effects of environmental flow upon tropical cyclone structure

2044 VOLUME 127M O N T H L Y W E A T H E R R E V I E W

q 1999 American Meteorological Society

Effects of Environmental Flow upon Tropical Cyclone Structure

WILLIAM M. FRANK AND ELIZABETH A. RITCHIE*

Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

(Manuscript received 9 February 1998, in final form 27 July 1998)

ABSTRACT

Numerical simulations of tropical-cyclone-like vortices are performed to analyze the effects of unidirectionalvertical wind shear and translational flow upon the organization of convection within a hurricane’s core regionand upon the intensity of the storm. A series of dry and moist simulations is performed using the PennsylvaniaState University–National Center for Atmospheric Research Mesoscale Model version 5 (MM5) with idealizedinitial conditions. The dry simulations are designed to determine the patterns of forced ascent that occur as thevortex responds to imposed vertical wind shear and translational flow, and the mechanisms that modulate thevertical velocity field are explored. The moist simulations are initialized with the same initial conditions as thedry runs but with a cumulus parameterization and explicit moisture scheme activated. The moist simulationsare compared to the dry runs in order to test the hypothesis that the forced vertical circulation modes modulatethe convection and hence latent heat release in the hurricane core, as well as to evaluate the net effect of theimposed environmental flow on the storm intensity and structure.

The results indicate that the pattern of convection in the storm’s core is strongly influenced by vertical windshear, and to comparable degree by boundary layer friction. In the early stages of moist simulations, typical ofthe tropical depression stage, the regions of forced ascent and the mechanisms that cause them are similar tothose in the dry runs. However, once the moist storm runs deepen enough to develop saturation in part of theeyewall, the patterns of vertical motion and associated rainfall differ between the paired dry and moist runswith identical initial conditions. The dry runs tend to produce a strong, deep region of ascent in the sector ofthe storm that lies downshear right of the center. The moist runs begin similarly, but as the storms intensifythey strongly favor upward motion and rainfall downshear left of the center.

It appears that the vertical motion patterns in the dry and moist simulations are dominated by similar adiabaticlifting mechanisms prior to the development of partial eyewall saturation. Once the moist runs reach saturation,this adiabatic lifting mechanism no longer occurs due to the latent heat release within the ascending air. Hence,the patterns of forced ascent in the dry runs should be relevant for understanding patterns of convection inloosely organized systems such as tropical depressions, but not in mature hurricanes. The rainfall patternsproduced by the moist simulations are in good agreement with recent observational analyses of the relationshipsbetween rainfall distribution and vertical wind shear in Atlantic hurricanes.

1. Introduction

a. Overview

Tropical cyclones are remarkably intense and stablevortices. They frequently exhibit lifetimes of 2 weeksor more, and they rarely dissipate over tropical waters.Nevertheless, their robust nature does not imply thatthese storms are impervious to external influences. Thestorms frequently undergo major changes in structureduring their lifetimes. These structural variations cause

* Current affiliation: Department of Meteorology, U.S. Naval Post-graduate School, Monterey, California.

Corresponding author address: William M. Frank, Department ofMeteorology, The Pennsylvania State University, University Park, PA16802.E-mail: [email protected]

major variations in the distribution and intensity of windand rain, and through interactions with the ocean surfacethey also have large effects upon waves and storm surge.While some fluctuations in core structure are probablydue to internally generated wave processes, there is in-creasing evidence that many structural variations in cy-clones are caused by interactions between the storm andits environment. Therefore, much of the variability intropical cyclone structure and intensity should be pre-dictable from knowledge of the storm’s environment.

Previous research has revealed that even moderatechanges in the magnitude or vertical shear of the meanwinds can alter the storm in ways that could potentiallyaffect the structure and intensity of the cyclone, as wellas its path (e.g., Jones 1995; DeMaria 1996; Bender1997). The current paper examines the basic questionof how the mean zonal winds and the vertical shear ofthese winds affect storm structure. The major emphasisis upon the manner in which the zonal winds and bound-

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SEPTEMBER 1999 2045F R A N K A N D R I T C H I E

ary layer processes modulate the vertical velocity fieldwithin the storm. It is hypothesized that these processesdynamically force regions of ascent and descent withinthe cyclone, and that they thereby organize and controlthe amount and distribution of latent heat release. Thisprocess should have significant effects upon the struc-ture and intensity of the system.

Although tropical cyclones have been studied inten-sively throughout the twentieth century, we have sur-prisingly little quantitative knowledge as to how thestorms interact with their environments, particularlywith respect to changes in core structure. (Storm motion,while hardly a solved problem, is much better under-stood.) The major problems that inhibit progress in thisarea are the chronically sparse data over the tropicaloceans and the difficulties in separating cause and effectin complex systems with important, interacting pro-cesses occurring on several scales. Numerical simula-tion provides a viable alternative to observations for thepurpose of analyzing tropical cyclone–environmentalinteractions. While models are subject to a great manylimitations of their own, they nonetheless allow the re-searcher to isolate and control both features of the large-scale environment of the storm and some of its internalprocesses.

This paper presents results of a series of numericalsimulations designed to study effects of imposed ex-ternal circulation features upon the structure of tropical-cyclone-like vortices. The current paper examines thefirst-order effects of mean zonal flow, including verticalshear, and of surface friction upon the structure of aninitially balanced baroclinic vortex that resembles atropical depression. Future work will address interac-tions between tropical cyclones and more complex ex-ternal circulations.

b. Background

The structure and evolution of tropical cyclones wasreviewed by Willoughby (1995). The primary energeticprinciples of these storms are thought to be well un-derstood. They extract significantly above-normalamounts of latent and sensible heat from the sea surfacedue to the intense winds in the core region. The latentheat is released as air ascends to the upper tropospherein the eyewall cloud and other rainbands that containdeep convective cores, and this heating warms the coreto virtual temperatures close to those of a moist pseu-doadiabat for boundary layer air. The air diverges in theupper levels and gradually descends on larger scales asit cools radiatively. The storm’s energetics have beencompared to a Carnot-cycle steam engine by Emanuel(1986). During the intensification stage of the life cycle,the strong diabatic heating in the eyewall region leadsto contraction of the core, which in turn spins up thewinds (e.g., Shapiro and Willoughby 1982). In a mature,approximately steady-state tropical cyclone there is abalance in the core’s kinetic energy cycle between the

frictional dissipation in the boundary layer and its gen-eration by downgradient inflow (Frank 1977).

