in the form (11.2) if one uses the component of14
vorticity that is perpendicular to surfaces of constant spe-15
cific entropy, and if one treats h as a differential mass per16
unit area between surfaces of constant specific entropy.17
The simplest stability theorem, which dates back to18
Rayleigh, with modification for rotating planets, is the19
Charney-Stern criterion (Vallis 2006). It says that a zonal20
flow is stable—infinitesimal disturbances cannot grow—if21
PV varies monotonically in the cross-stream direction. If22
we ignore the stretching term by treating h as a constant, we23
obtain the barotropic stability criterion, which states that a24
steady zonal flow u(y) is stable provided25
d(ζ + f)
dy= β − uyy ≥ 0 (11.3)
where β = df/dy = 2Ω cosφ/a and dζ/dy = −uyy. Here26
β is the planetary vorticity gradient, φ is latitude and a is27
the radius of the planet. Note that β is always positive but 1
it goes to zero at the poles. The subscript y is a derivative, 2
and uyy is the curvature of the zonal velocity profile, which 3
is positive at the centers of the westward jets (Figure 11.2). 4
If this curvature is less than β at every latitude, the flow is 5
stable provided we can ignore the stretching term. Jupiter’s 6
zonal jets violate the barotropic stability criterion (Ingersoll 7
et al. 1981; Limaye 1986; Li et al. 2004). Here we describe 8
an application of stability criteria to Saturn, starting with 9
the barotropic stability criterion and moving on to the more 10
general Ertel and quasi-geostrophic versions. 11
Figure 11.12, from Read et al. (2009a), shows the zonal- 12
mean velocity u(y), the vorticity ζ = −uy , and the cur- 13
vature uyy = −ζy in the left, center, and right panels, re- 14
spectively. The smooth curve in the right panel is β, which 15
varies with latitude as cosφ. One can see that the curvature 16
exceeds β at the latitudes of the westward jets, indicating a 17
violation of the barotropic stability criterion. The violation 18
is more evident near the poles, i.e., the difference β − uyy 19
is more negative there, partly because the jets have more 20
curvature there, but also because β is approaching zero. 21
Read et al. (2009a) also use temperature profiles derived 22
from infrared observations by the Cassini CIRS instrument 23
to estimate the magnitude of the stretching term. They cal- 24
culate Ertel PV and quasi-geostrophic PV, including the 25
stretching term, as functions of latitude and show that the 26
stretching term has little effect, at least in the upper tropo- 27
sphere and lower stratosphere where the analysis was done. 28
At these altitudes the atmosphere is so stably stratified that 29
the stretching is small. Although Ertel PV is the right quan- 30
tity to use, the barotropic stability criterion gives the same 31
result, that the centers of the westward jets are where the 32
stability criterion is violated. One might get a different re- 33
sult if one could measure Ertel PV within and below the 34
14
Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHERE
Mean zonal wind (m s−1) Relative vorticity (s−1) Curvature of zonal wind uyy (m−1 s−1)
Fig. 11.12.— Stability of Saturn’s zonal jets. The barotropic stability criterion states that a zonal flow is stable provided thecurvature uyy of the zonal velocity profile does not exceed the planetary vorticity gradient β. Stable means that disturbancesto the profile cannot grow, but violation of the criterion does not mean that they will grow. The left panel shows the zonalvelocity profile u. The middle panel shows the relative vorticity −uy associated with the zonal flow, where the subscriptmeans differentiation of u with respect to the northward coordinate y. The right panel shows the curvature uyy (jaggedcurve) and β (smooth curve, given by 2Ω cosφ/a), along with the zero-curvature line for reference (straight vertical line).At the latitudes where the curvature is positive, it clearly exceeds β, indicating that the barotropic stability criterion isviolated. The barotropic stability criterion belongs to a more general class of stability theorems that use potential vorticity(PV) as the diagnostic quantity. The rigorous form uses Ertel’s PV, but the results are the same, at least for the uppertroposphere where the velocity profile is measured. From Read et al. (2009a).
clouds, but that is not possible with the remote sensing data1
that we have.2
Violation of the barotropic stability criterion or any of3
the related stability criteria does not mean that the flow4
is unstable. Further, instability does not mean that the5
flow cannot exist. The hexagon that surrounds the pole at6
mean planetocentric latitude of 76 marks the path of a me-7
andering jet that violates the barotropic stability criterion8
(Antunano et al. 2015). The jet may be unstable, but the9
disturbance has grown into a steady finite-amplitude wave.10
Presumably the wave stopped growing due to non-linear11
effects that are not included in the linear stability analy-12
sis. Ingersoll and Pollard (1982) describe a stability crite-13
rion that invokes interior flow, in which the zonal winds are14
aligned on cylinders concentric with the planets axis of rota-15
tion. Dowling (1995a,b) has argued that Jupiter’s jets could16
be stable according to Arnol’d’s second stability criterion, 1
which states that the flow will be stable to nonlinear pertur- 2
bations if there is a reference frame in which the reversals 3
of the PV gradient coincide with reversals in the sign of ve- 4
locity. Read et al. (2009b) found that the upper tropospheric 5
and stratospheric winds appear to be close to neutral stabil- 6
ity according to this criterion; see Dowling (2014) for a de- 7
tailed discussion. The reference period they derived is ∼5 8
minutes shorter than the System III reference period, and 9
they propose that the period derived from Arnol’d second 10
stability criterion is the rotation period of Saturn’s interior. 11
11.3. Observations of the Stratosphere 12
In the absence of visible tracers, the primary source 13
of data constraining the winds and circulation in Saturn’s 14
15
Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHERE
stratosphere is from observations in the thermal infrared.1
Observations in the collision-induced hydrogen continuum2
longward of 16µm provide information on the temperatures3
in the upper troposphere between roughly 50 to 500 mbar.4
Observations in the ν4 band of methane near 7.7µm provide5
information on temperatures in the middle and upper strato-6
sphere, between 0.5 and 5 mbar for typical observations,7
extending to about 0.01 mbar for observations with very8
high spectral resolution, or limb viewing observations from9
Cassini. However, these thermal observations have verti-10
cal resolution of a pressure scale height, and are thus not11
sensitive to wave structure on small vertical scales.3 Tem-12
perature profiles with vertical resolution of a few kilometers13
can be obtained through radio occultation observations, in14
which the radio signal from a spacecraft is observed as the15
spacecraft passes behind a planet at seen from Earth, and16
from stellar occultations. Radio occultations are generally17
sensitive to the lower stratosphere and upper troposphere18
between about 0.1 mbar and 1 bar, while stellar occultations19
generally sense the upper stratosphere or higher.20
The first spatially resolved thermal observations of Sat-21
urn were made in the ν9 band of ethane at 12µm (Gillett22
and Orton 1975; Rieke 1975) during southern summer, and23
showed emission increasing from north to south, peaking at24
the south pole. Subsequent observations in the ν4 methane25
band at 8µm (Tokunaga et al. 1978; Sinton et al. 1980)26
showed similar variations. Since methane is expected to be27
meridionally mixed, these observations indicated that the28
emission variations are caused by a north-to-south temper-29
ature gradient, with stratospheric temperatures warmest at30
the south (summer) pole.31
The first spacecraft observation in the thermal infrared32
was made by the Pioneer 11 infrared radiometer (IRR) in33
1979, just prior to northern spring equinox. IRR observed34
in two bands at 20µm and 45µm, sensitive to the upper35
troposphere, between 10N and 30S (Ingersoll et al. 1980;36
Orton and Ingersoll 1980), finding the temperatures within37
10 of the equator ∼2.5 K colder than higher latitudes.38
Soon afterward, the Infrared Interferometer Spectrometer39
(IRIS) on Voyagers 1 (1980) and 2 (1981) mapped Sat-40
urn at 5 to 45µm. Retrievals of upper tropospheric tem-41
peratures (Hanel et al. 1981, 1982; Conrath and Pirraglia42
1983) showed no equator to pole temperature gradient in the43
southern hemisphere, and north polar temperatures roughly44
3Atmospheric waves generated in the troposphere can propagate into thestratosphere where they can exert a strong effect on the dynamics. Broadly,such waves fall into two classes (neglecting acoustic waves which tend tobe unimportant for the meteorology). Gravity (or buoyancy) waves ariseby virtue of buoyancy forces associated with vertical motion of air parcelsin a stably stratified medium; they are the internal atmosphere equivalentof the waves one observes on the surface of the ocean. Rossby waves arisefrom a restoring force associated with meridional motion of air parcels inthe presence of a latitudinal gradient of the planetary vorticity (i.e., theCoriolis parameter f ). Rossby waves tend to have larger scales and longerperiods than gravity waves. Mixed wave modes also exist, as well as wavetypes specific to the equatorial regions, such as Kelvin wave modes. All ofthese waves can influence the mean flow when they break or are absorbed.See Holton and Hakim (2013) for introductions to these waves.
5 K colder than the equator in the upper troposphere at pres- 1
sures less than about 300 mbar. In addition to the large- 2
scale gradient, the upper tropospheric temperatures showed 3
variations of around 2 K, with the gradient anticorrelated 4
with the zonal winds (Conrath and Pirraglia 1983). A lim- 5
ited set of temperature profiles, covering roughly between 1 6
bar and 1 mbar, were also obtained by the radio occultation 7
experiments on Pioneer 11 (Kliore et al. 1980) and Voy- 8
agers 1 and 2 (Lindal et al. 1985). These profiles showed 9
a broad tropopause with the temperature minimum at about 10
50 mbar, with mid-stratospheric temperatures of∼ 140K at 11
midlatitudes and ∼ 120K near the equator. The near equa- 12
torial profiles also showed small-scale vertical oscillations 13
that were interpreted as vertically propagating waves. 14
Subsequent ground-based observations taken during 15
northern summer showed enhanced emission at the north 16
pole in the stratospheric methane and ethane bands (Gezari 17
et al. 1989), but not at wavelengths sensitive to the tro- 18
posphere (Ollivier et al. 2000). These observations, when 19
compared to earlier observations, were interpreted as ev- 20
idence for seasonal evolution of the temperatures as pre- 21
dicted by radiative models (Cess and Caldwell 1979; 22
Bezard and Gautier 1985), with warm temperatures at the 23
summer pole and the strength of the radiative response 24
weaker at higher pressures where the radiative time con- 25
stants are longer. 26
Just prior to the arrival of Cassini at Saturn, Greathouse 27
et al. (2005) observed Saturn at high spectral resolution in 28
2002 near southern summer solstice, using the methane ν4 29
band to retrieve southern hemisphere temperatures between 30
0.01 and 10 mbar. They found a general equator to pole 31
temperature gradient, with the south pole 10 K warmer than 32
the equator. In early 2004, Orton and Yanamandra-Fisher 33
(2005) used the Keck telescope to image Saturn in the CH4 34
and H2 bands, allowing the retrieval of temperatures at 100 35
mbar and 3 mbar at 3000 km spatial resolution. They also 36
found a 10 K temperature increase between the equator and 37
the summer pole in the stratosphere, with a sharp ∼5 K 38
increase between 69S and 74S planetocentric latitude. 39
The arrival of Cassini at Saturn in mid-2004, near south- 40
ern mid-summer, began a period of quasi-continuous mon- 41
itoring of Saturn’s thermal emission by the Cassini Com- 42
posite Infrared Spectrometer (CIRS) which is planned to 43
continue until northern summer solstice in 2017. Flasar 44
et al. (2005) showed temperature retrievals of the south- 45
ern hemisphere from data taken during the approach of 46
Cassini to Saturn. They found a 15 K temperature gradi- 47
ent between the equator and south pole at 1 mbar, decreas- 48
ing with increasing pressure. This temperature gradient is 49
larger than the 5 K expected from radiative models for the 50
season, which Flasar et al. (2005) suggested may be caused 51
by adiabatic heating from subsidence at the pole. The first 52
global temperature cross-sections were made by Fletcher 53
et al. (2007, 2008), using CIRS data to retrieve zonal-mean 54
temperatures between 0.5 and 5 mbar in the stratosphere 55
and 50 to 800 mbar in the troposphere; an updated version 56
of their results is shown in Figure 11.5. At the 1-mbar level, 57
16
Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHERE
they found a 30 K temperature difference between the warm1
southern summer pole and the cold northern winter pole;2
the temperature gradient is nearly monotonic from pole to3
pole except for a local temperature maximum at the equa-4
tor, and a roughly 3 K warming between 80N and the north5
pole. At higher pressures, the global temperature gradient6
becomes weaker, and small-scale variations correlated with7
the zonal winds appear. CIRS limb viewing observations8
allowed Fouchet et al. (2008) and Guerlet et al. (2009) to9
extend temperature retrievals up to the 0.01 mbar pressure10
level. Surprisingly, they found that the large-scale pole-11
to-pole temperature gradient was weaker at 0.1 mbar and12
0.01 mbar than at 1 mbar, despite the thermal timescales13
becoming shorter at lower pressures. They also found that14
the temperature profile oscillates with altitude at equatorial15
and low latitudes, with equatorial temperature alternately16
warmer and colder than temperature at ±15. Long-term17
monitoring from ground-based observations by Orton et al.18
(2008) showed that the difference between equatorial and19
low-latitude temperatures also oscillates in time, with a pe-20
riod near 15 Earth years. This equatorial oscillation will be21
discussed in more detail in section 11.3.3.22
Cassini CIRS has continued to monitor Saturn’s thermal23
structure through equinox and into northern spring (Fletcher24
et al. 2010; Fletcher et al. 2015; Guerlet et al. 2011; Sin-25
clair et al. 2013; Sylvestre et al. 2015). Outside of the26
equatorial region, the seasonal temperature variations are27
broadly consistent with models (Fletcher et al. 2010; Fried-28
son and Moses 2012; Guerlet et al. 2014), with a warm-29
ing of the northern hemisphere and cooling of the southern30
hemisphere. The seasonal variations are discussed in detail31
in the chapter by Fletcher et al. in this volume.32
11.3.1. Zonal Mean Winds33
As described in Section 11.2, the meridional tempera-34
ture gradients observed in the upper troposphere are posi-35
tively correlated with the measured cloud-top zonal winds36
at many latitudes. Using the thermal-wind equation (11.1),37
this result implies that the zonal winds observed at cloud38
level decay with altitude into the stratosphere, over a verti-39
cal scale of about six pressure scale heights. Furthermore,40
because the eastward and westward wind gradients are of41
similar magnitude, while the cloud top winds are predomi-42
nantly eastward, the decay of the jets is to a finite eastward43
velocity and not zero, as measured in the System III refer-44
ence frame. Further evidence for net eastward stratospheric45
winds was provided by the analysis of the 1989 occultation46
of 28 Sgr by Nicholson et al. (1995), who found that winds47
of around 40 m s−1 were needed near the 2.5 mbar level48
between 25N and 70N to fit the observed timings of the49
central flash. As can be seen in Figure 11.5, many—though50
not all—of the off-equatorial jets decay in speed with de-51
creasing pressure. Figure 11.5 also makes plain that the52
middle stratosphere winds are generally eastward as mea-53
sured System III, except at high southern latitudes. As men-54
tioned previously, however, the System III reference frame55
may not represent the true interior rotation rate, and other 1
possible interior rotation rates would imply different val- 2
ues for the overall stratospheric winds (in particular, several 3
proposals for the interior rotation rate are faster than the 4
System III rotation rate, which would imply stratospheric 5
winds weaker—that is, more westward—than shown in Fig- 6
ure 11.5). That said, there is no dynamical reason to expect 7
that the mean zonal velocity in the troposphere or strato- 8
sphere is the same as in the deep interior. 9
Observations of seasonal changes in the zonal mean 10
stratospheric temperatures into early northern spring (Fletcher 11
et al. 2010; Sinclair et al. 2013; Fletcher et al. 2015) show 12
a weakening of the equator-to-pole temperature gradients, 13
with the hemispheric average stratospheric ∂T/∂y becom- 14
ing less negative. This implies corresponding changes in the 15
stratospheric zonal winds, with northern hemispheric winds 16
becoming more westward and southern hemispheric winds 17
more eastward, as can be seen in the results of Fletcher 18
et al. (2015), who used the thermal wind approximation to 19
estimate the winds at 100, 1 and 0.5 mbar poleward of 60 20
from 2005 to 2013. 21
11.3.2. Meridional Circulation 22
The zonal-mean circulation in the stratosphere can be in- 23
ferred from the observed temperature field using the ther- 24
modynamic energy equation 25
∂T
∂t+ v
∂T
∂y+ w
(∂T
∂z+
g
cp
)=
q
cp, (11.4)
where v and w are the meridional and vertical velocities, 26
cp is the specific heat, and q is the specific radiative heat- 27
ing/cooling rate. Due to the strong stratification in Saturn’s 28
stratosphere, the vertical advection term is much larger than 29
the meridional advection term, and so the meridional advec- 30
tion is often ignored when estimating the vertical velocity.4 31
Observations of stratospheric temperature allow estimates 32
of the time derivative term and the factor in parentheses. 33
Given estimates of the radiative heating/cooling q/cp from 34
radiative-transfer models and observations, Equation (11.4) 35
can be used to estimate the vertical velocity. The veloci- 36
ties v, w in (11.4) are the so-called “residual mean veloci- 37
ties” (see e.g., Andrews et al. 1987, section 3.5) which in- 38
clude eddy fluxes as well as the advective transport. In the 39
Earth’s stratosphere, the residual mean circulation is a good 40
4The meridional advection term scales as v∆Tmerid/L, where ∆Tmerid
is the characteristic meridional temperature contrast, which occurs over ameridional scale L. Considering a vertically isothermal temperature pro-file for simplicity, the vertical advection term scales simply as w g/cp.The continuity equation implies that v/L ∼ w/D, where D is the char-acteristic vertical scale of the circulation. The ratio of the meridional tothe vertical advection term is therefore cp∆Tmerid/(gH). We insertnumbers for the global-scale seasonal meridional circulation, for which∆Tmerid ∼ 20 K (see Figure 11.5). Noting that the circulation is coher-ent over many scale heights vertically (Figure 11.13), and that the scaleheight is H ∼ 50 km at these temperatures, we adopt D ∼ 300 km. Us-ing cp ≈ 1.3 × 104 J kg−1 K−1 and g ≈ 10 m s−2 shows that the ratioof horizontal to vertical advection terms is ∼0.1.
