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TIC FILE COPYNPS 68-89-008
NAVAL POSTGRADUATE SCHOOLMonterey, California
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THESISTHE EFFECTS OF CLIMATOLOGICAL AND TRANSIENT
WIND FORCING ON EDDY GENERATIONIN THE CALIFORNIA CURRENT SYSTEM
by
Robert W. Edson
September, 1989
Thesis Advisor: M.L. Batteen
Approved for public release; distribution is unlimited.
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NAVAL POSTGRADUATE SCHOOLMonterey, CA. 93943
Rear Admiral Ralph W. West, Jr. Harrison ShullSuperintendent Provost
This report was prepared in conjunction with researchconducted for Chief of Naval Research and Funded by the NavalPostgraduate School.
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Released By:
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11 TITLE (Include Security Classification) EFFECTS OF CLIMATOLOGICAL AND TRANSIENT WIND FORCING ONEDDY GENERATION IN THE CALIFORNIA CURRENT SYSTEM
12 PERSONAL AUTHOR(S)Robert W. Edson in conjunction with M.L. Batteen and C.S. Nelson
13a TYPE OF REPORT 13b TIME COVERED 14 DATE OF REPORT (Year, Month, Day) I15 PAGE COUNT
Master's Thesis FROM _ TO I September, 1989J 15516 SUPPLEMENTARY NOTATION The views expressed in this thesis are those of the author and do
not reflect the official policy or position of the Department of Defense or theU.S. Government.
17 COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number)FIELD GROUP SUB-GROUP Primitive equation model, eddies, jets, filaments,
wind forcing, coastal jet and undercurrent, wind stresscurl, California Current Svytem
19 ABSTRACT (Continue on reverse if necessary and identify by block number)
) A high-resolution, multi-level, primitive equation ocean model is used to examinethe response to transient and climatological wind forcing of an idealized, flat-bottomedoceanic regime on a beta-plane, along an eastern boundary. An annually periodic windforcing function with zonal variability is used as transient forcing in several exper-iments using both winter and summer initializations. When the curl component of theforcing is stronger than the stress, as in the wintertime, a surface poleward flowdevelops in the nearshore region with an equatorward flow offshore. When wind stressdominates the forcing, as in the summertime, a coastal jet develops with an undercurrent.
* In other experiments, spatially varying one degree and two tenths degree steady windstress data are used as climatological forcing. The one degree climatological windstress data has positive curl at the coast which causes a poleward surface flow to de-velop. When two tenths degree wind stress data is used in the nearshore area, both)
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positive and negative curl in the coastal region result in the formation of polewardand equatorward currents, respectively. As a result of convergence in the surfaceflow, eddies and a well defined cold filament develop. These results show that theinteraction of diverse coastal currents driven by an equally diverse wind field canpLay an important role in the production of cold filaments and eddies.-7\,;.
DD com 1473, JUN 86
I' ['t i if i e
Approved for public release; distribution is unlimited
The Effects of Climatological and TransientWind Forcing on Eddy Generation
in the California Current System
by
Robert W. EdsonLieutenant, United States NavyB.S., George Mason University
Submitted in partial fulfillmentof the requirements for the degree of
MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY
from the
NAVAL POSTGRADUATE SCHOOLSeptember, 1989
Author: ____________________________Robert W. Edson
Approved by: e2j " .
Mary L. Batteen, Thesis Advisor
e6 t J. 2 emtner, r. cn Reader
Curtis A. Collins, ChairmanDepartment of Oceanography
(;ordon ., Schachcr,Dean of Sciencc and Enpiinccring
iii
ABSTRACT
A high-resolution, multi-level, primitive equation ocean model is used to examine
the response to transient and climatological wind forcing of an idealized, flat-
bottomed oceanic regime on a P3-plane, along an eastern boundary. An annually
periodic wind forcing function with zonal variability is used as transient forcing in
several experiments using both winter and summer initializations. When the curl
component of the forcing is stronger than the stress, as in the wintertime, a surface
poleward flow develops in the nearshore region with an equatorward flow offshore.
When wind stress dominates the forcing, as in the summertime, a coastal jet develops
with an undercurrent. In other experiments, spatially varying one degree and two
tenths degree steady wind stress data are used as the climatological forcing. The one
degree climatological wind stress data has positive curl at the coast which causes a
poleward surface flow to develop. When two tenths degree wind stress data is used
in the nearshore area, both positive and negative curl in the coastal region result in
the formation of poleward and equatorward currents, respectively. As a result of
convergence in the surface flow, eddies and a well defined cold filament develop.