Given the dominant role of latent heat release in trop-ical cyclone energetics, it is not surprising that mosthypotheses on the causes of storm structure and intensitychange relate in some way to processes that affectamounts and distributions of latent heat release. Mostresearch in this area has focused on processes that affectthe total supply of moisture to the storm or the maximumvalues of equivalent potential temperature that may beachieved in the boundary layer. There has been somesuccess in relating sea surface temperatures (SST) be-neath the core to cyclone intensity (DeMaria and Kaplan1994), and there have been cases where dry advectionin the middle troposphere has been suggested as a causeof storm weakening. Thermodynamic arguments sug-gest an upper limit to the maximum intensity of a trop-ical cyclone that is proportional to the SST and somemeasure of the depth of the convection, such as theheight of the tropopause (Emanuel 1988, 1997; Holland1997). Applications of this concept to intensity forecastsof individual storms has met with limited success, ap-parently due to the fact that few storms reach their max-imum potential intensity (e.g., Lighthill et al. 1994).However, the thermodynamic controls on the total latentheat release are only part of the story.

Other recent studies have found that both the totalamount of convection and the storm intensity (definedeither in terms of the minimum sea level pressure orthe maximum wind speed) appear to be strongly affectedby interactions between the storm and external circu-lations. For example, case studies by Molinari et al.(1995) and others have shown that upper-level potentialvorticity (PV) anomalies, such as those associated withupper-level troughs, can weaken a tropical cyclone byincreasing vertical shear over the core, or intensify iteither by unbalancing the upper-level flow leading toenhanced divergence of mass from the core (hence in-creasing the total convection) or as a result of super-position of the upper- and lower-level PV anomalies.Modeling studies such as Pfeffer and Challa (1992) sup-port the positive influence of enhanced upper-level out-flow on storm intensification.

While the organization of moist convection usuallydefies simplistic explanations, it appears to be univer-sally true that it is heavily modulated by circulationsthat cause dynamically forced regions of vertical mo-tion. The secondary circulations that result in regionsof ascending and descending motion within tropical cy-clones have been ascribed to several mechanisms. Partof a tropical cyclone’s inflow results from direct re-sponse to the latent heat release in the core, which causesa thermally direct secondary circulation (Willoughby1995). The mean, axisymmetric inflow resulting fromthis process tends to be relatively weak (less than 1 ms21), but it occurs through a deep layer, typically ex-tending from the surface up to about 300 hPa. Withinthe rainbands themselves, the latent heating produces



such a strong positive feedback on the local upwardmotion that it is difficult to ascribe the underlying causesof the preferred regions of ascent. There are severaltheories relating the organization of tropical cyclonerainbands to various wave types, as reviewed by Wil-loughby (1995), but this paper will not directly addressthat problem. Rather, it will seek to examine and com-pare the relative effects of vertical shear and boundarylayer processes upon the vertical velocity field in thecore region and how they thereby modulate the storm’sconvection and intensity.

As shown by many studies, the typical tropical cy-clone has a distinct inflow layer extending from the seasurface to a height of about 2 km, with the strongestinflow occurring near the surface. The top of this layerappears to be roughly constant over a large area, but itdecreases to sea level near the eyewall (Frank 1982,1984). Most sources attribute the majority of this inflowto the effects of friction, though aircraft measurementsof stress typically have not noted large values of stressabove about 500–600 m (e.g., Moss and Merceret 1976;Frank 1984). Because boundary layer stress varies qua-dratically with wind speed, it produces a band of con-vergence near the radius of maximum winds, hence ator near the eyewall (Willoughby 1995). Depending uponthe radial profile of the rotational winds in a particularstorm, boundary layer friction may also cause bands oflow-level convergence outside the eyewall. Shapiro(1983) used a simple slab boundary layer model to an-alyze the effects of storm movement on the pattern offrictional convergence. He found that for slow-movingstorms the convergence was concentrated in the rightfront quadrant (looking downstream), while for faster-moving storms it was located more directly in front ofthe center.

Several observational studies of Atlantic hurricaneshave shown that patterns of convection in the eyewallregion tend to exhibit persistent asymmetries that appearto be related to the asymmetric wind field in or near thecenter of the storms (Willoughby et al. 1984; Marks etal. 1992; Franklin et al. 1993). In particular, each of thecase studies described in these papers suggests that theprecipitation in hurricanes tends to be maximum on theleft side of the vertical shear vector (looking down-shear).

The manner in which vertical shear modulates thesecondary circulations of tropical cyclones and producesasymmetries has been explored in recent modeling stud-ies by Shapiro (1992), Jones (1995), DeMaria (1996),and Bender (1997). Vertical wind shear has long beenknown to be unfavorable for tropical cyclogenesis, andstrong shear also tends to favor weakening of maturecyclones (Gray 1968; Merrill 1988). Early studies fo-cused on the possible role of the shear in advecting thewarm, moist air out of the core, but more recent analyseshave tended to focus on its dynamic effects on the struc-ture of the core.

Shapiro (1992) used a three-layer model to examine

the effects of westerly shear in the upper troposphereupon the motion of a hurricane-like vortex on anf -plane. He found that the vortex drifted slowly to thesoutheast due to the interactions between the vortex andthe negative meridional PV gradient in the middle layerof his model that was associated with the imposed ver-tical shear.

Jones (1995) used a primitive equation model to studythe effects of vertical shear upon the motion and struc-ture of dry, frictionless, barotropic vortices on anf -plane. She imposed linear shear profiles and foundthat as the shear tilted the initially balanced vortex, theflow responded in a manner that kept the flow close toa balanced state. Upper- and lower-level vorticity cen-ters tended to rotate around each other, and the vortexdeveloped a secondary circulation pattern with a wave-number one structure. This vertical circulation patternresulted from an isentropic flow mechanism that is dis-cussed later. Jones also explored the effects of variationsin vortex structure and of several environmental prop-erties (shear strength, static stability, and Coriolis pa-rameter) upon her results.

DeMaria (1996) examined the effects of vertical shearon tropical cyclone intensity change using a two-layermodel. His results suggested that the negative influenceof shear on cyclone intensity results not from ventilationof the core, as had been suggested in earlier studies, butfrom inhibition of convection due to midlevel warmingand hence stabilization associated with the balanced re-sponse to tilt of the vortex by the shear. He noted thatlarger, stronger, and higher-latitude storms are less sen-sitive to shear than are their counterparts.

Bender (1997) simulated the effects of mean flow,vertical shear, friction, and variable f (Coriolis param-eter) on hurricane structure using the full-physics Geo-physical Fluid Dynamics Laboratory model. He ana-lyzed patterns of convergence, vertical velocity, andrainfall in the model under the influence of various im-posed mean flow conditions, and he examined the ef-fects of relative flow on the relative vorticity field. Forthe range of conditions studied, Bender’s (1997) sim-ulations indicated that the b-gyres resulting from var-iable f tended to force low-level convergence and ascenton the rear side of the eyewall. Adding mean flowcaused the upward motion to be concentrated in the leftfront quadrant, while vertical shear tended to cause up-lifting on the downshear side. Rainfall patterns showedagreement with the regions of uplifting. All of the sim-ulations involving mean flow were performed with thecumulus parameterization activated, making it some-what difficult to isolate the nature and magnitudes ofindividual dynamical processes, but sensitivity of themodel to variations in the mean flow were clearly es-tablished. Bender (1997) concluded that most of theasymmetries that occurred in his simulations resultedfrom changes in the direction and vertical shear of thestorm-relative asymmetric winds in the core.