17
Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHEREShowman et al.: The Global Atmospheric Circulation of Saturn 4 OBSERVATIONS OF THE STRATOSPHERE
Fig. 11.13.— Zonal-mean vertical velocities (in mm s1) versus latitude and pressure obtained diagnostically from Equa-tion (12) using the observed temperature and its seasonal variation, combined with estimates of radiative heating andcooling. From Fletcher et al. (2015).
Fig. 11.14.— Low-latitude stratospheric temperatures on Saturn (in K) determined from Cassini/CIRS observations in2005/2006 (left) and 2010 (middle). The difference in shown in the right panel. Note the existence of a low-latitudeoscillatory structure whose phase shifted downward between 2005/2006 and 2010. From Guerlet et al. (2011).
was produced by Friedson and Moses (2012), using a fully1501
3D general circulation model adapted to Saturn. Their1502
model also uses a mechanical forcing at the lower bound-1503
ary to produce the observed tropospheric zonal winds,1504
along with random thermal perturbations in the tropo-1505
sphere to simulate generation of waves by convection,1506
and includes realistic radiative forcing. Their model pro-1507
duced global scale temperature gradients generally con-1508
sistent with observations, though temperatures were 5 K1509
too warm in the summer stratosphere. The modeled merid-1510
ional transport was dominated at low latitudes by a season-1511
ally reversing Hadley circulation, with broad upwelling at1512
low latitudes and strong subsidence near 25 in the winter1513
hemisphere, consistent with the circulation inferred from1514
the ethane and acetylene measurements of Guerlet et al.1515
(2009). At mid-latitudes they found 1-mbar eddy mixing1516
timescales of just over 100 years, slightly longer than the1517
photochemical timescale for acetylene and shorter than for1518
ethane, consistent with the observations.1519
22
Fig. 11.13.— Zonal-mean vertical velocities (in mm s−1) versus latitude and pressure obtained diagnostically from Equa-tion (11.4) using the observed temperature and its seasonal variation, combined with estimates of radiative heating andcooling. From Fletcher et al. (2015).
approximation to the net transport of conserved constituents1
(Dunkerton 1978).2
Flasar et al. (2005) estimated the vertical velocities3
needed to produce the observed warm temperatures at the4
south pole by balancing the vertical advection with the time5
derivative of the temperature, assuming temperature varia-6
tions on the order of the observed equator-to-pole gradient7
on a seasonal timescale, finding w ∼ 0.1 mm s−1. Fletcher8
et al. (2015) used the thermodynamic energy equation to9
estimate the vertical velocity at latitudes poleward of 6010
averaged over the first ten years of the Cassini mission11
(2004-2014), using temperatures from Cassini CIRS and12
net radiative heating from the model of Guerlet et al. (2014).13
They also found velocities of the order of 0.1 mm s−1 near14
1 mbar, becoming weaker at higher pressures, with rising15
motion in the southern hemisphere and subsidence in the16
north (Figure 11.13). At this speed, it would take an air par-17
cel 15 years to rise 50 km, which is about one scale height18
in Saturn’s stratosphere.19
Information on the stratospheric meridional circulation20
can also be obtained from the observed distribution of dis-21
equilibrium chemical species. The most useful species are22
ethane (C2H6) and acetylene (C2H2), which have photo-23
chemical timescales in excess of a Saturn year in the mid-24
dle and lower stratosphere, with ethane having a somewhat25
longer timescale. Photochemical models predict that in the26
absence of meridional transport, ethane and acetylene will27
have a meridional distribution that follows the yearly mean28
solar insolation at pressures of 1 mbar and greater, with the29
abundance a maximum at the equator and decreasing to-30
ward the poles; at lower pressures the chemical timescales31
become shorter and the expected profiles follow the sea-32
sonally varying insolation (Moses and Greathouse 2005;33
Fouchet et al. 2009, see also the chapter by Fletcher et al.34
in this volume). Observations of ethane and acetylene from35
ground-based (Greathouse et al. 2005) and Cassini CIRS36
data (Howett et al. 2007; Guerlet et al. 2009; Hesman et al. 1
2009; Sinclair et al. 2013; Sylvestre et al. 2015) found the 2
1–2-mbar acetylene abundance decreased from the equa- 3
tor towards the poles as predicted by photochemical mod- 4
els, while the ethane abundance was approximately constant 5
with latitude. These observations have been interpreted as 6
evidence that meridional mixing occurs on a timescale in- 7
termediate between the photochemical timescale of acety- 8
lene and ethane (Greathouse et al. 2005; Guerlet et al. 2009; 9
Hesman et al. 2009). However, Moses et al. (2007) have 10
pointed out that the ethane and acetylene photochemistry 11
are strongly coupled, such that the meridional profile of 12
acetylene should track that of ethane even in the presence 13
of transport. Furthermore, CIRS observations by Sinclair 14
et al. (2013) and Fletcher et al. (2015) show an increase in 15
the 2-mbar abundances of ethane and acetylene in the north- 16
ern hemisphere and decrease in the southern hemisphere, 17
which they interpret as evidence of hemispheric transport 18
on seasonal timescales. Thus, the global meridional distri- 19
bution of ethane and acetylene is poorly understood. 20
In addition to the large-scale variations, acetylene and 21
ethane both show a localized enhancement at the south pole 22
at millibar pressures (Hesman et al. 2009; Sinclair et al. 23
2013; Fletcher et al. 2015). As the acetylene and ethane 24
abundances increase with altitude, this is consistent with 25
downward transport at the south pole indicated by tempera- 26
ture data. Using CIRS limb data, Guerlet et al. (2009) found 27
a local maximum in the acetylene and ethane abundance at 28
25N at 0.1 and 0.01 mbar, which they attribute to subsi- 29
dence in the downward branch of a meridional circulation. 30
This interpretation is consistent with the general circula- 31
tion model of Friedson and Moses (2012) which produces a 32
seasonally varying low-latitude circulation with rising mo- 33
tion in the summer hemisphere and subsidence in the winter 34
hemisphere. The Equatorial Semi-Annual Oscillation (see 35
Section 11.3.3) may also contribute to the subsidence at this 36
18
Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHERE
Fig. 11.14.— Low-latitude stratospheric temperatures on Saturn (in K) determined from Cassini/CIRS observations in2005/2006 (left) and 2010 (middle). The difference is shown in the right panel. Note the existence of a low-latitudeoscillatory structure whose phase shifted downward between 2005/2006 and 2010. From Guerlet et al. (2011).
latitude (Fouchet et al. 2008).1
The earliest, pre-Cassini, models of the meridional cir-2
culation (Conrath and Pirraglia 1983; Conrath et al. 1990)3
assumed a circulation that is mechanically forced in the tro-4
posphere, modeled by imposing the observed zonal winds5
at the lower boundary, and assumed zonal momentum bal-6
ance between the Coriolis acceleration of the meridional7
wind and damping of the zonal wind by eddies. Parame-8
terizing the zonal acceleration due to the eddies as −u/τf ,9
where τf is the eddy-damping timescale, this balance can10
be written fv = u/τf . Conrath et al. (1990) also included11
radiative forcing from solar heating and radiative cooling.12
This model produces upward motion and cold temperatures13
on the equatorward side of eastward jets, and downward14
motion and warm temperatures on the poleward side, as15
well as the observed decay of the zonal jet with altitude.16
The resulting upper tropospheric temperature perturbations17
are consistent with the Voyager IRIS observations when the18
frictional and radiative timescales are comparable, τf ∼ τr.19
A more detailed model of the stratospheric circulation20
was produced by Friedson and Moses (2012), using a fully21
3D general circulation model adapted to Saturn. Their22
model also uses a mechanical forcing at the lower boundary23
to produce the observed tropospheric zonal winds, along24
with random thermal perturbations in the troposphere to25
simulate generation of waves by convection, and includes26
realistic radiative forcing. Their model produced global27
scale temperature gradients generally consistent with ob-28
servations, though temperatures were ∼5 K too warm in29
the summer stratosphere. The modeled meridional trans-30
port was dominated at low latitudes by a seasonally revers-31
ing Hadley circulation, with broad upwelling at low lati- 1
tudes and strong subsidence near 25 in the winter hemi- 2
sphere, consistent with the circulation inferred from the 3
ethane and acetylene measurements of Guerlet et al. (2009). 4
At mid-latitudes they found 1-mbar eddy mixing timescales 5
of just over 100 years, slightly longer than the photochem- 6
ical timescale for acetylene and shorter than for ethane, 7
consistent with the observations. Note, however, that the 8
model was unable to reproduce the Semi-Annual Oscilla- 9
tion (see next section), which compromised the model’s 10
ability to capture the observed variations in temperature and 11
constituents at low latitudes associated with the oscillation. 12
11.3.3. Equatorial Semi-Annual Oscillation 13
A common feature of equatorial stratospheres in rapidly 14
rotating atmospheres is the presence of quasi-periodic os- 15
cillations, in both time and altitude, of the zonally averaged 16
temperature and wind fields. The best studied of these are 17
the Quasi-Biennial Oscillation (QBO) in the Earth’s lower 18
stratosphere, in which alternating layers of eastward and 19
westward zonal mean winds, with associated warm and cold 20
temperatures, slowly descend with a variable periodicity av- 21
eraging approximately 28 months (Baldwin et al. 2001). A 22
similar oscillation, with a more regular semi-annual period, 23
is also seen in the upper stratosphere and mesosphere. An 24
approximately four year periodicity in Jupiter’s equatorial 25
temperatures was found in an analysis of groud-based data 26
by Orton et al. (1991). Leovy et al. (1991) proposed that 27
this Quasi-Quadrennial Oscillation (QQO) was analogous 28
to the terrestrial QBO, and calculation of the stratospheric 29
winds from CIRS temperature measurments by Flasar et al. 30
19
Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHERE
(2004) showed the presence of a vertical oscillation in the1
zonal winds.2
Using 24 years of ground-based data, Orton et al. (2008)3
found an oscillation of Saturn’s equatorial brightness tem-4
peratures, in both 7.8µm methane emission and 12.2µm5
ethane emission, with a period of roughly 15 Earth years,6
which has been labeled the Saturn Semi-Annual Oscilla-7
Fig. 11.15.— Low-latitude, stratospheric zonal winds onSaturn calculated based on the observed meridional tem-perature gradients using the thermal-wind equation (11.1).The equation is integrated from the 20-mbar level and so theplotted winds are differences relative to those at 20 mbar.The thermal-wind equation breaks down near the equator,and the winds equatorward of the dashed lines are interpo-lated on isobars from regions outside the dashed lines. Notethe existence of an oscillatory structure in the magnitude ofthe zonal wind with height, which has shifted downward in2010 relative to its phase in 2005/2006. The difference isplotted in the bottom row. From Guerlet et al. (2011).
tion (SSAO). Using CIRS limb observations from 2005 to 1
2006, Fouchet et al. (2008) retrieved temperatures between 2
20 and 0.003 mbar and found equatorial temperature oscil- 3
lations similar to those seen in the QBO and QQO (Fig- 4
ure 11.14), confined within ∼10 of the equator and oscil- 5
lating in height with a wavelength of several scale heights. 6
These equatorial perturbations are flanked by temperature 7
perturbations of opposite sign from ∼10–20 latitude. Cal- 8
culation of the zonal winds from the thermal wind equa- 9
tion reveals vertically alternating eastward and westward 10
jets (Figure 11.15); the presence of a stratospheric jet was 11
also inferred from CIRS nadir viewing data (Li et al. 2008). 12
CIRS limb observations from 2010 (Guerlet et al. 2011) 13
showed that the pattern of winds and temperatures had de- 14
scended in altitude over the intervening five years, as is seen 15
in the QBO. The descent of the temperature field was also 16
observed in equatorial temperature profiles from Cassini ra- 17
dio occultations (Schinder et al. 2011), and cloud tracking 18
measurments from Cassini imaging have shown variations 19
in the velocity of the equatorial jet at the tropopause (Li 20
et al. 2011). Comparisons of Cassini CIRS temperatures 21
from 2009 with a reanalysis of Voyager IRIS thermal data 22
from one Saturn year earlier (Sinclair et al. 2013) found that 23
temperatures at 1–2 mbar were ∼7 K warmer in 2010 than 24
1980 at the equator, and ∼4 K cooler at ±10 latitude, in- 25
dicating the that period of the SSAO is not exactly one-half 26
of a Saturnian year. 27
The terrestrial QBO is driven by the interaction of a spec- 28
trum of vertically propagating waves—of both eastward and 29
westward phase velocities—with the zonal wind. Absorp- 30
tion of the waves by the zonal flow, through radiative or 31
frictional damping, produces a momentum transfer between 32
the wave and zonal flow that accelerates the flow toward 33
the zonal phase velocity of the wave (Lindzen and Holton 34
1968). The momentum transfer is most effective as the 35
wave approaches a critical level where the zonal phase ve- 36
locity of the wave matches the zonal wind velocity and the 37
vertical wavelength and vertical velocity go to zero. In the 38
presence of a jet with vertical wind shear, this results in 39
the waves being absorbed at altitudes slightly below where 40
the wind speed matches the wave phase velocity—and be- 41
low the altitude where the jet speed peaks. This causes the 42
pattern of zonal winds to slowly migrate downward over 43
time (note that, as contours of zonal wind are not mate- 44
rial surfaces, this does not imply downward transport of air 45
parcels themselves). As the jet descends, its lower bound- 46
ary becomes sharper and as the jet descends to the tropo- 47
sphere it dissipates, allowing the waves to now propagate to 48
higher altitudes, where they accelerate a new jet. Equato- 49
rial confinement of the oscillation can be explained by two 50
possible mechanisms. First, the waves driving the oscilla- 51
tion may be equatorially confined. Secondly, at latitudes 52
away from the equator, Coriolis forces become important, 53
and the wave induced momentum convergences may be par- 54
tially balanced by Coriolis forces on the meridional circu- 55
lation induced by the waves, instead of by the momentum 56
changes to the winds. Full details on the terrestrial QBO 57
20
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
can be found in the review by Baldwin et al. (2001). The1
wave modes responsible for the observed oscillations are2
poorly constrained, even on the Earth, although Kelvin and3
eastward-propagating gravity waves are most likely for con-4
tributing the eastward jet accelerations, and mixed Rossby-5
gravity waves and westward-propagating gravity waves are6
most likely for contributing the westward jet accelerations.7
In case of Saturn’s SAO, the amplitude and period of8
the oscillation likely contain information about the types,9
spectra, and amplitudes of the wave modes that drive it, and10
detailed dynamical modeling may thus provide information11
about the wave properties in Saturn’s stratosphere. Anal-12
ogy with the Earth would suggest that such waves might13
arise from convective forcing in the troposphere, so in prin-14
ciple the properties of the SSAO might lead to improved un-15
derstanding of the extent to which tropospheric convection16
on Saturn couples to the overlying stratified atmosphere.17
Moreover, although primarily an equatorial phenomenon,18
Earth’s QBO exerts a global influence, and this is also likely19
to be the case on Saturn, though detailed observations and20
modeling will be necessary to quantify this possibility.21
11.3.4. Stratospheric Response To the 2010 Storm22
One of the most surprising consequences of the large23
convective storm, known as a Great White Spot (GWS) that24
began in December 2010 (see chapter by Sanchez-Lavega25
et al.), was the observation of large changes in the ther-26
mal structure of the stratosphere at northern midlatitudes.27
Observations taken in January 2011 by Cassini CIRS and28
ground-based telescopes (Fletcher et al. 2011) showed a29
cool region in the stratosphere above the anticyclonic vortex30
associated with the storm, flanked by two warmer regions31
nicknamed the “beacons,” 16 K warmer than the cold region32
at roughly 0.5 mbar, much larger than any zonal contrasts33
previously seen in thermal observations of Saturn’s strato-34
sphere. Subsequent observations from CIRS and ground35
based telescopes (Fletcher et al. 2012) showed the beacons36
moving westward at differing rates, with one of the bea-37
cons remaining located above the convective plume asso-38