These results show that the interaction of diverse coastal currents driven by an equally
diverse wind field can play an important role in the production of cold filaments and
eddies.
iv
ACKNOWLEDGEMENTS
I wish to thank my thesis advisor, Dr. Mary L. Batteen, for her guidance and
help throughout my thesis research and writing. I would especially like to thank her
for her seemingly endless patience with my seemingly endless procrastination. The
help and data supplied by Craig S. Nelson is also gratefully acknowledged.
I would also like to thank my favorite coach, Arlene Bird, for her much
appreciated assistance in programming and for her understanding when I needed
someone to complain to. Finally, a special thanks to Chuck and Bernice without whom
finishing this thesis would not have been nearly as much fun.
Loosuon For
-iiS GRA&i
DTIC TABUnannounced QJustification
Avall.l..ty Coass
Aval ndorDist Speojal
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TABLE OF CONTENTS
I. INTRODUCTION ...................................... 1
A. BACKGROUND ON THE CALIFORNIA CURRENT SYSTEM ... 1
1. Regional Description ............................ 1
2. Climatological W inds ........................... 3
3. Numerical Model Studies ......................... 5
B. OBJECTIVES FOR THESIS .......................... 8
II. NUMERICAL MODEL OF THE CALIFORNIA CURRENT SYSTEM .... 17
A. MODEL DESCRIPTION ............................ 17
1. M odel Equations .............................. 17
2. Model Domain and Resolution ...................... 20
3. Finite Difference Scheme ......................... 21
4. Heat and Momentum Diffusion ..................... 22
5. Surface Thermal Forcing ......................... 22
6. Boundary Conditions ............................ 23
7. Initial Conditions . ............................. 24
B. SPECIFIC EXPERIMENTAL CONDITIONS ................ 24
1. Transient Wind Forcing (Exps. 1-2) .................. 24
2. One Degree Climatological Wind Forcing (Exps. 3-5) ....... 27
3. Two Tenths Degree Climatological Wind Forcing (Exp. 6) .... 29
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Ill. EXPERIMENT RESULTS ................................ 39
A. TRANSIENT WIND FORCING ........................ 39
1. Experim ent I ................................. 39
2. Experim ent 2 ................................. 41
B. ONE DEGREE CLIMATOLOGICAL WIND FORCING ......... 44
1. Experim ent 3 ................................. 44
2. Experiment 4 ................................. 47
3. Experiment 5 ................................. 49
C. TWO TENTHS DEGREE CLIMATOLOGICAL WIND FORCING . . 53
1. Experim ent 6 ................................. 53
D. STABILITY ANALYSIS ............................ 58
1. Experim ent 5 ................................. 59
2. Experim ent 6 ................................. 60
IV. COMPARISON OF MODEL RESULTS WITH OBSERVATIONS .... 119
V. SUMMARY AND RECOMMENDATIONS ................... 126
A. SUM M ARY ................................... 126
B. RECOMMENDATIONS ............................ 129
LIST OF REFERENCES .................................. 131
INITIAL DISTRIBUTION LIST ............................. 137
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LIST OF TABLES
Table I Constants used in the model .......................... 21
Table II Summary of experimental conditions .................... 32
Table III Instantaneous comparison of model experiments with model results ofBatteen et al. (1989) and observations of the CCS ............ 123
Viii
LIST OF FIGURES
Figure 1.1 Climatological wind stress for June (from Nelson, 1977)..... 11
Figure 1.2 Climatological wind stress for July (from Nelson, 1977)..... 12
Figure 1.3 Climatological wind stress for August (from Nelson, 1977). . 13
Figure 1.4 Climatological wind stress curl for June (from Nelson, 1977). 14
Figure 1.5 Climatological wind stress curl for July (from Nelson, 1977). 15
Figure 1.6 Climatological wind stress curl for August (from Nelson, 1977). 16
Figure 2.1 Study domain ............................... 33
Figure 2.2 Wind stress versus offshore distance for December ........ 34
Figure 2.3 Wind stress versus offshore distance for June .............. 35
Figure 2.4 Wind stress isopleths for one degree resolution climatological data overthe model domain .............................. 36
Figure 2.5 Sampling domain for the two tenths degree climatological wind stressforcing ......................................... 37
Figure 2.6 Wind stress isopleths for one degree / two tenths degree resolutionclimatological data over the model domain .............. .. 38
Figure 3.1 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s1), and (c) temperature (°C) for Experiment 1 at day 60......................................... 64
Figure 3.2 Surface isopleths of (a) zonal (u) velocity (cm s-'), (b) meridional (v)velocity (cm s'), and (c) temperature (°C) for Experiment 2 at day 5......................................... 6 5