The current study has several aspects in common with



FIG. 1. Tangential winds for the initial balanced vortex (m s21).Only the fine mesh domain is shown.

TABLE 1. Model configuration for the cases shown in the first col-umn shows whether or not the boundary layer scheme was activated.The third column indicates whether the domain mean zonal wind waszero or 23 m s21 (easterly 5 E), and the fourth column shows thedirection of the shear (0 5 zero, W 5 westerly, E 5 easterly).

Case PBL Zonal flow Shear

A1A2BC1C2C3D3M (control)MC2MC3MD2MD3

NoYesYesNoYesYesYesYesYesYesYesYes

00E00EE00E0E

000EEEW0EEWW

Jones (1995) and Bender (1997), but it also has severalmajor differences. This study combines a series of ide-alized simulations using a dry model followed by com-plementary runs with the moist parameterizations ac-tivated. In this way we hope to isolate the differentphysical processes contributing to the secondary cir-culation as well as their relative magnitudes and inter-actions. The methodology followed for the dry runs issimilar to that of Jones (1995), but it differs in severalimportant ways. This study uses a baroclinic (rather thanbarotropic) initial vortex, and it includes a high-reso-lution boundary layer model, so that the effects ofboundary layer friction and vertical shear upon the sec-ondary circulation can be compared and contrasted. Inaddition, the dry model runs are compared to simula-tions performed using parameterized moist convectionto examine the effects of latent heat release upon theresults. The primary differences in methodology fromBender (1997) are that the current study uses the paireddry and moist runs, a different numerical model (thatincludes, e.g., fully explicit moist processes in additionto parameterization), and analyzes the results in termsof balance arguments rather than budgets.

2. Methodology

a. Experimental design

The simulations described below show the behaviorof an initial tropical-depression-like vortex (hereafterreferred to as the TD vortex) in different environmentalflows. The initial vortex (Fig. 1) resembles a strongtropical depression that is only slightly below the in-tensity threshold of 17 m s21 winds used to classify thesystem as a tropical storm in the Atlantic basin. It is

based on data from a composite analysis of a prestormtropical depression by McBride and Zehr (1981). It isa warm-core system with maximum winds of 15 m s21

at a radius of 135 km, and there is a weak upper-levelanticyclone. This relatively weak stage of the cyclonewas chosen because we did not want the relatively subtlecirculations caused by the interactions between stormand environment to be obscured by the primary flow.For example, tropical depressions are almost alwaysmore asymmetric than fully developed hurricanes, andone area of interest is the development of asymmetriesin the storm circulation.

The runs are performed with different mean valuesof the zonal wind, with different vertical shears of themean zonal wind, and with the boundary layer scheme(and hence friction) turned on and off (Table 1). Theresulting effects on vortex structure are analyzed, payingparticular attention to changes in the following quan-tities: the central pressures and maximum winds of theTD vortex, indicating a tendency for the system to weak-en or strengthen in response to environmental condi-tions; asymmetries in the core structure; and develop-ment of secondary circulations, especially regions oflow-level or deep-layer convergence or divergence thatwould be expected to cause changes in the amount anddistribution of moist convection within the core region.

Although diabatic heating, particularly latent heat re-lease, is of fundamental importance to the energetics oftropical cyclones, many of the simulations performedhere use a dry version of the model with no diabaticheating. This is done in order to isolate the relativelysubtle but direct interactions between imposed environ-mental flow properties and the structure of the TD vor-tex. The goal is to examine first-order effects of theseinteractions. The results are then used to guide subse-quent simulations using a relatively simple cumulus pa-rameterization to examine the effects of latent heatingupon the results. As noted above, ongoing and futureresearch will extend this work to include finer mesh



simulations with explicitly resolved convection and toexamine more complex external circulations.

b. Model description

The simulations are performed with the nonhydrosta-tic Pennsylvania State University–National Center forAtmospheric Research Mesoscale Model version 5(MM5) (Anthes et al. 1987). This model incorporatesmultiple nested grids and includes both explicit moistphysical processes and a variety of cumulus parame-terization and boundary layer schemes. It solves thenonlinear, primitive equations using Cartesian coordi-nates in the horizontal and a terrain-following sigmacoordinate in the vertical. The model has been adaptedfor use with idealized initial conditions to permit carefulcontrol of initial value experiments.

The use of a model of this type is crucial for accom-plishing the long-term goals of the project. Numericalsimulations of tropical cyclone–environmental interac-tions require a model with a very large domain, neededto resolve the storm’s environment and external circu-lation features, as well as a high-resolution core regioncapable of resolving the small, intense core of the storm.While many of the simulations shown in this paper aremade with a dry version of the model, only limitedprogress is possible without including the latent heatingprocesses and their effects. Ideally, the model shouldattempt to resolve moist processes explicitly, at least inthe core region, since the eyewall region of hurricaneshas too intense and complex a structure to permit fullresolution using cumulus parameterization techniques.However, first-order processes are often easier to di-agnose using simpler models, and the moist runs shownin this paper are performed using parameterized cu-mulus convection working in combination with the ex-plicit moisture scheme.

All simulations are performed on an f -plane valid at158N. Although use of a variable f would allow a morephysically consistent comparison between the simulatedhurricanes and real ones, it would also introduce com-plications in isolating directs effects of shear on the core.With a variable f the cyclone tends to develop b-gyrecirculations due to interactions between the storm’s pri-mary circulation and any existing PV gradient. Thischanges the asymmetric flow in the core region, makingit a function of both the large-scale flow imposed in theinitial conditions and the interactions between the stormand the vorticity field. The changes in the core windsare significant and involve not only alterations of theasymmetric wind speed and direction but also the ver-tical shear. This induced flow often exhibits a jetlikestructure with maximum winds occurring in the lowertroposphere [see Figs. 4 and 14 of Bender (1997)].Hence, the actual shear across the storm center couldbe quite different in strength, direction, and verticalmode from that proscribed in the initial conditions. Thef -plane was chosen for these initial simulations to pro-

vide a more controlled environment for isolating causeand effect in the eyewall region, but future work willinclude variable f as well as other model changes de-signed to allow a closer comparison to real storms.

The model is configured with 20 vertical levels, 7 ofwhich are below 850 hPa. The domain is square and is5400 km on each side. The coarse mesh is 45 km, andthere is a nested fine mesh region that is 1800 km ona side with 15-km resolution. Each mesh consists of 121by 121 points. The boundary layer is parameterized us-ing the Blackadar (1976, 1979) scheme, which was fur-ther described and tested by Zhang and Anthes (1982).The lower boundary is an ocean surface at a constanttemperature of 28.58C. For the moist simulations, a cu-mulus parameterization is used (Betts and Miller 1986).The explicit moisture scheme, which treats rainwaterand cloud water as explicit variables, is also activatedfor the moist runs to deal with any grid-scale conden-sate. The initial winds are in gradient balance with themass field. All simulations are performed with meanzonal flows of either zero or 23 m s21 (easterly). Somehave a zonal shear component added, as is discussedlater. All simulations begin with the baroclinic vortexshown in Fig. 1 and described earlier. Relative humidityvalues are from the McBride and Zehr (1981) prestormcluster composite with a positive anomaly added in thevortex core region to facilitate onset of convection.