ciated with the storm, while increasing in temperature. At39
the end of April 2011, the two beacons merged, resulting40
in a single warm oval, with a longitudinal extent of 70, a41
latitudinal extent of 30 and a peak temperature of 220 K42
at 2 mbar, 80 K warmer than the background atmosphere43
and the warmest stratospheric temperatures ever observed44
on Saturn. This new warm oval moved westward at a veloc-45
ity intermediate between the two original beacons, and was46
centered about 1.5 scale heights lower in the atmosphere.47
The temperature of the beacon dropped by 20 K over the48
next two months, after which the temperature slowly de-49
clined by 0.11 ± 0.01 K day−1 and the width of the warm50
spot shrank by 0.16±0.01 deg day−1. Fletcher et al. (2012)51
used the thermal-wind equation to calculate the wind fields52
for the initial beacons in March 2011, and for the merged53
beacon in August 2011. The winds reveal that the hot spots54
are coherent anticyclonic vortices, with tangential winds of55
70–140 m s−1 for the pre-merger vortices, and ∼200 m s−1 1
for the final merged vortex. 2
The beacons were associated with perturbations of 3
chemistry as well as temperature, providing additional 4
insight into the dynamics. The abundances of ethylene 5
(C2H4) and acetylene increased significantly in the hot bea- 6
con core (e.g., at pressures of order ∼1 mbar) relative to 7
pre-storm conditions, and ethane apparently also increased 8
in abundance, though more modestly (Fletcher et al. 2012; 9
Hesman et al. 2012; Moses et al. 2015). One-dimensional 10
photochemical models show that the temperature increase 11
alone, while modifying the chemisty, is insufficient to ex- 12
plain the observed increases (Cavalie et al. 2015; Moses 13
et al. 2015). Therefore, dynamics likely played a role. In 14
particular, all three species increase with altitude at pres- 15
sures of ∼1–10 mbar, so a likely explanation is that sub- 16
sidence occurred inside the beacon, advecting the greater 17
high-altitude abundances of these species downward into 18
the beacon core region. The compressive temperature in- 19
crease associated with such descent would also naturally 20
explain the high beacon temperatures. Nevertheless, the 21
descent velocity required to explain the chemical abun- 22
dances in photochemical models is surprisingly large— 23
Moses et al. (2015) suggest that ∼10 cm s−1 is required. 24
It is not clear whether this is consisent with the magnitude 25
of descent needed to explain the temperature increase, nor 26
how it would be generated. 27
Models of moist convection on Saturn indicate that the 28
convective plumes will not penetrate above the upper tro- 29
poshere, 150 mbar or so (Hueso and Sanchez-Lavega 2004), 30
and modeling of Cassini imaging data of the plume indi- 31
cated that the cloud tops were at 400 mbar or deeper. It is 32
thus unlikely that the stratospheric perturbations were pro- 33
duced directly by the convective plumes associated with the 34
GWS (Garcia-Melendo et al. 2013). Sayanagi and Show- 35
man (2007) showed that tropospheric storms can cause sig- 36
nificant wave generation, and that such waves can propagate 37
into the stratosphere where they exert a significant dynam- 38
ical effect when they break or become absorbed. Fletcher 39
et al. (2012) noted that the storm was located at a latitude 40
where the zonal winds have been suggested to be barotrop- 41
ically unstable (Achterberg and Flasar 1996; Read et al. 42
2009a), and where quasi- stationary Rossby waves may po- 43
tentially propagate upward from the troposphere to the strat- 44
sophere. They therefore suggested that the strong pertur- 45
bations in the stratosphere were the result of waves, either 46
gravity or Rossby waves, generated by the convection im- 47
pinging on the statically stable tropopause, propagating into 48
the stratosphere. This conjecture still needs to be tested with 49
additional numerical modeling. 50
11.4. Dynamics of the Zonal Jets 51
11.4.1. Jet Structure 52
As described in Section 11.2, Saturn rotates rapidly, and 53
the large-scale dynamics is in approximate geostrophic bal- 54
ance. Although we lack detailed observations of the deep 55
21
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
interior, dynamical balance arguments can be used to con-1
strain the structure of the jets there. In particular, for a zonal2
flow at low Rossby number, it can be shown that, to good3
approximation (Showman et al. 2010)4
2Ω∂u
∂z∗≈ g
ρ
(∂ρ
∂y
)p
, (11.5)
where z∗ is the coordinate parallel to the rotation axis, g is5
gravity, and ρ is density. This is a generalized thermal-wind6
equation that is valid in the deep molecular interior even7
in the presence of non-hydrostatic motions. If the density8
is constant on isobars—that is, if the fluid is barotropic—9
then Eq. (11.5) implies that the zonal wind is constant on10
surfaces parallel to the rotation axis, i.e.,11
∂u
∂z∗≈ 0. (11.6)
This result is analogous to the standard Taylor-Proudman12
theorem (Pedlosky 1987), except that it does not make13
any assumption of constant density. It implies that, for a14
barotropic flow, the zonal wind is constant along lines par-15
allel to the rotation axis, and is valid even if the mean den-16
sity varies by orders of magnitude from the atmosphere to17
the deep interior, as it does on Saturn. On the other hand, if18
density varies on isobars—that is, if the fluid is baroclinic—19
then (11.5) implies that the zonal wind varies along surfaces20
parallel to the rotation axis.21
These results have been used to argue for several end-22
point scenarios regarding the interior wind structure. Con-23
vective mixing is normally thought to homogenize the in-24
terior entropy, which would suggest a nearly barotropic in-25
terior in which variations of density on isobars are small.26
Convective plumes of course involve thermal perturbations,27
but simple mixing-length estimates suggest that at Saturn’s28
heat flux these convective density variations induce only29
slight deviations from a barotropic state (Showman et al.30
2010). Based on arguments of this type, Busse (1976) sug-31
gested that the observed zonal winds on Jupiter and Sat-32
urn extend downward into the interior on surfaces paral-33
lel to the rotation axis following Equation (11.6); the ob-34
served zonal winds would then be the surface manifesta-35
tion of concentric, differentially rotating cylinders of fluid36
centered about—and parallel to—the rotation axis. On the37
other hand, other authors have suggested that perhaps the38
jets on Jupiter and Saturn extend only a few scale heights39
into the interior (e.g. Ingersoll and Cuzzi 1969; Stone 1973;40
Ingersoll 1976). In this case, Eq. (11.5) demands the ex-41
istence of latitudinal thermal variations, and would imply42
that, just below the cloud deck, the cyclonic bands are43
cooler (denser) than the anticyclonic bands. The required44
temperature differences, ∼5–10 K, are modest, and could45
plausibly be supplied by variations in latent or radiative46
heating between latitude bands. Intermediate scenarios are47
also possible, with horizontal temperature gradients and48
vertical variation of the jets in the cloud layer superposed49
on deep, nearly barotropic jets in the interior (Vasavada and50
Showman 2005). Liu et al. (2013, 2014) suggested yet an- 1
other scenario based on the assumption that the interior en- 2
tropy is only homogenized in the direction of z∗, while al- 3
lowing for entropy variations in the direction toward/away 4
from the rotation axis. Via Equation (11.5), this scenario 5
also implies significant thermal wind shear and a gradual 6
decay of the jets with depth. 7
It has long been recognized that the above arguments 8
may break down in the metallic hydrogen interior at pres- 9
sures ≥ 106 bars. There, the high electrical conductivity 10
allows sufficiently strong Lorentz forces to alter the forces 11
balances, causing a breakdown of geostrophy. It has been 12
suggested that the Lorentz forces will act to brake the zonal 13
flows, leading to weak winds in the metallic region (e.g. 14
Busse 1976, 2002). The transition from molecular to metal- 15
lic hydrogen is gradual (Nellis 2000), and several authors 16
have pointed out that significant magnetic effects on the 17
flow can occur even in the extended semiconducting re- 18
gion between the metallic interior and the overlying molec- 19
ular (electrically insulating) envelope (Kirk and Stevenson 20
1987; Liu et al. 2008). In particular, Liu et al. (2008) ar- 21
gued that the observed zonal winds cannot penetrate deeper 22
than 96% and 86% of the radius on Jupiter and Saturn, re- 23
spectively, because otherwise the Ohmic dissipation would 24
exceed the planets’ observed luminosities. If such Lorentz- 25
force braking occurs at the base of the molecular region 26
and leads to weak winds there, and if the overlying jets are 27
nearly barotropic, then Equation (11.6) would suggest that 28
the winds may be weak throughout much of the molecular 29
interior—and not just in the metallic and semiconducting 30
regions (Liu et al. 2008). Nevertheless, the models to date 31
have been largely kinematic, and more work is needed to 32
determine self-consistent solutions to the full magnetohy- 33
drodynamic problem (Glatzmaier 2008). The main region 34
that can escape such coupling is at low latitudes—there, it is 35
possible for Taylor columns to extend throughout the planet 36
without ever encountering electrically conducting layers. 37
Interestingly, the width of this region is similar to the ob- 38
served width of the equatorial jets on Jupiter and Saturn. 39
An attractive scenario is therefore that the equatorial jets 40
penetrate throughout the planet along surfaces parallel to 41
the rotation axis (approximately following Equation 11.6 in 42
the deep atmosphere), while the higher-latitude jets truncate 43
at some as-yet poorly determined depth. Juno and Cassini 44
will provide observational constraints on this question in the 45
next year. 46
11.4.2. Models Of Jet Formation 47
Thorough reviews of models for jet formation on Jupiter 48
and Saturn were provided by Vasavada and Showman 49
(2005) and Del Genio et al. (2009); here, we summarize 50
only the highlights, emphasizing developments within the 51
last ten years. Two classes of model have been introduced 52
to explore the zonal jets on Jupiter and Saturn. In one ap- 53
proach, which we dub the “shallow forcing” scenario, it 54
is assumed that baroclinic instabilities, moist convection, 55
22
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
and other processes within the cloud layer are responsible1
for driving the jets. This scenario has mostly been explored2
with thin-shell, one-layer and multi-layer atmospheric mod-3
els from the terrestrial atmospheric dynamics community.4
In another approach, which we dub the “deep forcing” sce-5
nario, it is assumed that convection throughout the interior6
leads to differential rotation in the molecular envelope that7
manifests as the zonal jets at the surface. This scenario8
has primarily been explored with Boussinesq and anelastic9
models of convection in spherical shells that are derived10
from the geodynamo and stellar convection communities.11
The distinction between the approaches is artificial, but12
because of the different communities involved, and the dif-13
ficulty of constructing a truly coupled atmosphere-interior14
circulation model, the distinction has persisted over the15
∼40-year history of the field. Nevertheless, new attempts16
are being made to bridge this gap, an area that will see17
major progress in the next decade.18
It is important to emphasize that the issue of whether19
the jets exhibit deep or shallow structure is distinct from20
whether the jet driving occurs primarily in the atmosphere21
versus the interior (Vasavada and Showman 2005; Show-22
man et al. 2006). Because of the nonlocal nature of the at-23
mospheric response to eddy driving, zonal jets that extend24
deeply into the interior can result from eddy accelerations25
that are primarily confined to the atmosphere (Showman26
et al. 2006; Lian and Showman 2008; for theory, see Haynes27
et al. 1991). Likewise, under some conditions, convection28
throughout the interior can produce jets that may exhibit29
confinement near the outer margin of the planet (Kaspi et al.30
2009).31
Models for the atmospheric jet formation generally as-32
sume that the zonal jets result from the interaction of tur-33
bulence with the β effect that is associated with latitudinal34
variations in the Coriolis parameter. Early work empha-35
sized two-dimensional, horizontally non-divergent models36
and one-layer shallow-water models. More recently, sev-37
eral three-dimensional models have been performed.38
One-layer models are intended to represent an appropri-39
ate vertical mean of the atmospheric flow. They are mo-40
tivated by the observation that the atmospheric winds on41
Jupiter and Saturn are approximately horizontal—with gen-42
erally small horizontal divergence—and were originally in-43
tended to capture the flow in a presumed shallow weather44
layer below the clouds. More broadly, however, they serve45
as an ideal process model to explore the dynamics of zonal46
jets and vortices in the simplest possible context, thereby47
shedding insights into dynamical mechanisms that may also48
occur (but be harder to identify) in more realistic systems.49
In one-layer models, the effect of convection must be pa-50
rameterized, typically by introducing small-scale vorticity51
sources and sinks that flucuate in time. Damping is com-52
monly represented using a frictional drag.53
Most work to date has been performed with the two-54
dimensional, horizontally non-divergent model. This sys-55
tem captures the interaction of turbulence with the β ef-56
fect, but neglects buoyancy, gravity waves, and any effects57
associated with a finite Rossby deformation radius (an as- 1
sumption that is not strictly valid on Jupiter and Saturn, 2
where the deformation radius is comparable to or smaller 3
than the meridional jet width). When forced with small- 4
scale turbulence under conditions of fast rotation and rel- 5
atively weak frictional drag, these models generally pro- 6
duce multiple zonal jets whose meridional widths scale 7
with the Rhines scale (U/β)1/2, where U is a charac- 8
teristic wind speed5(e.g. Williams 1978; Nozawa and Yo- 9
den 1997; Huang and Robinson 1998; Sukoriansky et al. 10
2007, and many others). Interestingly, these models lack 11
an unusually strong equatorial jet as occurs on Jupiter and 12
Saturn—intead, the equatorial jet tends to resemble the 13
higher-latitude jets in speed and structure, and it often is 14
not centered precisely around the equator. These models 15
also tend not to produce large, long-lived coherent vortices 16
that coexist with the jets, such as Jupiter’s Great Red Spot 17
or smaller but analogous vortices on Saturn. Both of these 18
discrepancies likely result from the lack of a finite deforma- 19
tion radius in the 2D non-divergent model. Despite these 20
failures, the ease of analyzing this model has led to cru- 21
cial insights into the workings of inverse energy cascades 22
(Sukoriansky et al. 2007) and the physical mechanisms for 23
jet formation (e.g. Dritschel and McIntyre 2008). 24
The one-layer shallow-water model represents a more 25
realistic system because it includes the effect of buoyancy 26
(via a horizontally variable vertical layer thickness), gravity 27
waves, and a finite deformation radius, albeit still in a con- 28
text that does not capture detailed vertical structure. In the 29
context of giant planets, the model captures the behavior of 30
an active atmospheric weather layer that overlies an abyssal 31
layer (representing the deep planetary interior) whose winds 32
are specified, usually to be zero. The related, one-layer 33
quasi-geostrophic (QG) model provides a simplification by 34
restricting the flow to be nearly geostrophic, which filters 35
gravity waves while retaining the effect of a finite deforma- 36
tion radius. Showman (2007) and Scott and Polvani (2007) 37
presented the first forced turbulence calculations of jet for- 38
mation in the shallow water system, and Li et al. (2006) 39
performed a similar study in the QG system. These authors 40
showed that multiple zonal jets can result from small-scale 41
forcing, and that in many cases, the jet widths are compara- 42
ble to the Rhines scale (U/β)1/2. Interestingly, the defor- 43
mation radius influences jet formation, and when it is suf- 44
ficiently small, can suppress the formation of jets entirely, 45
leading to a flow dominated by vortices—an effect first de- 46
scribed in the QG system (Okuno and Masuda 2003; Smith 47
2004) before being extended to the shallow-water system 48
(Showman 2007; Scott and Polvani 2007). Thomson and 49
McIntyre (2016) showed in a QG model that the presence 50
of specified, zonally symmetric jets in the abyssal layer 51
can help to increase the straightness of the weather-layer 52
5In Rhines’ original theory, this corresponds to an eddy velocity associatedwith the turbulence, but in other contexts other velocity scales such asthe zonal-mean zonal wind can also be appropriate (see, e.g., Scott andDritschel 2012).