Figure 3.3 Vertical cross-shore section of meridional (v) velocity (cm sl ) forExperiment 2 at day 10 .............................. 66
Figure 3.4 Vertical cross-shore section of temperature (°C) for Experiment 2 at day10 ............................................. 67
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Figure 3.5 Surface isopleths of (a) zonal (u) velocity (cm s-), (b) meridional (v)velocity (cm s-), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 2 at day 25 ............. 68
Figure 3.6 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 2 at day 30 .............................. 69
Figure 3.7 Surface isopleths of (a) zonal (u) velocity (cm s1), (b) meridional (v)velocity (cm s'), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 2 at day 80 ............. 70
Figure 3.8 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s'), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 2 at day 120 .......... .. 71
Figure 3.9 Vertical cross-shore section of temperature ('C) for Experiment 2 atday 120 ......................................... 72
Figure 3.10 Vertical cross-shore section of meridional (v) velocity (cm s-) forExperiment 2 at day 120 ............................. 73
Figure 3.11 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s-), (c) temperature (*C), and (d) dynamic height (cm)relative to 2400 m for Experiment 3 at day 40 ........... .. 74
Figure 3.12 Vertical cross-shore section of meridional (v) velocity (cm s1) forExperiment 3 at day 40 .............................. 75
Figure 3.13 Vertical cross-shore section of temperature ('C) for Experiment 3 atday 40 .......................................... 76
Figure 3.14 Surface isopleths of zonal (u) velocity (cm s') for Experiment 3 at (a)day 40, (b) day 50, (c) day 70 and (d) day 80 ........... .. 77
Figure 3.15 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 4 at day 40 ........... .. 78
Figure 3.16 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 4 at day 40 .............................. 79
Figure 3.17 Vertical cross-shore section of temperature (°C) for Experiment 4 at day40 ............................................. 80
x
Figure 3.18 Surface isopleths of (a) zonal (u) velocity (cm s-), (b) meridional (v)velocity (cm s'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 4 at day 85 ........... .. 81
Figure 3.19 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s-), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 4 at day 110 ............ 82
Figure 3.20 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 4 at day 110 ............................. 83
Figure 3.21 Surface current vectors for Experiment 4 at (a) day 40, and (b) day110 .. ..................................... 84
Figure 3.22 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s-), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 5 at day 10 ............. 85
Figure 3.23 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 5 at day 10 .............................. 86
Figure 3.24 Vertical cross-shore section of temperature (°C) for Experiment 5 at day10 ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Figure 3.25 Surface isopleths of (a) zonal (u) velocity (cm s-), (b) meridional (v)velocity (cm s-'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 5 at day 20 ............. 88
Figure 3.26 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 5 at day 20 .......................... 89
Figure 3.27 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 5 at day 40 ........... .. 90
Figure 3.28 Surface isopleths temperature (°C) Experiment 5 at day 55. . . 91
Figure 3.29 Surface isopleths of (a) zonal (u) velocity (cm s"), (b) meridional (v)velocity (cm s'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 5 at day 80 ........... .. 92
Figure 3.30 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 5 at day 80 .............................. 93
Figure 3.31 Vertical cross-shore sect'An of temperature (°C) for Experiment 5 at day80 ............................................. 94
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Figure 3.32 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s-), (c) temperature (*C), and (d) dynamic height (cm)relative to 2400 m for Experiment 5 at day 110 .......... .. 95
Figure 3.33 Vertical cross-shore section of temperature ('C) for Experiment 5 atday 110 ......................................... 96
Figure 3.34 Vertical cross-shore section of meridional (v) velocity (cm s"') forExperiment 5 at day 110 ......................... 97
Figure 3.35 Surface current vectors for Experiment 5 at (a) day 20, (b) day 40, (c)day 80, and (d) day 110 ............................. 98
Figure 3.36 Surface isopleths of (a) zonal (u) velocity (cm s-1), (b) meridional (v)velocity (cm s'), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 5 ............ .. 99