3. Results

a. Dry model simulations

1) ZERO ENVIRONMENTAL FLOW: CASE A

Case A consisted of two simulations performed withthe environmental winds set to zero everywhere. In ex-periment A1 the model was initialized with the bal-anced, symmetric vortex described above, and theboundary layer scheme was turned off to remove surfacefriction effects. The simulation was run for 48 h, andthere were no apparent changes in vortex structure ex-cept for some very small wind changes due to diffusion.This run was made simply to demonstrate the stabilityof the initial vortex. Similar tests showed that the vortexalso remained stable when mean zonal environmentalflow was added. All simulations were performed usingthe same initial vortex unless otherwise noted.

The above simulation was rerun with the high-reso-lution boundary layer scheme activated (experimentA2). The primary effect of surface friction was to causesymmetric frictionally induced inflow in the boundarylayer, which produced an axisymmetric band of con-vergence near and outward from the radius of maximumwinds. The location of this convergence band agreedwell with that predicted from simple balance theory inwhich it is assumed that the frictional dissipation ofangular momentum is balanced by inward advection ofangular momentum, following Willoughby (1995) andbased on earlier work by Smith (1968).



FIG. 2. Plan view of the winds at 950 hPa, t 5 24 h, for case B(easterly zonal flow, no shear). Units are m s21, and the longest vectoris 13 m s21. The figure shows a portion of the fine mesh grid area(1200 km on a side), with latitude–longitude lines added for reference.

It should be noted that in case A2 (and in all sub-sequent cases in which the boundary layer scheme wasactivated at the beginning of the simulation) shallow,outward-propagating gravity waves occurred. These re-sulted from the initial imbalance created when frictionwas added to the flow. These gravity waves were ob-served to propagate outward at about 3.5 m s21, and across-sectional analysis (not shown) revealed them tobe largely confined to the lowest 2 km or so. This isalmost exactly equal to the speed of a linearly propa-gating gravity wave with vertical wavelength of 2 km(equal to 3.2 m s21 for the stability used in the model).These waves do not appear to have had any significantimpact on the results discussed below.

The ascent near the radius of maximum winds wasforced by boundary layer friction, and it decreased rap-idly with height. At 950 hPa (near cloud base for atypical tropical depression) the maximum vertical ve-locities between 12 and 24 h were about 1.2 cm s21. At700 hPa the maxima were of order 0.2 cm s21, and at500 hPa they were very weak, a mere 0.1 cm s21. Hence,any organization of convection driven by the conver-gence in this case would have had to occur due to con-vergence in the lowest levels, primarily at or belowcloud base.

The surface friction slowly reduced the wind speedsin the boundary layer, and without the positive feed-backs from latent heat release, the storm graduallyweakened. Both vertical velocities and the cyclonic cir-culation gradually decreased after about 6 h. In realsystems this spindown is offset by the latent heat release,but for dry runs the storm gradually evolved away froma structure that is typical of a tropical cyclone. There-fore, for dry runs with the boundary layer scheme ac-tivated, results are presented only for the first 24 h.

2) EASTERLY FLOW, NO SHEAR: CASE B

In case B the vortex was initialized in a horizontallyand vertically uniform mean easterly flow of 3 m s21

with the boundary layer scheme activated. The 3 m s21

flow is rather weak, but since dry simulations do nothave the strong vertical mass fluxes that help to providevertical coupling in a cyclone, we chose weak meanwinds and vertical shears to maintain the structural in-tegrity of the vortex as long as possible. Unlike the zero-flow case (A2) described above, the moving vortex be-gan with and maintained a horizontal wavenumber oneasymmetry in the low-level wind field. Figure 2 showsthe winds at approximately 950 hPa at t 5 24 h. Thesystem had moved westward with the mean flow, withthe maximum winds remaining on the right side of thecenter. This pattern was maintained vertically throughmost of the troposphere. There was no significant ten-dency for the low-level wind maximum to occur aheadof the storm center or in the right front quadrant as wasfound in a study of fully developed hurricanes by Sha-piro (1983). This difference may have been due to the

weaker and more slowly moving vortex used in thecurrent study, but it also could have resulted from dif-ferences in the nature of the models used. We are in-vestigating the causes of the differences.

The boundary layer friction combined with the move-ment of the storm caused a more complex pattern oflow-level vertical velocity (Fig. 3) than was observedfor the stationary storm. The 950-hPa w field at 24 hshowed a concentration of upward motion in the rightfront quadrant and generally descending air in the leftrear quadrant, in agreement with Shapiro (1983). Thepattern was complicated by a series of bands, whichagain appeared to be shallow gravity waves. There wasa slight tendency for the location of the maximum up-ward motion to rotate cyclonically during the simula-tion.

As was true for case A2, the vertical velocities weremuch weaker at 700 hPa than at 950 hPa, indicating therelatively shallow extent of the frictional effects. Thedipole of vertical velocity, with upward motion in theright front–downward motion in the left rear quadrants,was clearer at 700 hPa.

3) EASTERLY SHEAR: CASE C

In cases C1 (frictionless) and C2 (boundary layerscheme activated) the vortex was embedded in meaneasterly flow that varied from u 5 0 near the surfaceto 23 m s21 in the upper troposphere, with maximumshear near 500 hPa (Fig. 4). Case C3 was the same asC2 except an additional easterly mean flow of 3 m s21

was added at all levels. In C1 the shear caused the vortex



FIG. 3. Vertical velocity (cm s21 ) at 950 hPa, 24 h, for case B.The contour interval is 0.2, and positive values greater than 0.2are shaded.

FIG. 4. The vertical variation of the zonal wind (m s21) used forthe easterly shear cases.

FIG. 5. Positions of the vorticity centers at four vertical levels andat 12-h intervals for case C1 (easterly shear, no zonal flow, no bound-ary layer).

to tilt downstream with time. The 6-hourly positions ofthe vortex center at four different levels are shown inFig. 5 for a 48-h integration. The vorticity maximum at500 hPa, near the center of mass of the column, movedslightly to the south of due westward, while the upper-level vortex center (200 hPa) moved almost directlywestward with the mean flow. In both cases, they movedat the approximate velocity of the imposed winds at thatlevel. However, the vortex centers just above the surfaceand at 700 hPa moved to the right of the mean flow(toward the northwest) following nearly linear tracksthroughout the 48 h at speeds between 0.5 and 1.0 ms21. Comparing these latter motions to Fig. 4 it can beseen that the flow relative to the surface vortex is frontto back (looking down the track), and the relative flowis generally back to front above about 700 hPa.