23
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
jets, causing the flow to more closely follow latitude cir-1
cles. Using a simple parameterization of convective forcing,2
their model also naturally produces a preference for con-3
vection in belts rather than zones, as observed on Jupiter. In4
some cases, especially when jets in the abyssal layer exist,5
the weather-layer jets in one-layer shallow-water and QG6
models can violate the Charney-Stern stability theorem, in7
agreement with Jupiter and Saturn (Showman 2007; Scott8
and Polvani 2007; Thomson and McIntyre 2016).9
Under conditions appropriate to Jupiter and Saturn—10
namely, small Rossby number and a deformation radius a11
few percent of the planetary radius—shallow-water mod-12
els typically produce a broad, fast westward equatorial jet13
(Cho and Polvani 1996; Iacono et al. 1999; Showman 2007;14
Scott and Polvani 2007). This equatorial flow intensifica-15
tion could be considered a step forward from the 2D non-16
divergent model, since the equatorial jets of Jupiter and Sat-17
urn are faster and wider than the jets at higher latitudes.18
However, although Uranus and Neptune exhibit westward19
equatorial flow, this result represents a major failing for20
Jupiter and Saturn, where the equatorial flow is eastward.21
Nevertheless, Scott and Polvani (2008) showed that under22
certain conditions, shallow-water models can generate east-23
ward equatorial jets resembling those on Jupiter and Sat-24
urn. They speculate that the key property allowing emer-25
gence of eastward (rather than westward) equatorial flow26
is the usage of radiative rather than frictional damping.27
However, this is inconsistent with the findings of Show-28
man (2007), who adopted radiative damping and yet al-29
ways obtained westward equatorial jets. Most likely, spe-30
cific types of both forcing and damping are necessary. A31
similar “thermal shallow water” model presented by Warne-32
ford and Dellar (2014) exhibits equatorial superrotation at33
short radiative time constant but subrotation at long radia-34
tive time constant, although the value of the radiative time35
constant at the transition between these regimes is too short36
to explain the transition from the Jupiter/Saturn regime to37
the Uranus/Neptune regime. The dynamical mechanisms38
controlling the equatorial jet properties in all these shallow-39
water-type models remain poorly understood and deserve40
further study.41
Over the past 15 years, several three-dimensional mod-42
els have been published showing how zonal jets can develop43
in the atmosphere. Following on earlier work by Williams44
(2003), Lian and Showman (2008) showed that baroclinic45
instabilities in the weather layer (induced by meridional46
temperature differences associated with the latitudinal gra-47
dients in radiative heating) can generate multiple zonal jets.48
These jets do not remain confined to the cloud layer where49
they are driven, but rather can extend deep into the in-50
terior as long as friction there is weak. The model pro-51
duces statistical distributions of eddy momentum fluxes that52
match observations on Jupiter and Saturn, as well as jets53
that remain stable while violating the Charney-Stern stabil-54
ity criterion. Both Williams (2003) and Lian and Show-55
man (2008) showed that sharp latitudinal temperature gra-56
dients near the equator can lead to equatorial superrotation.57
Schneider and Liu (2009) presented a shallow 3D model 1
(truncated at 3 bars), which, as in Williams (2003) and Lian 2
and Showman (2008), produces multiple mid-to-high lat- 3
itude jets in response to baroclinic instabilities associated 4
with latitudinal temperature gradients. Moreover, they in- 5
troduced a simple convective parameterization which al- 6
lows the emergence of Jupiter-like equatorial superrotation 7
in response to equatorial convection in the model. 8
Several 3D models now exist that explain the overall fea- 9
tures of the circulation on all four giant planets, including 10
the transition from equatorial superrotation on Jupiter and 11
Saturn to equatorial subrotation on Uranus and Neptune. 12
Lian and Showman (2010) incorporated a hydrological cy- 13
cle that captures the advection, condensation, rain out, and 14
latent heating associated with water vapor, providing the 15
first test of the long-standing hypothesis that such latent 16
Showman et al.: The Global Atmospheric Circulation of Saturn 6 DYNAMICS OF ZONAL JETS
Fig. 11.37.— 3D atmosphere simulations demonstrating that latent-heat release associated with condensation of water canlead to zonal jet patterns qualitatively resembling all four giant planets. Top, middle, and bottom rows are three modelsrepresenting Jupiter, Saturn, and Uranus/Neptune, which are assumed to have water abundances of 3, 5, and 30 times solar,respectively. Colorscale represents zonal wind in m s1. Left column shows oblique view and right column shows viewlooking down over the north pole. The Jupiter and Saturn cases develop equatorial superrotation and many off-equatorialjets at higher latitudes, while the Uranus/Neptune model exhibits a three-jet pattern comprising broad equatorial subrotationand high-latitude eastward jets. From Lian and Showman (2010).
using a simple Newtonian relaxation scheme. Simulations3805
were performed for Jupiter, Saturn, and Uranus/Neptune3806
conditions. Although the water abundance on the gi-3807
ant planets is unknown, the abundance of methane is 33808
times solar on Jupiter, 5–10 times solar on Saturn, and3809
20–50 times solar on Uranus and Neptune, and so Lian3810
and Showman (2010) adopted water abundances similar to3811
these values. The Jupiter and Saturn simulations exhibited3812
numerous mid-to-high latitude zonal jets and equatorial3813
superrotation, whereas the Uranus/Neptune models ex-3814
hibited a three-jet pattern with high-latitude eastward jets3815
and broad westward flow at low latitudes (Figure 11.37).3816
These are the first models that explain the overall circula-3817
tion pattern of all four giant planets—including the tran-3818
sition from equatorial superrotation for Jupiter/Saturn to3819
subrotation for Uranus/Neptune—within the context of a3820
single mechanism. They also produce storms qualitatively3821
resembling those on Jupiter and Saturn, in some cases in-3822
cluding storms that expand to cover a significant range of3823
longitudes, perhaps analogous to Saturn’s GWS.3824
Schneider and Liu (2009) and Liu and Schneider3825
(2010) presented dry primitive-equation models that build3826
on the work of Williams (2003a) and Lian and Showman3827
(2008) by testing the hypothesis that the high-latitude3828
jets could result from baroclinic instability and explor-3829
ing the conditions that can lead to equatorial superro-3830
tation. Their model is much shallower than those of3831
Lian & Showman—they placed their bottom boundary at3832
only 3 bars. In simulations of Jupiter, Schneider and Liu3833
(2009) found that multiple mid-to-high latitude zonal jets3834
emerged due to baroclinic instabilities resulting from the3835
meridional insolation gradient, and they moreover found3836
that equatorial superrotation emerged in response to low-3837
latitude convection (represented in their model with a sim-3838
ple dry convective adjustment scheme). Specifically, they3839
suggest that convection leads to significant horizontal di-3840
vergence which causes a net Rossby wave source near3841
the equator, and that radiation of these Rossby waves to3842
surrounding latitudes causes a horizontal convergence of3843
eddy momentum onto the equator, driving the superro-3844
tation. Following Lian and Showman (2010), Liu and3845
Schneider (2010) extended the model of Schneider and3846
Liu (2009) to Saturn, Uranus, and Neptune, and likewise3847
showed that a transition can occur from equatorial super-3848
52
Fig. 11.16.— 3D atmosphere simulations demonstratingthat latent-heat release associated with condensation of wa-ter can lead to zonal jet patterns qualitatively resembling allfour giant planets. Top, middle, and bottom rows are threemodels representing Jupiter, Saturn, and Uranus/Neptune,which are assumed to have water abundances of 3, 5, and 30times solar, respectively. Colorscale represents zonal windin m s−1. Left column shows oblique view and right col-umn shows view looking down over the north pole. TheJupiter and Saturn cases develop equatorial superrotationand many off-equatorial jets at higher latitudes, while theUranus/Neptune model exhibits a three-jet pattern compris-ing broad equatorial subrotation and high-latitude eastwardjets. From Lian and Showman (2010).
24
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
heating is crucial in driving the circulation (e.g. Barcilon1
and Gierasch 1970; Ingersoll et al. 2000). Their results are2
shown in Figure 11.16. In addition to explaining the ob-3
served transition from superrotation to subrotation, as well4
as mid-to-high latitude jets qualitatively similar to those ob-5
served on the giant planets, their model also produces lo-6
cal “storm”-like features that crudely resemble convective7
thunderstorm events observed on Jupiter and Saturn. In8
some cases, their model exhibits large storm events, which9
bear resemblence to Saturn’s recent Great White Spot of10
2010-2011. Liu and Schneider (2010) extended the work of11
Schneider and Liu (2009) to all four planets, likewise show-12
ing a transition from equatorial superrotation on Jupiter and13
Saturn to equatorial subrotation on Uranus and Neptune, as14
well as other jet properties similar to those on the giant plan-15
ets. All of these models represent a major step forward.16
Nevertheless, the equatorial jet under Saturn conditions is17
insufficiently fast and broad, and more work is warranted to18
determine whether equatorial jets better resembling Saturn19
can be produced in this class of model.20
We now turn to discuss models of jet formation via con-21
vection in the interior. Busse (1976) first envisioned that22
the convection in the interior could organize into the form23
of Taylor columns aligned with the rotation axis, and that24
the Reynolds stresses associated with this convection would25
drive jets that would manifest as concentric, differentially26
rotating cylinders centered on the rotation axis. The ob-27
served zonal jets would then represent the outcropping of28
this differential rotation at the cloud level. Early investi-29
gations of this hypothesis involved analytical calculations,30
laboratory studies, and numerical simulations in the lin-31
ear and weakly nonlinear regime. These studies generally32
confirmed the columnar nature of the convection at low33
amplitude, and showed how the spherical planetary shape34
would promote the emergence of equatorial superrotation35
(see Busse 1994 and Busse 2002 for reviews). Only in re-36
cent years, however, have computational resources become37
sufficient to investigate the dynamics in the more strongly38
nonlinear regime relevant to the giant planets.39
The first such models adopted the Boussinesq approx-40
imation wherein the background density is assumed con-41
stant (i.e., the continuity equation is ∇ · v = 0). This as-42
sumption is not valid for the giant planets, but the dynam-43
ics are nevertheless rich and provide significant insights.44
Generally, these models explore convection in a spherical45
shell with boundaries that are free-slip in horizontal veloc-46
ity, and that are maintained at constant temperature (with47
the interior boundary being hotter than the outer bound-48
ary, allowing convection to occur). The earliest models ex-49
plored relatively thick shells, with an inner-to-outer radius50
ratio less than 0.7. These simulations showed that when51
the convection is sufficiently vigorous and friction suffi-52
ciently weak (i.e. the Rayleigh number sufficiently high53
and Ekman number sufficiently low), the convection can54
produce zonal jets whose speeds are signifantly faster than55
the convective velocities (Aurnou and Olson 2001; Chris-56
tensen 2001, 2002). The jets take the form of a broad equa-57
torial superrotating jet and, in some cases, a small number 1
of weaker jets at high latitudes. Despite the existence of 2
the superrotation, the zonal jet patterns in these models do 3
not resemble that on Jupiter and Saturn. Subsequent studies 4
considered thinner shells, with an inner-to-outer radius ra- 5
tio of∼0.9, and when appropriately tuned, these models are 6
able to produce superrotation comparable to that of Jupiter 7
and Saturn, along with multiple high-latitude jets (Heimpel 8
et al. 2005; Heimpel and Aurnou 2007; Aurnou et al. 2008, 9
see Figure 11.17). An issue is that, in all of these models, 10
the meridional width of the superrotation is controlled by 11
the depth of the inner boundary, and yet such a boundary 12
is artificial in the context of a giant planet (which lack any 13
such impermeable boundary in their molecular/metallic en- 14
velopes). 15
In Jupiter and Saturn, the density varies by a factor of 16
∼104 from the cloud deck to the deep interior, and re- 17
cently several models have started to include such radial 18
density variations via the anelastic approximation, which 19
allows the background density to vary radially, while (like 20
the Boussinesq system) filtering sound waves, which is a 21
reasonable approximation for the giant planet interiors. The 22
first such models were two-dimensional, considering con- 23
vection in the equatorial plane and investigating the emer- 24
gence of differential rotation (Evonuk and Glatzmaier 2004, 25
2006, 2007; Glatzmaier et al. 2009). These models demon- 26
© 2005 Nature Publishing Group
Previous analytical models of planetary zonal flow in a sphericalshell have assumed a relatively deep bottom boundary, such thathigh-latitude zonal jets develop from flows outside the tangentcylinder18. More recent numerical models of deep and stronglyturbulent three-dimensional quasigeostrophic convection10,11 haveproduced jets of realistic amplitudes. However, these moderatelythick fluid shells (with radius ratios x ¼ r i/ro ¼ 0.6–0.75) produceonly a pair of high-latitude jets in each hemisphere inside the tangentcylinder10,14, which cannot account for the observed pattern of jovianjets. Laboratory experiments of rotating convection in deep sphericalshells19 with x ¼ 0.35 and 0.70 have obtained zonal flow patterns thatare broadly comparable to the results of spherical numericalmodels9,10. However, multiple jets have been produced by idealizednumerical20 and experimental21 models with a cylindrical geometry, afree top surface, and a sloping bottom surface. In those local models,as well as our present global model, the jets are produced by thetopographic b-effect and follow Rhines scaling.There are various possible reasons why previous spherical shell
models have not produced multiple higher-latitude jets. Instead ofanalysing particular cases we list the following conditions that favourthe development of multiple high-latitude jets. Turbulent flow (thatis, high Reynolds number) constrained by rapid rotation (that is, lowRossby number) is necessary for the development of jets that followRhines scaling. A relatively thin fluid layer allows multiple jets toform at higher latitudes by decreasing the Rhines length andincreasing the latitudinal range inside the tangent cylinder.We use numerical modelling to study turbulent thermal convec-
tion in a rapidly rotating three-dimensional spherical shell, withsimulation parameters chosen to reflect our present understandingof Jupiter’s interior. The spherical shell geometry is defined by theradius ratio x ¼ r i/ro. We have chosen x ¼ 0.9, which represents asubstantially thinner shell than in previous models of rotatingconvection10,14. This value of the radius ratio corresponds to adepth in Jupiter of approximately 7,000 km, which is shallowerthan the phase boundary that separates the outer molecular fluid
from the liquid metal H–He core, estimated at 0.8–0.85 R J, whereR J < 70,000 km is the radius of Jupiter13. Measurements of increas-ing flow velocity with depth suggest that the surface winds are seatedin the deep molecular H2–He atmosphere22. However, increasingdensity and electrical conductivity with pressure result in inertial andLorentz forces that are expected to damp the zonal flow between 0.85and 0.95R J (refs 13 and 23). Thus we have chosen a simulation radiusratio that lies near the middle of current estimates. A description ofSaturn’s interior is similar to that of Jupiter except that lowersaturnian gravity roughly doubles the estimated layer depth.Selection of other simulation parameters (see Methods) is based
on recent numerical and experimental scaling analyses for convec-tion-driven zonal flows in thicker spherical shells11,24. An essentialingredient in this numerical simulation is that convective turbulenceis quasigeostrophic and close to the asymptotic state of rapid rotationin which viscosity and thermal diffusivity play a negligible role inthe dynamics. Thus, large discrepancies between the simulationparameters and those estimated for Jupiter should not stronglyaffect the character of the solution. We do not model the joviantroposphere, nor the effects of latitudinally varying insolation7,8.Furthermore, we model convection only within the region wherelarge-scale zonal flows are predicted to occur and we neglect deeperregions where convection may be vigorous but zonal flows areexpected to be weak. Although fluid compressibility effects areimportant to the dynamics of convection in the gas giants25, thefluid in our numerical model is assumed to be incompressible exceptfor thermal buoyancy effects (that is, the Boussinesq approximation).The omission of compressibility effects is possibly this model’sgreatest limitation. However, considering that we use a relativelythin convection layer, a Boussinesq treatment may be adequate tosimulate the large-scale dynamics12,13.Figure 2 shows the results of our numerical simulation and the
jovian zonal wind pattern. Figure 2a is a plot of Jupiter’s averagedsurface azimuthal (east–west) velocity profile relative to the deep-seated magnetic-field reference frame1. Although we focus here on
Figure 2 | Zonal flow for Jupiter and the numerical simulation. a, Thezonal wind of Jupiter. The Cassini space mission data was kindly providedby A. Vasavada. Wind speed may be converted to Rossby number usingRo ¼ v/Qro). b, Snapshot in time of the simulation’s outer-surfaceazimuthally averaged azimuthal (east–west) velocity. Dashed lines indicate
the latitude where the tangent cylinder intersects the outer surface, for thesimulation’s radius ratio (x ¼ r i/ro ¼ 0.9). c, Snapshot of the simulation’sazimuthal velocity field on the outer and inner spherical surface, and on ameridional slice. Red and blue colours represent prograde (eastward) andretrograde (westward) flow, respectively.
LETTERS NATURE|Vol 438|10 November 2005
194
Fig. 11.17.— The zonal flow on the outer and inner surfaceof a 3D convection simulation with an aspect ratio of 0.9,showing the eastward (red) and westward (blue) zonal ve-locities. The Boussinesq equations were solved, in whichthe background (reference) density is independent of ra-dius. Free-slip boundary conditions are used on both theinner and outer boundaries. Equatorial superrotation, andnumerous higher-latitude eastward and westward jets, de-velop. Adapted from Heimpel et al. (2005).