Figure 3.37 Surface isopleths of (a) zonal (u) velocity (cm s-), (b) meridional (v)velocity (cm s'), (c) temperature (0C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 10 .......... .. 100
Figure 3.38 Vertical cross-shore section of meridional (v) velocity (cm s") forExperiment 6 at day 10 ......................... 101
Figure 3.39 Vertical cross-shore section of temperature ('C) for Experiment 6 at day10 ... .................................... 102
Figure 3.40 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 6 at day 10 ......................... 103
Figure 3.41 Vertical cross-shore section of meridional (v) velocity (cm s1) forExperiment 6 at day 20 ............................ 104
Figure 3.42 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 6 at day 20 ............................ 105
Figure 3.43 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s1), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 25 .......... .. 106
Figure 3.44 Surface isopleths of (a) zonal (u) velocity (cm s"), (b) meridional (v)velocity (cm s"), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 40 .......... .. 107
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Figure 3.45 Vertical cross-shore section of meridional (v) velocity (cm s1 ) forExperiment 6 at day 40 ............................ 108
Figure 3.46 Vertical cross-shore section of temperature (°C) for Experiment 6 atday 40 ......................................... 109
Figure 3.47 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 80 .......... .. 110
Figure 3.48 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s-), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 100 ........... 111
Figure 3.49 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 120 ........... 112
Figure 3.50 Vertical cross-section of the cross-stream derivative of potential vorticitymultiplied by the grid size (°C m1 s-) scaled by 106 for the time-averaged days 90-99 of Experiment 5 ................ ... 113
Figure 3.51 Vertical cross-section of the cross-stream derivative of potential vorticitymultiplied by the grid size (°C m- s') scaled by 106 for the time-averaged days 1-12 of Experiment 6 ................... 114
Figure 3.52 Kinetic energy (ergs cm 3 ) time series for Experiment 6. . . . 115
Figure 3.53 Basin-averaged energy diagram for days 1 to 12 of Experiment 6.116
Figur.. 3.54 Vertical cross-section of the cross-stream derivative of potential vorticitymultiplied by the grid size (°C m s-') scaled by 106 for the time-averaged days 100-120 of Experiment 6 .............. ... 117
Figure 3.55 Basin-averaged energy diagram for days 100 to 120 of Experiment6 ............................................. 118
Figure 4.1 Current vector time series for a station (a) north of Cape Mendocinoand a station (b) south of Cape Mendocino ............ ... 124
Figure 4.2 Pilot moored instrument station locations during NCCCS program.125
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xi'
I. INTRODUCTION
A. BACKGROUND ON THE CALIFORNIA CURRENT SYSTEM
1. Regional Description
The California Current System (CCS) is a complex combination of several
ocean currents. Dominating this system is the California Current (CC), an eastern
boundary current extending approximately 1000 kilometers offshore with a
southeastward flow (Sverdrup et al., 1942; Chelton, 1984). The CC represents the
eastern limb of the North Pacific gyre (Lynn and Simpson, 1987), and is driven by the
large-scale North Pacific High (Huyer, 1983). Typically extending to only 300 meters,
this current is characterized by low temperature, low salinity and high dissolved oxygen
(Lynn and Simpson, 1987). The core of the CC is found approximately 100-200 km
offshore (Chelton, 1984). Average current speeds are less than 25 cm s- (Reid and
Schwartzlose, 1962; Bernstein et al., 1977), but daily average speeds as high as
50 cm s- have been recorded (Davis, 1985).
From the shoreline to roughly 100 km off the coast, there is evidence of a
separate current (Chelton, 1984; Hickey, 1979). This current has a seasonal variation
in flow direction which serves to demarcate it from the broader CC (Chelton, 1984;
Hickey, 1979). This nearshore surface current has been observed to have equatorward
flow from February through September extending - 125 km offshore (Hickey, 1979).
From November to February, this nearshore flow reverses direction and flows
northward in the area from Pt. Conception to Cape Mendocino (Hickey, 1979). Dtring
the winter season this flow is called the Davidson Current (Chelton, 1984; Hickey,
1979). This simplistic interpretation of the nearshore current is deceptive. The
nearshore mean flow between Pt. Conception and Pt. Sur has been observed to be
poleward during the summer, while the flow further north to Cape Mendocino has been
documented as flowing both poleward and equatorward during the same summer
months (Chelton et al., 1988; Freitag and Halpern, 1981). These observations further
highlight the variable nature of this region.