The simplest explanation for the component of north-ward movement of the lower portions of the vortex maybe visualized by considering the tilt of the balancedvortex by the imposed shear. This process has been de-scribed by Jones (1995) and others and is applicable tothe current case where the relatively weak flow tilts avortex that is initially in gradient balance. Briefly, asthe vortex begins to tilt downshear, the winds and massfield become unbalanced, and a compensating secondarycirculation develops to restore the balance. The mostconvenient way to think of this process is in terms ofthe downward and upward reflections of PV centers atdifferent levels as they advect downshear. Thus, as mid-level slabs of PV are advected downshear, they inducelow-level convergence and increasing vorticity west ofthe low-level vortex center. The resulting flow is north-

ward at the location of the low-level vortex, advectingit northward. The reverse effect occurs in the upper-middle troposphere. Jones (1995) found similar move-ments in her simulations of barotropic hurricane-likevortices, but in her results the vortex centers rotatedaround each other. In the present case the vortex centersshown near the surface and at 200 hPa moved with



FIG. 6. (a) Wind barbs and potential temperature contours (K) at950 hPa, 24 h, for case C1. (b) Vertical velocity (cm s21) at 950 hPa,24 h, for case C1. The contour interval is 0.1, and positive valuesgreater than 0.1 are shaded.

FIG. 7. Vertical velocity (cm s21) at 500 hPa, 24 h, for case C1.The contour interval is 0.4, and positive values greater than 0.4 areshaded.

almost constant direction. We feel that this differenceresulted in part from the use of a baroclinic vortex inthe current study, which had decreasing intensity withheight, and also from the weaker intensity and largerdiameter of the vortex used in the present study.

The secondary circulation described above caused up-ward displacement of the potential temperature surfaces

‘‘down-tilt’’ from the surface vortex and downward dis-placement of the isentropes on the opposite side. Thisproduced a cold anomaly west-southwest of the low-level vortex center and a warm anomaly to the east-northeast of the surface low (Fig. 6a). The primary cir-culation in the low levels (i.e., the main vortex) thenproduced a wavenumber one asymmetry in the verticalmotion field as the strong rotational flow moved alongthe sloping isentropes. This is illustrated in Fig. 6b,which shows a vertical velocity dipole at 950 hPa withascending motion in the right front quadrant and descentin the left rear quadrant. Maximum vertical velocitiesat this time (t 5 24 h) and level were about 60.6 cms21. The vertical velocities in Fig. 6b were almost totallydue to the isentropic flow, as the ascent along the is-entropes was almost two orders of magnitude greaterthan the diagnosed vertical velocities that were causingthe vertical displacement of the isentropes. The patternextended through most of the troposphere, with the ver-tical velocities extending upward to between 200 and300 hPa and reaching maximum values of about 63.5cm s21 in the middle levels (Figs. 7, 8).

In case C2 the boundary layer scheme was activated.Note that in this run the low-level environmental flowwas near zero, so the first-order effects of the frictionwould be expected to be symmetric. The vertical ve-locities at 24 h at 950 hPa and 500 hPa are shown inFigs. 9 and 10, respectively. At 950 hPa the combinedeffects of easterly shear and friction in the boundarylayer produced asymmetrical low-level convergencethat resulted in a vertical velocity pattern that looksroughly like a simple sum of the fields generated by



FIG. 8. Vertical cross section of vertical velocity along a northwest–southeast line through the center of the vortex in case C1 at 24 h.The units are cm s21, the contour interval is 0.4, and positive valuesgreater than 0.4 are shaded.

FIG. 9. Vertical velocity (cm s21) at 950 hPa, 24h, for case C2(easterly shear, no zonal flow, with boundary layer). The contourinterval is 0.2, and positive values greater than 0.2 are shaded.

FIG. 10. Vertical velocity (cm s21) at 500 hPa, 24h, case C2. Thecontour interval 0.4, and values greater than 0.4 are shaded.

each process, with banded structure and upward/down-ward motion in the right front/left rear quadrant. Themaximum upward motion in Fig. 9 is 1.0 cm s21. Thevertical motion field at 500 hPa for t 5 24 h was verysimilar to that for case C1, showing that the frictionaleffects were shallow in the core region. (The maximumupward motion at 500 hPa in C2 was about 3.0 cm s21,slightly less than the 3.4 cm s21 of C1.)

Case C3 was similar to C2, except that with the addedlow-level storm motion, there was increased asymmetryof the frictional effects upon the divergence field. After24 h there were two bands of concentrated low-levelupward motion at 950 hPa in front of and on the rightside of the vortex, with subsidence concentrated on theleft side close to the center and to the left and rear atlarger radii (Fig. 11). Interestingly, the maximum ver-tical velocity at this level was 2 cm s21, stronger thanin any of the other cases. Therefore, the combined ef-fects of friction acting on the moving vortex and easterlyshear increased the magnitude of the forced uplifting inthe right front quadrant. At 500 hPa the vertical velocitypattern had the same dipole structure as for the fric-tionless case (C1), with the rising motion occurring inthe right front quadrant (not shown).

Finally, case C2 was rerun twice with the verticalshear profile shifted such that the maximum shear leveloccurred near 700 hPa and 350 hPa, respectively. Withthe shear shifted to lower levels, the storm behavedalmost exactly as shown in the above figures for caseC2, though the maximum values of the induced verticalvelocity field were about 10% stronger. When the shearwas shifted to higher levels, the effects on the low-level

storm structure were greatly reduced. In terms of mod-ulating the secondary circulation of a tropical cyclone,low-level and midlevel shear appear to be much moreimportant than is upper-level shear.

4) WESTERLY SHEAR CASE: CASE D

The final dry case (D3) had westerly shear, exactlyopposite in sign to that shown in Fig. 4, and an easterly



FIG. 11. Vertical velocity (cm s21) at 950 hPa, 24h, case C3 (easterlyzonal flow, easterly shear). The contour interval is 0.2, and valuesgreater than 0.2 are shaded.

FIG. 12. As in Fig. 11, but for case D3 (easterly zonal flow, west-erly shear).

background flow of 3 m s21 was added to the shear. Theboundary layer scheme was active. The vertical veloc-ities at t 5 24 h for the 950-hPa level are shown in Fig.12. At this level the storm formed a pattern of spiralbands, with the maximum upward motion occurringahead and slightly to the right of the storm, but theregion of upward motion was much more symmetricthan in the easterly shear case. The increased symmetryreflects the fact that for this case the low-level conver-gence areas induced by shear and by friction occur onopposite sides of the center. The maximum vertical ve-locity in Fig. 12 is 1.2 cm s21, weaker than the maximumfrom case C3. At 500 hPa the w pattern was almostexactly a mirror image of case C3, with ascent in theleft rear quadrant and descent in the right front quadrantlooking downshear (not shown). As in the other shearruns, the vertical velocity field in the middle levels andabove resulted almost entirely from the effects of shearrather than from friction.