25
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
strated a new mechanism for generating equatorial superro-1
tation that does not exist in the Boussinesq system; as con-2
vective plumes rise and sink, the compressibility alters their3
vorticity in such a way as to promote Reynolds stresses that4
cause superrotation (Glatzmaier et al. 2009).5
More recently, several 3D anelastic convection mod-6
els have been developed (Kaspi 2008; Kaspi et al. 2009;7
Jones and Kuzanyan 2009; Jones et al. 2011; Gastine and8
Wicht 2012, and others). Like the Boussinesq models, these9
anelastic simulations generally exhibit equatorial superrota-10
tion and (in some cases) several higher-latitude zonal jets.11
If the spherical shell is thin, then the shell thickness con-12
trols the meridional width of the equatorial jet—just as in13
Boussinesq simulations. However, if the shell thickness be-14
comes sufficiently deep, then the equatorial jet width tends15
to become invariant to the location of the bottom boundary,16
which is an improvement over the situation in Boussinesq17
models. Nevertheless, in this situation, the superrotation in18
the simulations tends to be too broad and the higher lati-19
tude jets fewer in number compared to Jupiter and Saturn.20
In the models of Kaspi (2008) and Kaspi et al. (2009), the21
jets exhibit significant shear, becoming weaker with depth;22
in contrast, some other models exhibit weaker shear, with a23
more barotropic structure (Jones and Kuzanyan 2009; Gas-24
tine and Wicht 2012; Cai and Chan 2012; Gastine et al.25
2013; Chan and Mayr 2013). The difference likely result26
from the different treatment of the fluid’s thermodynamic27
properties, including the radial variation of density and es-28
pecially the entropy expansion coeffient, in these different29
models.30
A concern with these models is that the simulated pa-31
rameter regime is far from that of the giant planets; the32
simulated heat fluxes and viscosities are both too large33
by many orders of magnitude. Even within the simulated34
range, the jet speeds vary strongly with Rayleigh number35
and Ekman number. Therefore, even though it is possible to36
choose values of the Rayleigh number and Ekman number37
that yield realistic jet speeds, it is unknown whether such38
models would produce realistic jet speeds at the values of39
Rayleigh and Ekman number relevant to Jupiter and Sat-40
urn. Unforunately, computational resources will be insuf-41
ficient for directly simulating the planetary regime for the42
foreseeable future. Therefore, answering this question re-43
quires the development of scaling laws that can be extrap-44
olated from the simulated regime to the planetary regime.45
Christensen (2002) made a first attempt at this, suggesting46
a scaling law that could bridge the gap based based on an47
empirical assessment of his Boussinesq simulations. Show-48
man et al. (2011) used anelastic simulations to show that,49
within the simulated range of Rayleigh and Ekman num-50
bers, two distinct regimes exist, leading to distinct depen-51
dences of jet speeds on convective heat flux and viscosity.52
Christensen (2002) and Showman et al. (2011) both sug-53
gested an additional regime may exist wherein jet speeds54
become independent of viscosity when the viscosity is suf-55
ficiently small. More recent work, however, challenges the56
existence of a regime independent of viscosity and thermal57
diffusivity (Gastine et al. 2013, 2014). Additional work is 1
warranted. 2
All of the above models neglect any coupling to the 3
magnetic field. Recently, however, several models have in- 4
cluded the effect of an electrically conducting interior and 5
its coupling to the dynamics, allowing a joint investigation 6
of zonal-jet formation and dynamo generation of a magnetic 7
field. This is a challenging problem because the electrical 8
conductivity varies by many orders of magnitude with ra- 9
dius, a situation different from that encountered in the geo- 10
dynamo problem. This situation was first investigated in 11
Boussinesq models (Heimpel and Gomez Perez 2011) and 12
more recently in anelastic models (Duarte et al. 2013; Yadav 13
et al. 2013; Jones 2014) that allow both density and electri- 14
cal conductivity to vary strongly with radius. These models 15
show that the equatorial jet penetrates to a depth where the 16
Lorentz force becomes comparable to the Reynolds stress 17
associated with the convection (which effectively means 18
the jet is confined to the electrically insulating outer enve- 19
lope). Jets poleward of the equatorial superrotation tend 20
to be suppressed, because their bottoms penetrate into the 21
electrically conducting region where Lorentz forces can act 22
to brake the flows—an effect that extends throughout the 23
molecular envelope due to the nearly barotropic nature of 24
these jets (cf Equation 11.6). This suggests the possibil- 25
ity that the equatorial jet results from interior convection, 26
but the higher latitude jets result from atmospheric pro- 27
cesses including baroclinic instability and moist convection 28
(Vasavada and Showman 2005). 29
11.4.3. Detection Of Deep Dynamics By Gravity Mea- 30
surements 31
Information to date on Saturn’s deep winds has been in- 32
direct. This is likely to change in 2017, as towards the cul- 33
mination of its 13-year-long survey of the Saturnian system, 34
the Cassini spacecraft will shift into a highly inclined orbit 35
with a periapse between the planet and its rings—an orbit 36
ideally suited to measuring the small-scale structure of Sat- 37
urn’s gravitational field. During this phase, known as the 38
Cassini Grand Finale, the spacecraft will complete 22 or- 39
bits, six of which will be dedicated to gravity science. This 40
will be the final maneuver of Cassini before it descends into 41
the planet, terminating the mission. These gravity measure- 42
ments will allow the determination of Saturn’s gravity field 43
to much higher accuracy than exists today (Jacobson et al. 44
2006). The gravitational field is commonly represented us- 45
ing a spherical harmonic expansion (Hubbard 1984), and 46
so far only the lowest zonal harmonics J2, J4, and J6 have 47
been measured. These reflect the long-wavelength gravita- 48
tional perturbations associated primarily with the planet’s 49
rotational bulge, and provide essentially no information on 50
interior flows. Cassini’s proximal orbits will allow the mea- 51
surement of the gravity field at least up to J10, including the 52
possibility of measuring the odd gravity harmonics for the 53
first time (Kaspi 2013). 54
If the strong cloud-level winds extend sufficiently deep 55
26
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
The role of Lorentz forces in defeating zonal winds and therebyenabling dipole-dominated magnetic fields also offers an explana-tion why larger magnetic Prandtl numbers help. The reason likelyis that larger Pm values lead to stronger magnetic fields and thusstronger Lorentz forces. We can also now interpret the highly
time-dependent solutions with intermediate mean dipolarities.Here, the balance seems to be undecided (Fig. 4). Stronger Lorentzforces successfully suppress the zonal winds at times but never en-ough to establish the solution on the highly dipolar more stablebranch. At other times, Reynolds stresses succeed in driving stron-ger zonal flows that mostly create a weaker multipolar magneticfield.
To further test the theory that the zonal flows are decisive forthe field geometry we ran a few E = 10!4 cases with a no-slip outerboundary condition that largely prevents zonal flows from devel-oping. The results are mixed and not entirely conclusive, whichmay have to do with the fact that other flow components are alsoaffected by this change in boundary conditions. At vm = 95%, Nq = 0and Ra/Racr = 23.0, the no-slip boundary conditions indeed pro-mote a dipole-dominated solution with weak zonal flows wherewe only find multipolar solutions with strong zonal flows for afree-slip outer boundary condition (compare cases 3 and 4). Thesame positive effect was found for vm = 90%, Nq = 0 and Ra/Racr = 11.5 (cases 7 and 8). At vm = 90%, Nq = 1 and Ra/Racr = 5.2,however, we find bistable cases for both type of boundary condi-tions (cases 22d/m and 23d/m). In the no-slip case, both the di-pole-dominated and the multipolar solution have weak zonalflows. Free-slip outer boundary condition promotes dipolarity,but it is not a necessary condition to find this feature. Note thatsuch a bistable case for no-slip conditions has already been re-ported by Christensen and Aubert (2006).
Nρ=0 Nρ=1 Nρ=3 Nρ=4 Nρ=5
–0.031
–0.021
–0.010
0
+0.010
+0.021
+0.031
Fig. 7. Azimuthal averages of the zonal component of the flow. Each column of three plots has a different Nq, namely 0, 1, 3, 4 and 5 from left to right. In the bottom andmiddle rows, the poloidal field lines are plotted on top of the zonal velocity contours in units of Rossby number Ro = u/(Xro). The dotted line in the middle and bottom rowscorresponds to rm = 95% and rm = 80%, respectively. The top row shows the corresponding hydrodynamical solutions.
Fig. 8. Radial profile of magnetic energy flux (r2 Emag) averaged over time. Thedashed black line is the location of vm = 80%. These results correspond to the redtriangles and red dashed line from Fig. 5. The poloidal (dashed lines) and toroidal(dot-dashed lines) components are also shown for Nq = 5 and Nq = 0, with thecorresponding colours. The magnetic energy fluxes are normalized by theirmaximum values.
30 L.D.V. Duarte et al. / Physics of the Earth and Planetary Interiors 222 (2013) 22–34
Fig. 11.18.— Anelastic 3D simulations of convection in a giant planet interior including coupling to the magnetic field,from Duarte et al. (2013). Each image shows the zonal-mean structure of a distinct simulation; the color scale shows thezonal-mean zonal wind (expressed as a Rossby number) and the contours show poloidal magnetic field. Nρ denotes thenumber of density scale heights spanned from the outer to the inner boundary; the left column (Nρ = 0) denotes Boussinesqsimulations, while the right column (Nρ = 5) presents simulations with five density scale heights (inner density 148 timesthe outer density). The top row represent hydrodynamic models (no MHD effects). The middle and bottom rows representMHD simulations, with electrically insulating outer regions and electrically conducting inner regions. The transitionoccurs at a fractional radius of 0.95 and 0.8 for simulations in the middle and bottom rows, respectively. Robust equatorialsuperrotation can be seen in all models, which is confined to the electrically insulating region when MHD is used. Theinclusion of compressibility and magnetic effects suppress the formation of zonal jets at mid-to-high latitudes.
into the planet’s interior, then the density perturbations as-1
sociated with the jets will induce gravitational perturba-2
tions that are measurable. Because the equatorial bulge is3
an extremely broad-scale (long-wavelength) feature, it af-4
fects primarily the lowest harmonics, and contributes only5
a much smaller signal at the higher harmonics. In con-6
trast, the meridional scale associated with the zonal jets7
is smaller, and thus—if the jets extend sufficiently deep—8
they will induce substantial gravity signal at small merid-9
ional scales, corresponding to higher harmonics. This was10
first noted by Hubbard (1999), who used potential theory11
to show that if differential rotation on Jupiter penetrates the12
depth of the planet, then the high-order gravity moments13
will be dominated by the dynamical contribution rather than14
the contribution from rotational flattening. This study in-15
spired the Juno mission gravity experiment of Jupiter, and16
in turn motivated the Cassini Grand Finale gravity exper- 1
iment on Saturn. This potential-theory approach has re- 2
cently been further developed using more accurate concen- 3
tric Maclaurin-based interior models (Hubbard 2012; Kong 4
et al. 2012; Hubbard 2013; Hubbard et al. 2014; Kaspi et al. 5
2016). 6
A difficulty with these potential-theory approaches, 7
however, is that they are limited to fully barotropic systems 8
satisfying the Taylor-Proudman theorem (Equation 11.6), 9
where the flows are constant along cylinders. Therefore, 10
this approach cannot explore the possible consequences for 11
the gravity field if the flows penetrate only partway into the 12
interior and die off below some critical depth. 13
A second approach that allows an evaluation of winds 14
varying on cylinders is to use thermal-wind balance models 15
(Kaspi et al. 2010; Kaspi 2013; Kaspi et al. 2013; Liu et al. 16
27
Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS
2013). Given some assumed structure of the zonal winds,1
the thermal-wind relation (Equation 11.5) can be used to2
calculate the dynamically induced density gradients in the3
interior. These density perturbations in turn cause pertur-4
bations to the gravity field. The dynamical contributions to5
the gravity harmonics are defined as (Kaspi et al. 2010)6
∆Jdynn = − (Man)
−1∫Pnρ
′rnd3r, (11.7)
where ρ′ is the deviation of the density caused by dynam-7
ics (i.e., the deviation from some static density distribution,8
ρstatic, that would exist in the absence of dynamics), Pn9
is the n-th Legendre polynomial, M is the planetary mass10
and a is the mean planetary radius. Kaspi et al. (2016)11
showed that in the barotropic limit the thermal-wind and12
potential-theory approaches give very similar results. How-13
ever, the thermal-wind models have typically been limited14
to spherical symmetry, resulting in inability to calculate the15
static (solid-body) gravity spectrum and neglecting the ef-16
fect of the oblateness of the planet on the dynamic grav-17
ity moments. Zhang et al. (2015) suggested that such ef-18
fects, namely the self gravity due to the dynamical varia-19
tion itself g(r, θ), can be important, and Cao and Steven-20
son (2015) suggested that the effect of the oblateness on the21
background mean state can be important for the gravity mo-22
ments. However, solving self-consistently for the full oblate23
system, Galanti et al. (2017) have shown that these oblate-24
ness effects give a very small contribution to the gravity25
moments, meaning that the spherical thermal wind captures26
well the leading order balance, and therefore can be used27
for calculating the gravity moments.28
Figure 11.19 shows the gravity field resulting from a29
model using the thermal-wind approach, where the grav-30
ity harmonics are shown as a function of the depth that the31
cloud-level winds extend beneath the cloud-level. It shows32
that beyond n = 10 the gravity signal induced by the wind33
structure becomes larger than the solid-body (static) gravity34
harmonics.35
Because Jupiter and Saturn are gaseous, aside from the36
cloud-level winds there is no apparent asymmetry between37
the northern and southern hemispheres. Therefore, the38
gravitational moments resulting from the shape and verti-39
cal structure of the planets have identically zero odd mo-40
ments (Hubbard 1984, 1999). Unlike the even gravity mo-41
ments that have a contribution both from the static den-42
sity distribution and the dynamics, the odd moments are43
caused purely by dynamics. Thus, any odd signal de-44
tected (J3, J5, J7, ...) will be a sign of a dynamical con-45
tribution to the gravity. Indeed, the cloud-level winds are46
not precisely symmetrical around the equator, and if these47
hemispheric differences extend into the interior, they could48
produce measurable odd harmonics (Figure 11.19)(Kaspi49
2013). Using also the thermal-wind approach, Liu et al.50
(2013) calculated the penetration depth of the winds on51
Jupiter with the additional assumption that the entropy gra-52
dient in the direction of the spin axis must be zero. This53
requirement sets the penetration depth of the winds, and54
they have also found that such a wind structure (which ex- 1
tends deep throughout the molecular envelope) should be 2
detectable by Juno and Cassini (Liu et al. 2013, 2014). 3
The main challenge of interpreting the gravity data will 4
be to invert the gravity measurements into meaningful wind 5
fields. Until recently all studies have been only in the direc- 6
tion of forward modeling; thus, given a hypothetical wind 7
structure (based on the observed surface winds and some 8
assumption regarding the penetration depth) the gravity mo- 9
ments are calculated via the effect of the winds on the den- 10
sity structure (e.g., Hubbard 1999; Kaspi et al. 2010; Liu 11
et al. 2013; Kong et al. 2012). However, in order to analyze 12
the gravity field that will be detected by Juno and Cassini 13
the inverse problem needs to be solved—calculating the 14
zonal wind profile given the gravity field. This causes a dif- 15
ficulty since a gravity field is not necessarily invertible and 16
a given gravity field might not have a unique corresponding 17
wind structure. Galanti and Kaspi (2016, 2017) propose to 18
address this using an adjoint based inverse method that will 19
allow the investigation of the giant planet dynamics using 20
the observed measured gravity field. This method has been 21
used extensively in the study of oceanic and atmospheric 22
fluid dynamics (e.g., Tziperman and Thacker 1989; Moore 23
et al. 2011). This method can be applied to any forward 24
relation between the gravity and the wind structure (e.g., 25
thermal-wind, potential-theory, etc.), and to 3D wind struc- 26
0 5 10 15 20
−10
−8
−6
−4
−2
Zonal harmonic degree n
log(|∆
Jn|)
Solid BodyH=10000H = 3000H = 1000H = 300
Fig. 11.19.— The gravity harmonics of Saturn correspond-ing to the static, rotationally flattened contribution (squares)and the contribution from dynamics (circles) calculated us-ing the thermal-wind model of Kaspi (2013). The dy-namical contributions to the gravity harmonics (∆Jn) areshown for four different assumptions about the character-istic length scale, H , over which the jets decay with depthinto the interior: H = 300 km (purple), H = 1000 km (or-ange), H = 3000 km (blue) and H = 10000 km (maroon).Filled (open) symbols indicate positive (negative) zonal har-monics. Black plus signs show the observed values of Jn,and the dashed line is the expected detectability limit of theCassini proximal orbits. The static values (Hubbard 1999)have only even components (odd harmonics are identicallyzero). From Kaspi (2013).