5) SUMMARY OF DRY SIMULATIONS

Frictional effects tended to focus convergence in aband surrounding the vortex center. When the low-levelvortex center moved due to advection by the mean flow,the convergence became asymmetrical and was orga-nized into spiral bands with maximum uplifting aheadof the moving storm center. The boundary layer pro-cesses had little effect on the dry vortex above about850 hPa, but since low-level convergence can play amajor role in organizing deep convection and hencelatent heat release, these processes could be significantin modulating cyclone structure.

Vertical wind shear caused a three-stage sequence ofevents. First, the shear tilted the vortex generally down-shear, and the lower and upper vortex centers tended tomigrate with components to the right/left of the meanshear vector (producing a slight cyclonic rotation of thetilt from directly downshear). The direction of tilt re-mained almost constant throughout the dry runs. Sec-ond, the tilting rapidly unbalanced the vortices creatingweak ascent downshear and descent upshear of the low-level vortex center. This initial secondary circulationpattern caused upward/downward bulging of the cold/warm isentropes downshear/upshear of the surface vor-tex. Third, as this pattern developed, the primary vortexcirculation flowed up and down the tilted isentropesproducing a vertical circulation pattern with maximumupward motion in the downshear right quadrant (lookingdownshear) and subsidence in the upshear left quadrant.This shear-induced vertical velocity dipole was quitedeep, extending upward to well above 300 hPa in thecurrent study. In these dry simulations the vertical mo-tion was dominated by the final mechanism, that is, theisentropic flow of the primary circulation. Low-leveland midlevel shear were found to have much strongereffects on the secondary circulation than upper-levelshear for shears of similar magnitude.

The secondary circulation patterns induced by therelatively modest environmental perturbations shown inthis study are quite striking, and they strongly suggestshear can modulate the pattern, and perhaps amount, oflatent heat release in the core region. Friction plays amore complex role in tropical cyclone structure, but ittoo appears to be capable of affecting the distribution



FIG. 13. (a) Time series of the minimum central pressures of thecontrol run (case M) and cases MC2 (no zonal flow, easterly shear),MD3 (easterly zonal flow, westerly shear), and MC3 (easterly zonalflow, easterly shear). (b) As in (a) but for the maximum wind at 950hPa. (c) Time series of the total rainfall and of the rainfall from theexplicit moisture scheme (lower set of curves) for the control runand cases MC2, MD3, and MC3.

of latent heating. This is explored below using the full-physics version of the model.

b. Moist simulations

1) INTENSITY AND MEAN RAINFALL VARIATIONS

Addition of latent heating processes causes profoundchanges in the evolution of the simulated tropical cy-clone, as expected. A control simulation was performedwith the same initial conditions as used in the dry runsbut with no mean zonal flow (case M). This was fol-lowed by four other moist simulations that includedsheared zonal flow (Table 1). Case MC2 had the sameeasterly shear and no added zonal flow as dry case C2.Case MC3 had the easterly shear plus added easterlymean flow used in case C3. Case MD3 had the samewesterly shear and easterly zonal flow as dry case D3,and case MD2 had westerly zonal shear but no addi-tional zonal flow.

The control simulation resulted in rapid intensifica-tion of the initial vortex into a hurricane. The evolutionof the central pressure and rainfall for each of the moistruns can be seen in Fig. 13. The control run reached anapproximate steady state at about 36 h with winds ofabout 60 m s21 and a central pressure that subsequentlyremained between 946 and 948 hPa. As expected, the

storm maintained a symmetric structure throughout thesimulation. For the 28.58C SST used in these runsDeMaria and Kaplan’s (1994) data would indicate amaximum potential intensity of around 920 hPa. Giventhe relatively coarse resolution of the fine mesh (15 km),the control central pressure appears to be reasonable.Based on similarly configured runs being performed lo-cally by colleagues, we would expect the simulation toeventually approach the approximate intensity predictedby DeMaria and Kaplan if it were to continue for severalmore days (J. L. Evans and S. K. Drury 1998, personalcommunication).

The rainfall in all of the runs rapidly builds up to amaximum at about t 5 9 h (Fig. 13). The control runtotal rainfall then decreases to a minimum value, whichoccurs near 42 h, and then increases again. The threesheared runs follow similar patterns but experiencesmaller decreases in total rainfall and reach their minimaearlier. The lower set of curves in Fig. 13 show theexplicit rainfall for each run, and the parameterized rain-fall is equal to the difference between the curves. Forthe first 15–18 h virtually all rainfall is convective (pa-rameterized) in all of the runs. Beginning around 18 hthe explicit rainfall begins to grow, and it is of the orderof half of the total rainfall in the sheared runs fromabout 36 h onward. In the control run, however, the



FIG. 14. Vertical velocity (cm s21) at 950 hPa, t 5 12 h, case MC2(easterly shear, no zonal flow). The contour interval is 4.0, and valuesgreater than 4.0 are shaded. The area shown is 600 km square.

explicit rainfall grows faster and represents a much larg-er fraction of the total rainfall. The rainfall shown isaveraged over the fine mesh area, but most of the rainfalls within 300 km of the storm center. Explicit rain isconcentrated primarily within and immediately adjacentto the eyewall cloud. The control run develops a morecompact structure with a greater fraction of its overallrainfall occurring in the eyewall than do any of the shearruns.

All of the simulations exhibit rather stable intensitiesfrom 30 h onward despite relatively large changes intotal rainfall. However, the explicit rainfall, which isconcentrated in the storm cores, is much steadier thanthe parameterized rainfall during this period. The datain Fig. 13 suggest that the storm intensity is closelyrelated to the rainfall in the eyewall but not to variationsin the convective rainfall at greater radii.

2) EVOLUTION OF STORM STRUCTURE

Cases MC2 and MD2 (easterly/westerly shear, no ad-ditional zonal flow) produced identical results exceptthat the patterns are rotated 1808 from each other. Thisis expected for the initial conditions used since the sim-ulations are on an f -plane. We present results only forthe MC2 run here, but the results for MD2 can be vi-sualized by rotating the MC2 results. Case MC2 inten-sified and developed into a hurricane, reaching an ap-proximate steady-state intensity near 36 h (Fig. 13). Themature storm reached a central pressure of about 963hPa and maximum winds of about 51 m s21. Only slightfluctuations in these values occurred throughout the re-mainder of the 72-h simulation. The mature MC2 stormwas weaker than the control run storm by about 15 hPaand 5–10 m s21.

Due to the lack of large-scale winds in the lowerlevels, the MC2 storm moved very slowly, driftingslightly to the northwest under the influence of the shear.Low-level convergence rapidly produced nearly sym-metric uplifting and rainfall in run MC2. However, with-in a few hours the storm developed a significant asym-metry in the vertical velocity field, with the maximumuplifting occurring due west of the storm center (directlydownshear). This appeared to result initially from thesame process that caused vertical velocity in the veryearly stages of dry case C2. That is, the shear beginsto tilt the vortex downshear due to increasing vorticityadvection with height. The downward projection of themidlevel PV anomaly causes convergence in the lowlevels and uplifting through the lower and middle tro-posphere directly west/downshear of the surface center.Midlevel convergence, low-level divergence, and sub-sidence are induced east (upshear) of the surface centerby this process. The modulation of the vertical velocityfield causes a similar modulation of the convection (notshown).

From 6 to 12 h, MC2 continued to behave somewhatlike run C2 but with convection greatly amplifying the

vertical velocity field. A cold anomaly developed at 700hPa west (downshear) of the storm, and for a while therewas maximum upward motion at this level in the north-west (downshear right) quadrant where the isentropicuplifting of the primary flow was strongest (Figs. 14,6). However, between 18 and 24 h the flow in the eye-wall became saturated at many grid points, and the com-bined effects of the explicit and parameterized latentheat release destroyed the cold anomaly and hence theisentropic uplifting mechanism. The maximum upliftingand rainfall tended to become collocated with the warm-est temperatures, southwest of the center. After 24 h,the vertical velocity field of MC2 at 950 hPa indicatesthat the convection in the eyewall had become somewhatcellular but was strongest in the southwest quadrant(Fig. 15).

Figures 16a–c show the 700-hPa vertical velocity,cloud water, and rainwater at 48 h, when the storm struc-ture was mature and relatively steady. (The 700-hPalevel was chosen for display since vertical motion atthis level has a strong correlation with net latent heatrelease.) Note that the rainwater pattern was slightlycyclonically rotated from the maximum upward motionand cloud water due to advection of the rainwater. Thisis generally true throughout the moist runs. The cloudwater was coincident with the upward motion. Through-out most of the 72 h of this run the strongest rainfalloccurred to the downshear left (southwest) of the stormcenter. The strongest winds tended to occur in the south-east quadrant of the storm (upshear left, looking down-shear), and there was also a weak local maximum dueeast of the center at 48 h (Fig. 17). Summarizing, the



FIG. 15. As in Fig. 14, but at t 5 24 h. The contour interval is5.0, and values greater than 5.0 are shaded.

addition of moist processes resulted in a shift of themaximum convection from the downshear right quad-rant predicted from the adiabatic simulation, to thedownshear left quadrant. This was primarily becausethe isentropic lifting mechanism that dominated the dryruns was removed when the eyewall became saturatedallowing the first-order vorticity advection effects todominate the vertical motion field instead.

When easterly zonal flow was added to the easterlyshear background (MC3), the storm moved on a trackthat was just slightly north of westerly and evolvedthrough a life cycle pattern that closely resembled thatof MC2 with respect to patterns of growth and intensitychange. In the dry version of this case (C3), the adiabaticuplifting mechanism and frictional convergence in theboundary layer both tended to produce forced upliftingin the downshear-right quadrant, northwest of the west-ward-moving storm. Hence, C3 was the most asym-metrical of the dry runs. However, this did not hold truefor the moist version. Once the storm in MC3 ap-proached maturity and developed a saturated eyewallcloud, the region of maximum vertical motion and latentheat release tended to shift to the downshear-left quad-rant, south of the westward-moving storm center. How-ever, by 48 h, the low-level, upward motion in the eye-wall was relatively evenly distributed around the center(Fig. 18), with the maximum value occurring in the frontright quadrant of the storm center, consistent with fric-tional forcing asymmetries for a westward-movingstorm. The cloud water and rainwater for this run at 700hPa and 48 h (Fig. 19) were typical of the mature stageof the simulation. They show the tendency for upwardmotion and rainfall to be concentrated in the eyewall

cloud ranging from north of the center counterclockwisethrough south to southeast of the center. The eyewallwas open, or clear, to the northeast (upshear right), andmaximum winds were located in the northeast quadrant,which for this case was both the right back quadrantrelative to motion and the upshear right quadrant relativeto the shear vector (Fig. 20).

When the zonal flow remained easterly, but the di-rection of the background shear was changed fromeasterly to westerly (MD3), the storm evolved througha life cycle pattern that resembled those of MC2 andMC3. In the dry version of this case (D3), the adia-batic uplifting mechanism produced forced upliftingin the downshear right quadrant (southeast), whereasfrictional convergence in the boundary layer tendedto produce forced uplifting in the front right quadrant(northwest) of the westward-moving storm. Hence,D3 was the most symmetrical of the dry runs. Whenmoist physics were included, the storm motion pro-duced frictional convergence in the boundary layer tothe west and northwest of the center similar to thatdiscussed for MC3. By 48 h the vertical velocity at950 hPa showed maximum uplifting in the eyewallconcentrated in a band that ran clockwise from west(in the direction of motion) through northeast (down-shear left) of the storm center (Fig. 21). The verticalvelocity at 700 hPa at this time was even more asym-metrical and showed the effects of convection con-centrated in two regions, west and northeast of thecenter (not shown). The cloud water and rainwater at700 hPa showed an open or clear region of the eyeto the south-southeast, with maximum values gener-ally west and north of the center (Fig. 22). Maximumwinds were located in the northwest quadrant, whichfor this case was both the right front quadrant relativeto motion and the upshear left quadrant relative to theshear vector (Fig. 23). The patterns throughout the 48h of the simulation tended to resemble those of MC3,though rotated between 908 and 1808 in the counter-clockwise direction. However, the difference in di-rection between the zonal flow and shear vector incase MD3 resulted in a second area of preferred con-vection forced by asymmetries in the boundary layerfriction. The convection in this region located westto northwest of the center was comparable in mag-nitude to that in the region forced by the westerlyshear (downshear left or northeast of the center).

In both MC3 and MD3 the frictional convergence andthe shear tended to force ascent in different sectors oftheir eyewall clouds. There were differences in the rel-ative locations of the two modes, with the shear-induceduplifting occurring upstream of the frictional conver-gence area in MD3 and downstream in MC3. (Upstreamin this instance refers to the rotational flow in the eye-wall region, not the storm motion vector.) However, thetwo runs contained about the same degree of wave-number one asymmetry, and their intensities were onlyslightly different.



FIG. 16. (a) Vertical velocity (cm s21) at 700 hPa, 48 h, case MC2.The contour interval is 30, and values greater than 30 are shaded.(b) Cloud water (g kg21) at 700 hPa, 48 h, case MC2. The contourinterval is 0.2, and values greater than 0.2 are shaded. (c) Rainwater(g kg21) at 700 hPa, 48 h, case MC2. The contour interval is 0.4,and values greater than 0.4 are shaded.