28
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
ture which give the full 3D gravity fields including contri-1
butions from longitudinal variations in the wind structure2
and meridional winds (Parisi et al. 2016).3
The coincidental timing of the Cassini proximal orbits4
with the Juno gravity experiment will provide an oppor-5
tunity to simultaneously probe the deep dynamics of both6
Saturn and Jupiter. Comparing the atmospheric dynamics7
on the two planets shows that the equatorial jet is much8
stronger and wider on Saturn, extending to latitude 30,9
with fewer high-latitude jets—but the jets are much stronger10
on Saturn reaching about 400 m s−1 depending on the ref-11
erence frame chosen (see section 11.2). The fact that the12
jets are stronger on Saturn means that the induced gravity13
anomalies will be generally larger as well. However, as Sat-14
urn is more oblate than Jupiter (Jupiter has an oblateness of15
6.5%), the static gravity harmonics due to the non-dynamic16
density distribution will likewise be larger than on Jupiter.17
These two factors imply that the ratio between the static and18
the dynamic gravity harmonics are roughly similar on both19
planets (Kaspi 2013).20
Despite the fact that no spacecraft will be visiting Uranus21
and Neptune in the near future, the strong and broad wind22
structure and smaller mass on these planets allows the use23
of these same techniques to infer the depth of the winds us-24
ing gravity moments that have already been measured. In25
particular, the speed and meridional breadth of the jets on26
Uranus and Neptune allow the possibility that—unlike the27
case of Jupiter and Saturn—even the low harmonics such28
as J4 can be significantly affected by dynamics. Using29
the gravity data then available, Hubbard et al. (1991) first30
showed that the fast winds must be confined to the out-31
ermost few % of these planets’ masses. Exploiting recent32
updates on the gravity harmonic J4 and its uncertainty (Ja-33
cobson 2007, 2009), Kaspi et al. (2013) were able to re-34
fine this constraint considerably, showing that the observed35
flows must be constrained to the outermost 1000 km of36
the planetary radius—corresponding to no more than 0.15%37
and 0.2% of the mass of Uranus and Neptune, respectively.38
Thus, the fast jets on Uranus and Neptune are relatively39
shallow.40
In summary, within the next few years, using the fact41
that if deep flows exist on giant planets they will induce a42
measurable gravity signal, we will finally address one of the43
longest-standing debates in planetary science regarding the44
depth of the observed zonal flows on all four giant planets45
(Vasavada and Showman 2005). Understanding if the flows46
are deep or shallow will allow tests between the theories of47
jet formation and energetics as discussed in Section 11.4.1–48
11.4.2. The upcoming few years therefore provide an excit-49
ing opportunity in the study of the atmospheric dynamics of50
Saturn and the other giant planets.51
11.5. CONCLUSIONS52
Saturn’s atmosphere exhibits a wealth of interacting dy-53
namical processes that present an interesting contrast with54
Jupiter. The dynamics are dominated by fast zonal jets55
whose meridional width, latitudinal positions, and speeds 1
have remained relatively constant over many decades. Sat- 2
urn’s clouds are organized into zonal bands that are modu- 3
lated by (and perhaps affect) the zonal jets, but the relation- 4
ship of the cloud bands to the jets themselves differs from 5
that on Jupiter and remains poorly understood. Observa- 6
tions indicate that eddies transport momentum up-gradient 7
into the cores of the zonal jets at cloud level, thereby main- 8
taining the jets. This points toward the importance of cloud 9
level processes in jet dynamics, but the exact processes 10
that power these jet-pumping eddies—baroclinic instability, 11
moist convection, or interaction of dry convection with the 12
stratified atmosphere—remain poorly understood. Light- 13
ning and storm activity—including small storms as well as 14
the Great White Spot of 2010-2011—provide constraints on 15
the thermal structure and vertical motion below the clouds. 16
There also exist a variety of vortices, waves, and other local 17
features at cloud level, with lifetimes of months to decades, 18
whose relationship to the jet dynamics remains enigmatic. 19
Notable features include the string of pearls (Sayanagi et al. 20
2014), the Ribbon, the polar hexagon (Baines et al. 2009), 21
and a significant population of small vortices that tend to 22
cluster predominantly at the latitudes of the westward jets 23
(e.g., Vasavada et al. 2006; Choi et al. 2009). Interestingly, 24
at and above the cloud level, the jets exhibit reversals in the 25
meridional gradient of potential vorticity, and the relative 26
stability of the jets despite these reversals has important im- 27
plications for the flow below the clouds. 28
A variety of observations place constraints on the cir- 29
culation in the upper troposphere and stratosphere, which 30
has important analogies to the stratospheric circulation on 31
the other giant planets as well as Earth. Saturn’s obliquity 32
of 27 causes seasonal temperature changes in the strato- 33
sphere, but there also exist a wealth of temperature vari- 34
ations at a variety of length and timescales that are likely 35
dynamical in origin. The temperature patterns above the 36
clouds suggest, through thermal-wind balance, that most 37
of the zonal jets decay with altitude in the upper tropo- 38
sphere. These temperature patterns, along with the am- 39
monia abundance near the clouds, are best explained by 40
a meridional circulation comprising ascent in the anticy- 41
clonic regions, producing the cold temperatures and high 42
ammonia abundances, and descent in the cyclonic regions, 43
producing the warm temperatures and low ammonia abun- 44
dances. Interestingly, such a circulation is thermally indi- 45
rect and is likely driven by absorption of waves propagating 46
from below. This is directly analogous to the wave-driven 47
circulations that exist in Earth’s stratosphere and that have 48
been inferred in the stratospheres of Jupiter, Uranus, and 49
Neptune. The source of the waves and the specific details 50
of this circulation in the Saturn context remain poorly un- 51
derstood. Additionally, stratospheric thermal perturbations 52
have been observed at low latitudes that suggest an oscil- 53
lation of equatorial winds and temperatures with a period 54
close to 15 years, which seems to be analogous to the terres- 55
trial Quasi-Biennial Oscillation, which is driven by a pop- 56
ulation of upward propagating waves generated by convec- 57
29
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
tion and other processes in the troposphere.1
Dynamical models do not yet come close to explain-2
ing this wealth of phenomena; nevertheless, significant3
progress in understanding the dynamics of zonal jets and4
local features has been made over the past ∼15 years. Over5
the past decade, highly idealized models have greatly im-6
proved our understanding of the processes that cause the7
flow to self-organize into zonal jets. More realistic three-8
dimensional models of the weather-layer flow are now ca-9
pable of explaining the equatorial superrotation and mul-10
tiple high-latitude jets on Jupiter and Saturn, although the11
superrotation in these models tends to be narrower and12
slower than that on Saturn. Models of convection through-13
out the planetary interior now include the multi-order-of-14
magnitude variation of density with radius and are like-15
wise starting to incorporate the coupling to magnetic fields,16
including the transition from electrically insulating in the17
molecular envelope to electrically conducting in the deeper18
interior. These models are now elucidating how the com-19
pressibility and coupling to magnetic fields influences the20
zonal jets and other aspects of the dynamics. These models21
show that convection in the interior can naturally produce a22
Saturn-like equatorial jet, but the coupling to magnetic ef-23
fects tends to suppress any higher latitude jets. An attractive24
hybrid scenario, which combines the strengths of the shal-25
low and deep models, might suggest that convection in the26
molecular envelope outside some tangent cylinder causes27
the broad equatorial jet, but that the mid-to-high-latitude28
jets result from atmospheric processes such as baroclinic in-29
stabilities or moist convection in the cloud layer (Vasavada30
and Showman 2005).31
Future progress in modeling and theory will occur on32
several fronts. Investigations of atmospheric, weather-layer33
processes and of deep, convective dynamics are usually34
conducted separately, using distinct classes of dynamical35
model that solve distinct equation sets and use distinct36
numerical codes. The distinction between “shallow” and37
“deep” processes is artificial, however, and in reality atmo-38
spheric and interior processes may interact in a variety of39
ways not included in current models. A new generation of40
GCMs that spans both atmosphere and interior processes is41
needed to explore this coupling, and this will be a major42
area of progress over the next decade. Global atmospheric43
models of jet formation do not yet include clouds, and yet44
clouds represent a significant fraction of the observational45
database for both Jupiter and Saturn, as well as influencing46
the dynamics through their mass loading, interaction with47
radiation, and latent heating and cooling due to their forma-48
tion and sublimation. Thus, significant progress is possible49
by including clouds in models, both in widening the range50
of observations against which the models can be tested, and51
by illuminating the extent to which clouds influence the at-52
mospheric circulation. Inclusion of realistic radiative trans-53
fer and chemistry into stratospheric GCMs will be a growth54
area, and will help shed light on the implications of tracers55
such as ethane and acetylene for the dynamics. The nature56
of the eddies or waves that apparently cause a deceleration57
of the upper tropospheric and lower stratospheric zonal jets, 1
and that cause the SSAO, are poorly understood. These and 2
many related topics concerning the zonal jets are amenable 3
to continued idealized theory and modeling. 4
Future progress will also depend crucially on improved 5
observations. Due to the Cassini mission, Saturn is perhaps 6
now the best-observed giant planet—outpacing Jupiter— 7
but many of the Cassini observations have yet to be ana- 8
lyzed, and significant progress is possible with the existing 9
data. For all four giant planets, improvements over the past 10
decade in groundbased astronomical facilities have led to a 11
renaissance in observations of cloud features and upper tro- 12
pospheric temperature structure from the ground—by pro- 13
fessional and amateur astronomers alike. These ground- 14
based observations will continue to play a crucial role in 15
filling in the temporal gaps between higher-quality, but 16
episodic, coverage from spacecraft missions. Moreover, 17
over the next several years, the Juno mission to Jupiter and 18
the Cassini Grand Finale at Saturn will provide gravity mea- 19
surements that promise to constrain the depth to which the 20
zonal jets extend below the visible cloud decks. Close-in 21
microwave and IR sounding of Jupiter by Juno, as well 22
as close-in sensing of Saturn with Cassini’s suite of in- 23
struments during the proximal orbits, may produce qual- 24
itatively new constraints on the cloud-level dynamics of 25
both planets. The Juno microwave radiometer will mea- 26
sure the global water abundance and the latitudinal variation 27
of water and ammonia below cloud base. Future missions 28
to the giant planets include the NASA Europa Multiple 29
Flyby Mission and the European Jupiter Icy Moon Explorer 30
(JUICE) mission, which will obtain observations of Jupiter 31
in addition to their prime targets of icy satellites starting 32
around 2030. Prospects for giant-planet missions beyond 33
the 2030s are currently nebulous, but there is strong sci- 34
entific merit—and interest—in missions to Uranus and/or 35
Neptune, as well as an entry probe mission to Saturn. This 36
activity will not only revolutionize our understanding of the 37
grandest planets in our solar system, but will also provide 38
a foundation for understanding the many brown dwarfs and 39
extrasolar giant planets that are being discovered and char- 40
acterized light years away. 41
Acknowledgments. We thank M. Flasar and an anony- 42
mous reviewer for helpful comments. APS acknowledges 43
support from the NASA Planetary Atmosphere program. 44
YK acknowledges support from the Israeli Ministry of Sci- 45
ence and the Minerva Foundation. 46
47
REFERENCES 48
Achterberg, R. K., and F. M. Flasar, 1996: Planetary-scale thermal 49
waves in Saturn’s upper troposphere. Icarus, 119, 350–369. 50
Achterberg, R. K., P. J. Gierasch, B. J. Conrath, L. N. Fletcher, 51
B. E. Hesman, G. L. Bjoraker, and F. M. Flasar, 2014: Changes 52
to Saturn’s Zonal-mean Tropospheric Thermal Structure after 53
the 2010-2011 Northern Hemisphere Storm. Astrophys. J., 786, 54
92. 55
30
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
Anderson, J. D., and G. Schubert, 2007: Saturn’s Gravitational1
Field, Internal Rotation, and Interior Structure. Science, 317,2
1384–.3
Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle4
Atmosphere Dynamics. Academic Press, New York.5
Antunano, A., T. Rıo-Gaztelurrutia, A. Sanchez-Lavega, and6
R. Hueso, 2015: Dynamics of Saturn’s polar regions. Jour-7
nal of Geophysical Research (Planets), 120, 155–176.8
Atreya, S. K., 2006: Saturn probes: Why, where, how? Pro-9
ceedings: International Planetary Probe Workshop, IPPW-4,10
Pasadena, California.11
Aurnou, J., M. Heimpel, L. Allen, E. King, and J. Wicht, 2008:12
Convective heat transfer and the pattern of thermal emission on13
the gas giants. Geophysical Journal International, 173, 793–14
801.15
Aurnou, J. M., and P. L. Olson, 2001: Strong zonal winds from16
thermal convection in a rotating spherical shell. Geophys. Res.17
Lett., 28, 2557–2560.18
Baines, K. H., T. W. Momary, L. N. Fletcher, A. P. Show-19
man, M. Roos-Serote, R. H. Brown, B. J. Buratti, R. N.20
Clark, and P. D. Nicholson, 2009: Saturn’s north polar21
cyclone and hexagon at depth revealed by Cassini/VIMS.22
Planet. Space Sci., 57, 1671–1681.23
Baldwin, M. P., et al., 2001: The quasi-biennial oscillation. Re-24
views of Geophysics, 39, 179–230.25
Barcilon, A., and P. Gierasch, 1970: A Moist, Hadley Cell Model26
for Jupiter’s Cloud Bands. Journal of Atmospheric Sciences,27
27, 550–560.28
Barnet, C. D., J. A. Westphal, R. F. Beebe, and L. F. Huber, 1992:29
Hubble Space Telescope observations of the 1990 equatorial30
disturbance on Saturn - Zonal winds and central meridian albe-31
dos. Icarus, 100, 499–511.32
Beebe, R. F., A. P. Ingersoll, G. E. Hunt, J. L. Mitchell, and J.-P.33
Muller, 1980: Measurements of wind vectors, eddy momen-34
tum transports, and energy conversions in Jupiter’s atmosphere35
from Voyager 1 images. Geophys. Res. Lett., 7, 1–4.36
Bezard, B., and D. Gautier, 1985: A seasonal climate model of37
the atmospheres of the giant planets at the Voyager encounter38
time. I - Saturn’s stratosphere. Icarus, 61, 296–310.39
Busse, F. H., 1976: A simple model of convection in the Jovian40
atmosphere. Icarus, 29, 255–260.41
Busse, F. H., 1994: Convection driven zonal flows and vortices in42
the major planets. Chaos, 4, 123–134.43
Busse, F. H., 2002: Convective flows in rapidly rotating spheres44
and their dynamo action. Physics of Fluids, 14, 1301–1314.45