An interesting facet of runs MC2, MC3, and MD3 isthat once each storm became mature, it tended to de-velop asymmetries in the eyewall. The predominant pat-tern was usually a wavenumber one asymmetry. How-ever, at various times the eyewall structure developedasymmetries that appeared to have wavenumber 2 struc-ture, and occasionally it appeared as if the overall struc-ture exhibited wavenumber 4 features. It is difficult todistinguish whether apparent higher-order modes weredue to vortex-scale dynamics or reflected localizedgrowth of convective cells, but the persistence of thepatterns observed in the eyewall structure suggests thepresence of wavenumber four asymmetries during days

2 and 3. We did not explore this further in the currentpaper, but will do so in future studies. The occurrenceof asymmetries in the eyewall flow and the dominanceof the wavenumber one pattern are in qualitative agree-ment with the studies of vortex Rossby waves by Mont-gomery and Kallenbach (1997).

4. Conclusions and recommendations

The dry simulations showed that both storm motionand weak vertical shear produce wavenumber one asym-metries in the low-level convergence field. For the fric-tion, the area of forced ascent is ahead and to the right



FIG. 17. Wind speed (m s21) at 950 hPa, 48 h, case MC2. Contourinterval is 5 m s21.

FIG. 19. (a) Cloud water (g kg21) at 700 hPa, 48 h, case MC3. Thecontour interval is 0.2. (b) Rainwater (g kg21) at 700 hPa, 48 h, caseMC3. The contour interval is 0.4.

FIG. 18. Vertical velocity (cm s21) at 950 hPa, 48 h, case MC3(easterly zonal flow, easterly shear). The contour interval is 5.0, andvalues greater than 5.0 are shaded.

of the storm track for the values tested here, and thisagrees with the results of Shapiro (1983). The shear-induced ascent extends through a much deeper layer andtends to be concentrated in the quadrant downshear rightof the storm center. This pattern results from a three-stage process. The shear causes increasing advection ofPV with height, and this forces a weak secondary cir-culation with ascent downshear and descent upshear of

the surface vortex center. The vertical distortion of theisentropes resulting from this circulation causes the pri-mary rotational flow of the vortex to ascend and descendisentropically. The mechanism dominating the shear-induced vertical motion pattern in the dry runs is thelatter isentropic lifting mechanism, which was describedby Jones (1995). Low-level and midlevel shear havemuch stronger effects on the vertical motion field thandoes upper-level shear.

All of the moist runs stabilized in a quasi-mature state



FIG. 20. Wind speed (m s21) at 950 hPa, 48 h, case MC3. Thecontour interval is 5.0.

FIG. 22. (a) Cloud water (g kg21) at 700 hPa, 48 h, case MD3. Thecontour interval is 0.2. (b) Rainwater (g kg21) at 700 hPa, 48 h, caseMD3. The contour interval is 0.4.

FIG. 21. Vertical velocity (cm s21) at 950 hPa, 48 h, case MD3(easterly zonal flow, westerly shear). The contour interval is 5.0, andvalues greater than 5.0 are shaded.

after about 30 h, and the runs in sheared flow exhibitedcentral pressures that were markedly higher than thosein the control run. The control run did not develop moretotal rainfall than the sheared storms, but it did havemore explicit rainfall concentrated in the eyewall region.Each storm in sheared flow developed significant asym-metries in the azimuthal distribution of winds and rainwithin the eyewall region.

It was hypothesized that strong asymmetric forcingof upward vertical velocity in the core of the simulatedhurricanes would produce marked asymmetries in thepatterns of latent heat release in the core structure, andthat this would affect the storm’s intensity. This provedto be the case, but the results show that the effects ofthe latent heat release alter the pattern of convectiononce the storm approaches a mature structure.

The asymmetry in boundary layer convergenceshowed the same relationship with storm motion in the



FIG. 23. Wind speed (m s21) at 950 hPa, 48 h, case MD3. Thecontour interval is 5.0.

dry and moist runs, with the maximum convergenceoccurring ahead and to the right of the storm motionvector in the two cases that exhibited significant stormmotion. However, the vertical shear tended to producemaximum convection to the left of the shear vector,looking downshear, once the storms developed saturatedregions within their eyewalls. The upward motion andconvection were then concentrated in the downshear leftquadrant, while the rainwater was advected around tothe left of the shear. The reason for the differences inshear effects between dry and moist runs is that onceresolvable latent heat release is established in the eye-wall, the diabatic heating destroys the adiabatic liftingmechanism that dominates the vertical velocity patternsin the dry runs. In the moist runs the secondary cir-culation component forced by vertical shear is due tothe direct effects of differential vorticity advection upona quasi-balanced vortex.

The simulated rainfall patterns associated with ver-tical shear agree with radar observations of hurricanecores (Willoughby 1984; H. E. Willoughby 1998, per-sonal communication; Marks et al. 1992; Franklin et al.1993), and with the easterly shear case simulated byBender (1997). Since both storm motion and large-scaleshear can be predicted with some accuracy, the resultsof this study indicate that the structure of the hurricanecore and intensity should be predictable as well. Theresults suggest that the response to shear should be dif-ferent in loosely organized convective systems, such astropical depressions that usually lack a saturated eyewallcloud, than they are in mature hurricanes. This will beexamined in future work.

The current study examined a limited range of values

of zonal flow and unidirectional vertical shear. In thecurrent study the shear and boundary layer friction hadapproximately equal effects on modulating the latentheat release in the core. However, the values of shearused were relatively weak compared to the shears ex-perienced by many real hurricanes. The storm motions(or order 3 m s21) were more comparable to typicallyobserved storm speeds (though they were still belowaverage). Even these relatively modest values were ableto force the storms to develop major wavenumber oneasymmetries, and higher-order wavenumbers were sug-gested by temporal variations in the eyewall structures.It is hypothesized that these asymmetries in the eyewallstructure are responsible for the reduced intensities ofthe sheared storms relative to the control storm. How-ever, the physical link between asymmetrical structureand storm intensity change is a topic of our ongoingresearch. Further diagnostics and additional simulationsare in progress.

The work shown in this paper represents only onepart of the study. In addition, the same model and ap-proach are being used to examine the effects of vortexmergers and of asymmetrical distributions of latent heatrelease, both in the core and in the rainbands, uponcyclone structure and intensity. The next stage of theresearch, which will use a finer grid mesh and explicitmoist processes to resolve convective processes, is un-der way and will be reported upon in a subsequent paper.An obvious area for future work is to expand the studythrough a wider range of parameter space, including theintroduction of directional shear and of shear with dif-ferent orientations relative to the mean flow. We planto do this, as well as to study the effects of performingthe simulations on a b-plane and in regions with vari-ations in SST.

Acknowledgments. This research was supported bythe National Science Foundation Division of Atmo-spheric Sciences through Grant ATM-9523667, and theOffice of Naval Research Division of Marine Meteo-rology through Grant N00014-96-1-0582. The authorsalso wish to thank the two anonymous reviewers fortheir helpful comments.

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