Cai, T., and K. L. Chan, 2012: Three-dimensional numerical sim-46
ulation of convection in giant planets: Effects of solid core size.47
Planet. Space. Sci, 71, 125–130.48
Cao, H., and D. J. Stevenson, 2015: Gravity and zonal flows of gi-49
ant planets: From the euler equation to the thermal wind equa-50
tion. ArXiv e-prints.51
Cavalie, T., M. Dobrijevic, L. N. Fletcher, J.-C. Loison, K. M.52
Hickson, V. Hue, and P. Hartogh, 2015: Photochemical re-53
sponse to the variation of temperature in the 2011-2012 strato-54
spheric vortex of Saturn. Astron. Astrophys., 580, A55.55
Cess, R. D., and J. Caldwell, 1979: A Saturnian stratospheric 1
seasonal climate model. Icarus, 38, 349–357. 2
Chan, K. L., and H. G. Mayr, 2013: Numerical simulation of con- 3
vectively generated vortices: Application to the Jovian planets. 4
Earth Planet. Sci. Lett., 371, 212–219. 5
Cho, J. Y.-K., and L. M. Polvani, 1996: The emergence of jets 6
and vortices in freely evolving, shallow-water turbulence on a 7
sphere. Physics of Fluids, 8, 1531–1552. 8
Choi, D. S., A. P. Showman, and R. H. Brown, 2009: Cloud fea- 9
tures and zonal wind measurements of Saturn’s atmosphere as 10
observed by Cassini/VIMS. Journal of Geophysical Research 11
(Planets), 114, E04,007. 12
Christensen, U. R., 2001: Zonal flow driven by deep convection 13
in the major planets. Geophys. Res. Lett., 28, 2553–2556. 14
Christensen, U. R., 2002: Zonal flow driven by strongly super- 15
critical convection in rotating spherical shells. Journal of Fluid 16
Mechanics, 470, 115–133. 17
Conrath, B. J., and J. A. Pirraglia, 1983: Thermal structure of 18
Saturn from Voyager infrared measurements - Implications for 19
atmospheric dynamics. Icarus, 53, 286–292. 20
Conrath, B. J., P. J. Gierasch, and S. S. Leroy, 1990: Temperature 21
and circulation in the stratosphere of the outer planets. Icarus, 22
83, 255–281. 23
Del Genio, A. D., and J. M. Barbara, 2012: Constraints on Sat- 24
urn’s tropospheric general circulation from Cassini ISS images. 25
Icarus, 219, 689–700. 26
Del Genio, A. D., R. K. Achterberg, K. H. Baines, F. M. Flasar, 27
P. L. Read, A. Sanchez-Lavega, and A. P. Showman, 2009: 28
Saturn Atmospheric Structure and Dynamics. Saturn from 29
Cassini-Huygens (Dougherty, M. K., Esposito, L. W. and Krim- 30
igis, S. M., Eds.), Springer, pp. 113–159. 31
Desch, M. D., and M. L. Kaiser, 1981: Voyager measure- 32
ment of the rotation period of Saturn’s magnetic field. Geo- 33
phys. Res. Lett., 8, 253–256. 34
Dowling, T. E., 1995a: Dynamics of jovian atmospheres. Annual 35
Review of Fluid Mechanics, 27, 293–334. 36
Dowling, T. E., 1995b: Estimate of Jupiter’s deep zonal-wind pro- 37
file from Shoemaker-Levy 9 data and Arnol’d’s second stability 38
criterion. Icarus, 117, 439–442. 39
Dowling, T. E., 2014: Saturn’s Longitude: Rise of the Second 40
Branch of Shear-Stability Theory and Fall of the First. Interna- 41
tional Journal of Modern Physics D, 23, 30,006. 42
Dritschel, D. G., and M. E. McIntyre, 2008: Multiple Jets as 43
PV Staircases: The Phillips Effect and the Resilience of Eddy- 44
Transport Barriers. Journal of Atmospheric Sciences, 65, 855. 45
Duarte, L. D. V., T. Gastine, and J. Wicht, 2013: Anelastic dynamo 46
models with variable electrical conductivity: An application to 47
gas giants. Phys. Earth Planet. Int., 222, 22–34. 48
Dunkerton, T., 1978: On the mean meridional mass motions of the 49
stratosphere and mesosphere. J. Atmos. Sci., 35, 2325–2333. 50
Dyudina, U. A., A. P. Ingersoll, S. P. Ewald, C. C. Porco, G. Fis- 51
cher, and Y. Yair, 2013: Saturn’s visible lightning, its radio 52
emissions, and the structure of the 2009-2011 lightning storms. 53
Icarus, 226, 1020–1037. 54
Dyudina, U. A., et al., 2007: Lightning storms on Saturn observed 55
by Cassini ISS and RPWS during 2004 2006. Icarus, 190, 545– 56
555. 57
31
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
Dyudina, U. A., et al., 2008: Dynamics of Saturn’s South Polar1
Vortex. Science, 319, 1801.2
Evonuk, M., and G. A. Glatzmaier, 2004: 2D Studies of Vari-3
ous Approximations Used for Modeling Convection in Giant4
Planets. Geophysical and Astrophysical Fluid Dynamics, 98,5
241–255.6
Evonuk, M., and G. A. Glatzmaier, 2006: A 2D study of the7
effects of the size of a solid core on the equatorial flow in giant8
planets. Icarus, 181, 458–464.9
Evonuk, M., and G. A. Glatzmaier, 2007: The effects of rotation10
rate on deep convection in giant planets with small solid cores.11
Planet. Space Sci., 55, 407–412.12
Fischer, G., et al., 2011: A giant thunderstorm on Saturn. Nature,13
475, 75–77.14
Flasar, F. M., et al., 2004: An intense stratospheric jet on Jupiter.15
Nature, 427, 132–135.16
Flasar, F. M., et al., 2005: Temperatures, Winds, and Composition17
in the Saturnian System. Science, 307, 1247–1251.18
Fletcher, L. N., G. S. Orton, N. A. Teanby, P. G. J. Irwin, and G. L.19
Bjoraker, 2009: Methane and its isotopologues on Saturn from20
Cassini/CIRS observations. Icarus, 199, 351–367.21
Fletcher, L. N., K. H. Baines, T. W. Momary, A. P. Showman,22
P. G. J. Irwin, G. S. Orton, M. Roos-Serote, and C. Merlet,23
2011: Saturn’s tropospheric composition and clouds from24
Cassini/VIMS 4.6-5.1 µm nightside spectroscopy. Icarus, 214,25
510–533.26
Fletcher, L. N., et al., 2007: Characterising Saturn’s vertical tem-27
perature structure from Cassini/CIRS. Icarus, 189, 457–478.28
Fletcher, L. N., et al., 2008: Temperature and composition of29
Saturn’s polar hot spots and hexagon. Science, 319, 79–81.30
Fletcher, L. N., et al., 2010: Seasonal change on Saturn from31
Cassini/CIRS observations, 2004-2009. Icarus, 208, 337–352.32
Fletcher, L. N., et al., 2011: Thermal structure and dynamics of33
Saturn’s northern springtime disturbance. Science, 332, 1413–34
1417.35
Fletcher, L. N., et al., 2012: The origin and evolution of Saturn’s36
2011-2012 stratospheric vortex. Icarus, 221, 560–586.37
Fletcher, L. N., et al., 2015: Seasonal evolution of Saturn’s polar38
temperatures and composition. Icarus, 250, 131–153.39
Fouchet, T., S. Guerlet, D. F. Strobel, A. A. Simon-Miller,40
B. Bezard, and F. M. Flasar, 2008: An equatorial oscillation41
in Saturn’s middle atmosphere. Nature, 453, 200–202.42
Fouchet, T., J. I. Moses, and B. J. Conrath, 2009: Saturn: composi-43
tion and chemistry. Saturn from Cassini-Huygens (Dougherty,44
M. K., Esposito, L. W. and Krimigis, S. M., Eds.), Springer, pp.45
83–112.46
Friedson, A. J., and J. I. Moses, 2012: General circulation47
and transport in Saturn’s upper troposphere and stratosphere.48
Icarus, 218, 861–875.49
Galanti, E., and Y. Kaspi, 2016: An Adjoint-based Method for the50
Inversion of the Juno and Cassini Gravity Measurements into51
Wind Fields. Astrophys. J., 820, 91.52
Galanti, E., and Y. Kaspi, 2017: Deciphering Jupiter’s deep flow53
dynamics using the upcoming Juno gravity measurements and54
an adjoint based dynamical model. Icarus, in press.55
Galanti, E., Y. Kaspi, and E. Tziperman, 2017: A full, self- 1
consistent, treatment of thermal wind balance on fluid planets. 2
J. Fluid Mech., 810. 3
Garcıa-Melendo, E., S. Perez-Hoyos, A. Sanchez-Lavega, and 4
R. Hueso, 2011: Saturn’s zonal wind profile in 2004-2009 from 5
Cassini ISS images and its long-term variability. Icarus, 215, 6
62–74. 7
Garcia-Melendo, E., R. Hueso, A. Sanchez-Lavega, J. Legar- 8
reta, T. del Rio-Gaztelurrutia, S. Perez-Hoyos, and J. F. Sanz- 9
Requena, 2013: Atmospheric dynamics of saturn’s 2010 giant 10
storm. Nature Geoscience, 6, 525–529. 11
Gastine, T., and J. Wicht, 2012: Effects of compressibility on 12
driving zonal flow in gas giants. Icarus, 219, 428–442. 13
Gastine, T., J. Wicht, and J. M. Aurnou, 2013: Zonal flow regimes 14
in rotating anelastic spherical shells: An application to giant 15
planets. Icarus, 225, 156–172. 16
Gastine, T., J. Wicht, L. D. V. Duarte, M. Heimpel, and A. Becker, 17
2014: Explaining jupiter’s magnetic field and equatorial jet 18
dynamics. Geophys. Res. Lett., 41, 5410–5419. 19
Gezari, D. Y., M. J. Mumma, F. Espenak, D. Deming, G. Bjoraker, 20
L. Woods, and W. Folz, 1989: New features in Saturn’s at- 21
mosphere revealed by high-resolution thermal infrared images. 22
Nature, 342, 777–780. 23
Gierasch, P. J., J. A. Magalhaes, and B. J. Conrath, 1986: Zonal 24
mean properties of Jupiter’s upper troposphere from Voyager 25
infrared observations. Icarus, 67, 456–483. 26
Gierasch, P. J., et al., 2000: Observation of moist convection in 27
Jupiter’s atmosphere. Nature, 403, 628–630. 28
Giles, R. S., L. N. Fletcher, and P. G. J. Irwin, 2017: Latitudi- 29
nal variability in Jupiter’s tropospheric disequilibrium species: 30
GeH4, AsH3, and PH3. Icarus, p. in press. 31
Gillett, F. C., and G. S. Orton, 1975: Center-to-limb observations 32
of Saturn in the thermal infrared. Astrophys. J. Lett., 195, L47– 33
L49. 34
Glatzmaier, G. A., 2008: A note on “Constraints on deep-seated 35
zonal winds inside Jupiter and Saturn”. Icarus, 196, 665–666. 36
Glatzmaier, G. A., M. Evonuk, and T. M. Rogers, 2009: Differ- 37
ential rotation in giant planets maintained by density-stratified 38
turbulent convection. Geophys. Astrophy. Fluid Dyn., 103, 31– 39
51. 40
Greathouse, T. K., J. H. Lacy, B. Bezard, J. I. Moses, C. A. Grif- 41
fith, and M. J. Richter, 2005: Meridional variations of tem- 42
perature, c2h2 and c2h6 abundances in Saturn’s stratosphere at 43
southern summer solstice. Icarus, 177, 18–31. 44
Grevesse, N., M. Asplund, and J. Sauval, 2005: The new solar 45
composition.. In Element Stratification in Stars: 40 Years of 46
Atomic Diffusion, (Alecian. G., Richard, O., Vauclair, S. eds.), 47
pp. 21–30, EAS Publications Series. 48
Guerlet, S., T. Fouchet, B. Bezard, A. A. Simon-Miller, and 49
F. Michael Flasar, 2009: Vertical and meridional distribution 50
of ethane, acetylene and propane in Saturn’s stratosphere from 51
CIRS/Cassini limb observations. Icarus, 203, 214–232. 52
Guerlet, S., T. Fouchet, B. Bezard, F. M. Flasar, and A. A. Simon- 53
Miller, 2011: Evolution of the equatorial oscillation in Saturn’s 54
stratosphere between 2005 and 2010 from Cassini/CIRS limb 55
data analysis. Geophys. Res. Lett., 38, 9201. 56
32
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
Guerlet, S., et al., 2014: Global climate modeling of Saturn’s1
atmosphere. Part I: Evaluation of the radiative transfer model.2
Icarus, 238, 110–124.3
Hanel, R., et al., 1981: Infrared observations of the Saturnian4
system from Voyager 1. Science, 212, 192–200.5
Hanel, R., et al., 1982: Infrared observations of the Saturnian6
system from Voyager 2. Science, 215, 544–548.7
Haynes, P. H., M. E. McIntyre, T. G. Shepherd, C. J. Marks, and8
K. P. Shine, 1991: On the ‘Downward Control’ of Extratropi-9
cal Diabatic Circulations by Eddy-Induced Mean Zonal Forces.10
Journal of Atmospheric Sciences, 48, 651–680.11
Heimpel, M., and J. Aurnou, 2007: Turbulent convection in12
rapidly rotating spherical shells: A model for equatorial and13
high latitude jets on Jupiter and Saturn. Icarus, 187, 540–557.14
Heimpel, M., and N. Gomez Perez, 2011: On the relationship15
between zonal jets and dynamo action in giant planets. Geo-16
phys. Res. Lett., 38, L14,201.17
Heimpel, M., J. Aurnou, and J. Wicht, 2005: Simulation of equa-18
torial and high-latitude jets on Jupiter in a deep convection19
model. Nature, 438, 193–196.20
Helled, R., E. Galanti, and Y. Kaspi, 2015: Saturn’s fast spin21
determined from its gravitational field and oblateness. Nature,22
520, 202–204.23
Hesman, B. E., et al., 2009: Saturn’s latitudinal C2H2 and C2H624
abundance profiles from Cassini/CIRS and ground-based ob-25
servations. Icarus, 202, 249–259.26
Hesman, B. E., et al., 2012: Elusive Ethylene Detected in Saturn’s27
Northern Storm Region. Astrophys. J., 760, 24.28
Holton, J. R., and G. J. Hakim, 2013: An Introduction to Dynamic29
Meteorology, 5th Ed.. Academic Press, San Diego.30
Howett, C. J. A., P. G. J. Irwin, N. A. Teanby, A. Simon-Miller,31
S. B. Calcutt, L. N. Fletcher, and R. de Kok, 2007: Meridional32
variations in stratospheric acetylene and ethane in the south-33
ern hemisphere of the saturnian atmosphere as determined from34
Cassini/CIRS measurements. Icarus, 190, 556–572.35
Huang, H.-P., and W. A. Robinson, 1998: Two-Dimensional Tur-36
bulence and Persistent Zonal Jets in a Global Barotropic Model.37
Journal of Atmospheric Sciences, 55, 611–632.38
Hubbard, W. B., 1984: Planetary interiors. New York, Van Nos-39
trand Reinhold Co., 1984, 343 p.40
Hubbard, W. B., 1999: Gravitational Signature of Jupiter’s Deep41
Zonal Flows. Icarus, 137, 357–359.42
Hubbard, W. B., 2012: High-precision Maclaurin-based models43
of rotating liquid planets. Astrophys. J. Lett., 756, L15.44
Hubbard, W. B., 2013: Conventric maclaurian spheroid models of45
rotating liquid planets. Astrophys. J., 768(1).46
Hubbard, W. B., W. J. Nellis, A. C. Mitchell, N. C. Holmes, P. C.47
McCandless, and S. S. Limaye, 1991: Interior structure of Nep-48
tune - Comparison with Uranus. Science, 253, 648–651.49
Hubbard, W. B., G. Schubert, D. Kong, and K. Zhang, 2014: On50
the convergence of the theory of figures. Icarus, 242, 138–141.51
Hueso, R., and A. Sanchez-Lavega, 2004: A three-dimensional52
model of moist convection for the giant planets II: Saturn’s wa-53
ter and ammonia moist convective storms. Icarus, 172, 255–54
271.55
Iacono, R., M. V. Struglia, and C. Ronchi, 1999: Spontaneous 1
formation of equatorial jets in freely decaying shallow water 2
turbulence. Physics of Fluids, 11, 1272–1274. 3
Ingersoll, A. P., 1976: The atmosphere of Jupiter. Space Sci. Rev., 4
18, 603–639. 5
Ingersoll, A. P., 1990: Atmospheric dynamics of the outer planets. 6
Science, 248, 308–315. 7
Ingersoll, A. P., and J. N. Cuzzi, 1969: Dynamics of Jupiter’s 8
cloud bands. Journal of Atmospheric Sciences, 26, 981–985. 9
Ingersoll, A. P., and D. Pollard, 1982: Motion in the interiors and 10
atmospheres of Jupiter and Saturn - Scale analysis, anelastic 11
equations, barotropic stability criterion. Icarus, 52, 62–80. 12
Ingersoll, A. P., G. S. Orton, G. Munch, G. Neugebauer, and S. C. 13
Chase, 1980: Pioneer Saturn infrared radiometer - Preliminary 14
results. Science, 207, 439–443. 15
Ingersoll, A. P., R. F. Beebe, J. L. Mitchell, G. W. Garneau, G. M. 16
Yagi, and J.-P. Muller, 1981: Interaction of eddies and mean 17
zonal flow on Jupiter as inferred from Voyager 1 and 2 images. 18
J. Geophys. Res., 86, 8733–8743. 19
Ingersoll, A. P., R. F. Beebe, B. J. Conrath, and G. E. Hunt, 20
1984: Structure and dynamics of Saturn’s atmosphere. In Sat- 21
urn (T. Gehrels and M.S. Matthews, Eds.), pp. 195–238, Univ. 22
Arizona Press. 23
Ingersoll, A. P., P. J. Gierasch, D. Banfield, A. R. Vasavada, and 24
A3 Galileo Imaging Team, 2000: Moist convection as an en- 25
ergy source for the large-scale motions in Jupiter’s atmosphere. 26
Nature, 403, 630–632. 27
Ingersoll, A. P., T. E. Dowling, P. J. Gierasch, G. S. Orton, 28
P. L. Read, A. Sanchez-Lavega, A. P. Showman, A. A. Simon- 29
Miller, and A. R. Vasavada, 2004: Dynamics of Jupiter’s atmo- 30
sphere, pp. 105–128, Jupiter. The Planet, Satellites and Magne- 31
tosphere. 32
Jacobson, R. A., 2007: The gravity field of the Uranian system and 33
the orbits of the Uranian satellites and rings. AAS/Division for 34
Planetary Sciences Meeting Abstracts #39, vol. 38, pp. 453– 35
453. 36
Jacobson, R. A., 2009: The orbits of the Neptunian satellites 37
and the orientation of the pole of Neptune. Astrophys. J., 137, 38
4322–4329. 39
Jacobson, R. A., et al., 2006: The gravity field of the Saturnian 40
system from satellite observations and spacecraft tracking data. 41
Astrophys. J., 132, 2520–2526. 42
Janssen, M. A., et al., 2013: Saturn’s thermal emission at 2.2- 43
cm wavelength as imaged by the Cassini RADAR radiometer. 44
Icarus, 226, 522–535. 45
Jones, C. A., 2014: A dynamo model of Jupiter’s magnetic field. 46
Icarus, 241, 148–159. 47
Jones, C. A., and K. M. Kuzanyan, 2009: Compressible con- 48
vection in the deep atmospheres of giant planets. Icarus, 204, 49
227–238. 50
Jones, C. A., P. Boronski, A. S. Brun, G. A. Glatzmaier, T. Gastine, 51
M. S. Miesch, and J. Wicht, 2011: Anelastic convection-driven 52
dynamo benchmarks. Icarus, 216, 120–135. 53
Kaspi, Y., 2008: Turbulent convection in an anelastic rotating 54
sphere: A model for the circulation on the giant planets, Ph.D. 55
thesis, Massachusetts Institute of Technology. 56
33
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
Kaspi, Y., 2013: Inferring the depth of the zonal jets on Jupiter1
and Saturn from odd gravity harmonics. Geophys. Res. Lett.,2
40, 676–680.3
Kaspi, Y., G. R. Flierl, and A. P. Showman, 2009: The deep wind4
structure of the giant planets: results from an anelastic general5
circulation model. Icarus, 202, 525–542.6
Kaspi, Y., W. B. Hubbard, A. P. Showman, and G. R. Flierl, 2010:7
Gravitational signature of Jupiter’s internal dynamics. Geo-8
phys. Res. Lett., 37, L01,204.9
Kaspi, Y., A. P. Showman, W. B. Hubbard, O. Aharonson, and10
R. Helled, 2013: Atmospheric confinement of jet streams on11
Uranus and Neptune. Nature, 497, 344–347.12
Kaspi, Y., J. E. Davighi, E. Galanti, and W. B. Hubbard, 2016: The13
gravitational signature of internal flows in giant planets: Com-14
paring the thermal wind approach with barotropic potential-15
surface methods. Icarus, 276, 170–181.16
Kirk, R. L., and D. J. Stevenson, 1987: Hydromagnetic constraints17
on deep zonal flow in the giant planets. Astrophys. J., 316, 836–18
846.19
Kliore, A. J., I. R. Patel, G. F. Lindal, D. N. Sweetnam, H. B.20
Hotz, J. H. Waite, and T. McDonough, 1980: Structure of the21
ionosphere and atmosphere of Saturn from Pioneer 11 Saturn22
radio occultation. J. Geophys. Res., 85, 5857–5870.23
Kong, D., K. Zhang, and G. Schubert, 2012: On the variation of24
zonal gravity coefficients of a giant planet caused by its deep25
zonal flows. Astrophys. J., 748.26
Laraia, A. L., A. P. Ingersoll, M. A. Janssen, S. Gulkis, F. Oyafuso,27
and M. Allison, 2013: Analysis of Saturn’s thermal emission28
at 2.2-cm wavelength: Spatial distribution of ammonia vapor.29
Icarus, 226, 641–654.30
Leovy, C. B., A. J. Friedson, and G. S. Orton, 1991: The quasiqua-31
drennial oscillation of Jupiter’s equatorial stratosphere. Nature,32
354, 380–382.33
Li, L., A. P. Ingersoll, A. R. Vasavada, C. C. Porco, A. D. del34
Genio, and S. P. Ewald, 2004: Life cycles of spots on Jupiter35
from Cassini images. Icarus, 172, 9–23.36
Li, L., A. P. Ingersoll, and X. Huang, 2006: Interaction of moist37
convection with zonal jets on Jupiter and Saturn. Icarus, 180,38
113–123.39
Li, L., et al., 2008: Strong jet and a new thermal wave in Saturn’s40
equatorial stratosphere. Geophys. Res. Lett., 35, 23,208.41
Li, L., et al., 2011: Equatorial winds on Saturn and the strato-42
spheric oscillation. Nature Geoscience, 4, 750–752.43
Li, L., et al., 2013: Strong Temporal Variation Over One Saturnian44
Year: From Voyager to Cassini. Scientific Reports, 3, 2410.45
Li, L., et al., 2015: Saturn’s giant storm and global radiant energy.46
Geophys. Res. Lett., 42, 2144–2148.47
Lian, Y., and A. P. Showman, 2008: Deep jets on gas-giant planets.48
Icarus, 194, 597–615.49
Lian, Y., and A. P. Showman, 2010: Generation of equatorial jets50
by large-scale latent heating on the giant planets. Icarus, 207,51
373–393.52
Limaye, S. S., 1986: Jupiter - New estimates of the mean zonal53
flow at the cloud level. Icarus, 65, 335–352.54
Lindal, G., D. Sweetnam, and V. Eshleman, 1985: The atmo- 1
sphere of Saturn - an analysis of the voyager radio occultation 2
measurements. The Astronomical Journal, 90, 1136–1146. 3
Lindzen, R. S., and J. R. Holton, 1968: A Theory of the Quasi- 4
Biennial Oscillation. Journal of Atmospheric Sciences, 25, 5
1095–1107. 6
Little, B., C. D. Anger, A. P. Ingersoll, A. R. Vasavada, D. A. 7
Senske, H. H. Breneman, W. J. Borucki, and The Galileo SSI 8
Team, 1999: Galileo Images of Lightning on Jupiter. Icarus, 9
142, 306–323. 10
Liu, J., and T. Schneider, 2010: Mechanisms of Jet Formation on 11
the Giant Planets. Journal of Atmospheric Sciences, 67, 3652– 12
3672. 13
Liu, J., P. M. Goldreich, and D. J. Stevenson, 2008: Constraints 14
on deep-seated zonal winds inside Jupiter and Saturn. Icarus, 15
196, 653–664. 16
Liu, J., T. Schneider, and Y. Kaspi, 2013: Predictions of thermal 17
and gravitational signals of Jupiter’s deep zonal winds. Icarus, 18
224, 114–125. 19
Liu, J., T. Schneider, and L. N. Fletcher, 2014: Constraining the 20
depth of Saturn’s zonal winds by measuring thermal and gravi- 21
tational signals. Icarus, 239, 260–272. 22
MacGorman, D. R., and D. Rust, 1998: The Electrical Nature of 23
Storms. Oxford University Press. 24
Marcus, P. S., 1993: Jupiter’s Great Red SPOT and other vortices. 25
Annu. Rev. Astron. Astrophys., 31, 523–573. 26
Moore, A. M., H. G. Arango, G. Broquet, B. S. Powell, A. T. 27
Weaver, and J. Zavala-Garay, 2011: The regional ocean mod- 28
eling system (ROMS) 4-dimensional variational data assimila- 29
tion systems . part I - system overview and formulation. Prog. 30
Oceanogr., 91, 34–49. 31
Moses, J., and T. Greathouse, 2005: Latitudinal and seasonal mod- 32
els of stratospheric photochemistry on saturn: Comparison with 33
infrared data from irtf/texes. Journal of geophysical research, 34
110(E9), E09,007. 35
Moses, J. I., M.-C. Liang, Y. L. Yung, and R.-L. Shia, 2007: Two- 36
Dimensional Photochemical Modeling of Hydrocarbon Abun- 37
dances on Saturn. Lunar and Planetary Science Conference, 38
vol. 38 of Lunar and Planetary Inst. Technical Report, p. 2196. 39
Moses, J. I., E. S. Armstrong, L. N. Fletcher, A. J. Friedson, 40
P. G. J. Irwin, J. A. Sinclair, and B. E. Hesman, 2015: Evo- 41
lution of stratospheric chemistry in the Saturn storm beacon 42
region. Icarus, 261, 149–168. 43
Nellis, W. J., 2000: Metallization of fluid hydrogen at 140 GPa 44
(1.4 Mbar): implications for Jupiter. Planet. Space Sci., 48, 45
671–677. 46
Nicholson, P. D., C. A. McGhee, and R. G. French, 1995: Sat- 47
urn’s central flash from the 3 July 1989 occultation of 28 SGR. 48
Icarus, 113, 57–83. 49
Nozawa, T., and S. Yoden, 1997: Formation of zonal band struc- 50
ture in forced two-dimensional turbulence on a rotating sphere. 51
Physics of Fluids, 9, 2081–2093. 52
Okuno, A., and A. Masuda, 2003: Effect of horizontal divergence 53
on the geostrophic turbulence on a beta-plane: Suppression of 54
the Rhines effect. Physics of Fluids, 15, 56–65. 55
34
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
Ollivier, J. L., F. Billebaud, P. Drossart, M. Dobrijevic, M. Roos-1
Serote, T. August-Bernex, and I. Vauglin, 2000: Seasonal ef-2
fects in the thermal structure of Saturn’s stratosphere from in-3
frared imaging at 10 microns. Astronomy and Astrophysics,4
356, 347–356.5
O’Neill, M. E., K. A. Emanuel, and G. R. Flierl, 2015: Polar6
vortex formation in giant-planet atmospheres due to moist con-7
vection. Nature Geoscience, 8, 523–526.8
O’Neill, M. E., K. A. Emanuel, and G. R. Flierl, 2016: Weak Jets9
and Strong Cyclones: Shallow-Water Modeling of Giant Planet10
Polar Caps. Journal of Atmospheric Sciences, 73, 1841–1855.11
Orton, G. S., and A. P. Ingersoll, 1980: Saturn’s atmospheric12
temperature structure and heat budget. J. Geophys. Res., 85,13
5871–5881.14
Orton, G. S., and P. A. Yanamandra-Fisher, 2005: Saturn’s Tem-15
perature Field from High-Resolution Middle-Infrared Imaging.16
Science, 307, 696–698.17
Orton, G. S., et al., 1991: Thermal maps of Jupiter - Spatial or-18
ganization and time dependence of stratospheric temperatures,19
1980 to 1990. Science, 252, 537–542.20
Orton, G. S., et al., 2008: Semi-annual oscillations in Saturn’s21
low-latitude stratospheric temperatures. Nature, 453, 196–199.22
Parisi, M., E. Galanti, S. Finocchiaro, L. Iess, and Y. Kaspi, 2016:23
Probing the depth of Jupiter’s Great Red Spot with the Juno24
gravity experiment. Icarus, 267, 232–242.25
Pedlosky, J., 1987: Geophysical Fluid Dynamics, 2nd Ed..26
Springer-Verlag, New York.27
Peek, B. M., 1958: The Planet Jupiter. Faber and Faber.28
Phillips, O. M., 1969: Turbulent flow. Science, 163, 1441–1442.29
Porco, C. C., et al., 2003: Cassini Imaging of Jupiter’s Atmo-30
sphere, Satellites, and Rings. Science, 299, 1541–1547.31
Read, P. L., B. J. Conrath, L. N. Fletcher, P. J. Gierasch, A. A.32
Simon-Miller, and L. C. Zuchowski, 2009a: Mapping poten-33
tial vorticity dynamics on saturn: Zonal mean circulation from34
Cassini and Voyager data. Planet. Space Sci., 57, 1682–1698.35
Read, P. L., T. E. Dowling, and G. Schubert, 2009b: Saturn’s rota-36
tion period from its atmospheric planetary-wave configuration.37
Nature, 460, 608–610.38
Rieke, G. H., 1975: The thermal radiation of Saturn and its rings.39
Icarus, 26, 37–44.40
Rogers, J. H., 1995: The Giant Planet Jupiter. Cambridge Uni-41
versity Press, New York, NY, USA.42
Salyk, C., A. P. Ingersoll, J. Lorre, A. Vasavada, and A. D. Del43
Genio, 2006: Interaction between eddies and mean flow in44
Jupiter’s atmosphere: Analysis of Cassini imaging data. Icarus,45
185, 430–442.46
Sanchez-Lavega, A., J. F. Rojas, and P. V. Sada, 2000: Saturn’s47
Zonal Winds at Cloud Level. Icarus, 147, 405–420.48
Sanchez-Lavega, A., et al., 2011: Deep winds beneath Saturn’s49
upper clouds from a seasonal long-lived planetary-scale storm.50
Nature, 475, 71–74.51
Sanchez-Lavega, A., et al., 2012: Ground-based observations of52
the long-term evolution and death of Saturn’s 2010 Great White53
Spot. Icarus, 220, 561–576.54
Sayanagi, K. M., and A. P. Showman, 2007: Effects of a large 1
convective storm on Saturn’s equatorial jet. Icarus, 187, 520– 2
539. 3
Sayanagi, K. M., U. A. Dyudina, S. P. Ewald, G. Fischer, A. P. 4
Ingersoll, W. S. Kurth, G. D. Muro, C. C. Porco, and R. A. 5
West, 2013: Dynamics of Saturn’s great storm of 2010-2011 6
from Cassini ISS and RPWS. Icarus, 223, 460–478. 7
Sayanagi, K. M., U. A. Dyudina, S. P. Ewald, G. D. Muro, and 8
A. P. Ingersoll, 2014: Cassini ISS observation of saturn’s string 9
of pearls. Icarus, 229, 170–180. 10
Schinder, P. J., et al., 2011: Saturn’s equatorial oscillation: Ev- 11
idence of descending thermal structure from Cassini radio oc- 12
cultations. Geophys. Res. Lett., 38, 8205. 13
Schneider, T., 2006: The General Circulation of the Atmosphere. 14
Annual Review of Earth and Planetary Sciences, 34, 655–688. 15
Schneider, T., and J. Liu, 2009: Formation of Jets and Equatorial 16
Superrotation on Jupiter. J. Atmos. Sci., 66, 579–601. 17
Scott, R. K., and D. G. Dritschel, 2012: The structure of zonal jets 18
in geostrophic turbulence. J. Fluid Mech., 711, 576–598. 19
Scott, R. K., and L. Polvani, 2007: Forced-dissipative shallow 20
water turbulence on the sphere and the atmospheric circulation 21
of the giant planets. J. Atmos. Sci, 64, 3158–3176. 22
Scott, R. K., and L. M. Polvani, 2008: Equatorial superrotation in 23
shallow atmospheres. Geophys. Res. Lett., 35, L24,202. 24
Showman, A. P., 2007: Numerical simulations of forced shallow- 25
water turbulence: effects of moist convection on the large-scale 26
circulation of Jupiter and Saturn. J. Atmos. Sci., 64, 3132–3157. 27
Showman, A. P., and I. de Pater, 2005: Dynamical implications of 28
Jupiter’s tropospheric ammonia abundance. Icarus, 174, 192– 29
204. 30
Showman, A. P., P. J. Gierasch, and Y. Lian, 2006: Deep zonal 31
winds can result from shallow driving in a giant-planet atmo- 32
sphere. Icarus, 182, 513–526. 33
Showman, A. P., J. Y.-K. Cho, and K. Menou, 2010: Atmospheric 34
circulation of Exoplanets. In Exoplanets (S. Seager, Ed.), pp. 35
471–516, Univ. Arizona Press. 36
Showman, A. P., Y. Kaspi, and G. R. Flierl, 2011: Scaling laws 37
for convection and jet speeds in the giant planets. Icarus, 211, 38
1258–1273. 39
Sinclair, J. A., P. G. J. Irwin, L. N. Fletcher, J. I. Moses, T. K. 40
Greathouse, A. J. Friedson, B. Hesman, J. Hurley, and C. Mer- 41
let, 2013: Seasonal variations of temperature, acetylene and 42
ethane in Saturn’s atmosphere from 2005 to 2010, as observed 43
by Cassini-CIRS. Icarus, 225, 257–271. 44
Sinton, W. M., W. W. Macy, J. Good, and G. S. Orton, 1980: In- 45
frared scans of Saturn. Icarus, 42, 251–256. 46
Smith, K. S., 2004: A local model for planetary atmospheres 47
forced by small-scale convection. J. Atmos. Sciences, 61, 1420– 48
1433. 49
Sromovsky, L. A., K. H. Baines, P. M. Fry, and T. W. Momary, 50
2016: Cloud clearing in the wake of Saturn’s Great Storm of 51
2010-2011 and suggested new constraints on Saturn’s He/H2 52
ratio. Icarus, 276, 141–162. 53
Starr, V. P., 1968: Physics of Negative Viscosity Phenomena. Mc- 54
Graw Hill. 55
35
Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS
Stone, P. H., 1973: The Dynamics of the Atmospheres of the1
Major Planets (Article published in the Space Science Re-2
views special issue on ’Outer Solar System Exploration - An3
Overview’, ed. by J. E. Long and D. G. Rea.). Space Sci. Rev.,4
14, 444–459.5
Sukoriansky, S., N. Dikovskaya, and B. Galperin, 2007: On the6
”arrest” of inverse energy cascade and the Rhines scale. J. At-7
mos. Sci., 64, 3312–3327.8
Sylvestre, M., S. Guerlet, T. Fouchet, A. Spiga, F. M. Flasar,9
B. Hesman, and G. L. Bjoraker, 2015: Seasonal changes in10
Saturn’s stratosphere inferred from Cassini/CIRS limb obser-11
vations. Icarus, 258, 224–238.12
Thomson, S. I., and M. E. McIntyre, 2016: Jupiter’s Unearthly13
Jets: A New Turbulent Model Exhibiting Statistical Steadiness14
without Large-Scale Dissipation. Journal of Atmospheric Sci-15
ences, 73, 1119–1141.16
Tokunaga, A. T., J. Caldwell, F. C. Gillett, and I. G. Nolt, 1978:17
Spatially resolved infrared observations of Saturn. II - The tem-18
perature enhancement at the South Pole of Saturn. Icarus, 36,19
216–222.20
Tziperman, E., and W. C. Thacker, 1989: An optimal-21
control/adjoint-equations approach to studying the oceanic22
general circulation. J. Phys. Oceanogr., 19, 1471–1485.23
Uman, M. A., 2001: The Lightning Discharge. Dover Books.24
Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics:25
Fundamentals and Large-Scale Circulation. Cambridge Univ.26
Press, Cambridge, UK.27
van Helden, A., 1984: Saturn through the telescope: A brief his-28
torical survey. In Saturn (T. Gehrels and M.S. Matthews, Eds.),29
pp. 23–43, Univ. Arizona Press.30
Vasavada, A. R., and A. P. Showman, 2005: Jovian atmospheric31
dynamics: an update after Galileo and Cassini. Reports of32
Progress in Physics, 68, 1935–1996.33
Vasavada, A. R., S. M. Horst, M. R. Kennedy, A. P. Ingersoll,34
C. C. Porco, A. D. Del Genio, and R. A. West, 2006: Cassini35
imaging of Saturn: southern-hemisphere winds and vortices. J.36
Geophys. Res., 111, E05004(E10), 1–13.37
Warneford, E. S., and P. J. Dellar, 2014: Thermal shallow wa-38
ter models of geostrophic turbulence in Jovian atmospheres.39
Physics of Fluids, 26(1), 016,603.40
Williams, G. P., 1978: Planetary circulations. I - Barotropic rep-41
resentation of Jovian and terrestrial turbulence. Journal of At-42
mospheric Sciences, 35, 1399–1426.43
Williams, G. P., 2003: Jovian Dynamics. Part III: Multiple, Mi-44
grating, and Equatorial Jets. Journal of Atmospheric Sciences,45
60, 1270–1296.46
Yadav, R. K., T. Gastine, and U. R. Christensen, 2013: Scal-47
ing laws in spherical shell dynamos with free-slip boundaries.48
Icarus, 225, 185–193.49
Yair, Y., G. Fischer, F. Simoes, N. Renno, and P. Zarka,50
2008: Updated Review of Planetary Atmospheric Electricity.51
Space Sci. Rev., 137, 29–49.52
Zhang, K., D. Kong, and G. Schubert, 2015: Thermal-53
gravitational wind equation for the wind-induced gravitational54
signature of giant gaseous planets: Mathematical derivation,55
numerical method and illustrative solutions. Astrophys. J., 806,56
270–279.57 This 2-column preprint was prepared with the AAS LATEX macros v5.2.
36