The California Undercurrent (CU) makes up the third major part of the CCS.
The CU is found over the continental shelf with a northward flow 20 to 70 km wide
(Hickey, 1979; Reid 1962). It has a core velocity greater than 15 cm s-1 with some
measurements as high as 40 cm s1 (Hickey, 1979; Reid 1962). With a vertical extent
of approximately 300 m, the core is usually located 200-250 m below the surface
(Wickham et al., 1987; Hickey, 1979). Reed and Halpern (1976) found the
undercurrent off Washington to have a vertical extent in excess of 500 m. They also
felt that the undercurrent they observed was an extension of the CU seen further south,
making the CU have a latitudinal extent of over 2200 km.
The fourth constituent of the CCS is the Southern California Countercurrent
(SCC). This current is comprised of the poleward flow found in the California Bight,
south of Pt. Conception (Hickey, 1979). The SCC has a semi-permanent eddy-like
circulation which seems to be strongly affected by the topography of the region (Lynn
and Simpson, 1987). While this current is an important part of the CCS, it does not
enter into the area modeled and as such will not be considered further.
2
The California Current System is not a quiescent, stable system of currents
with a well defined, unchanging structure. Rather, the flow fluctuates greatly in both
time and space (Chelton, 1984). Irregularities in the flow were noted as early as 1950
(Reid, 1988). There exist mesoscale meanders, eddies, filaments and jet-like surface
currents which are superimposed on the large scale flow (Bernstein et al., 1977;
Chelton, 1984). Eddy-like features with wavelengths of 100-150 km (Freitag and
Halpern, 1981; Bernstein et al., 1977) have been documented and are prevalent in most
current satellite observations (e.g., Ikeda and Emery, 1984; Ikeda et al., 1984a,b; Kelly,
1985). The current itself may take the form of a meandering jet, with wavelengths of
300 to 500 km (Bernstein et al., 1977). These meanders have associated with them
cold filaments, exhibiting a 1 to 3 'C temperature change across their boundaries
(Bernstein et al., 1977). The filaments can extend to 100 m, with a width of 30 km
and peak speeds of up to 80 cm s' (Kosro and Huyer, 1986). The combination of
these features leads to a new conceptualization of the CCS as a system of currents with
filamented jets and synoptic-mesoscale eddies modifying the mean flow (Mooers and
Robinson, 1984).
2. Climatological Winds
Interaction between the North Pacific subtropical high and the southwest
United States thermal low, two relatively stationary systems in the summer, establishes
the summer wind patterns seen in the CCS (Nelson, 1977; Halliwell and Allen, 1987).
The wind regime is further complicated by the interaction of these two systems with
propagating atmospheric disturbances (Halliwell and Allen, 1987) and other atmospheric
mesoscale phenomena (Huyer, 1983). Within 100-200 km of the shore, the winds are
3
additionally affected by coastal atmospheric boundary layer processes, resulting in
measured wind fluctuations strongly polarized in the alongshore direction (Halliwell and
Allen, 1987).
The climatological wind stress for the summer months is favorable for
upwelling with a mean alongshore equatorward component (Nelson, 1977; Halliwell and
Allen, 1987; Wickham et al., 1987). An alongshore wind stress time series compiled
over nine years by Strub et al. (1987) clearly depicts the dominance of equatorward
wind stress during the summer. Halpern (1976) found similar conditions of southward
wind stress during July and August in a study conducted off the coast of Oregon. The
long term means for the surface wind stress for June, July, and August are shown in
Figures 1.1, 1.2, and 1.3, respectively. It is important to note the maximum core of
the wind stress (denoted by shading in the figures) which extends along the California
coast for 1000 km. The wind stress values reach a maximum off Cape Mendocino in
June and July (Nelson, 1977), with values greater than 1.5 dynes cm "2 . This maximum
is originally seen in March, south of Point Conception, and it intensifies and shifts
northward over the year. Also seen in these figures is that the alongshore stress
component is larger than the cross-shore component. The climatological winter wind
stress regime is much weaker (typically less than 0.5 dynes cm2 ) but is still
equatorward in the region from Cape Mendocino to Baja, California (Nelson, 1977).
Finally, Nelson (1977) found that the wind stress velocities can vary a large amount
both spatially and temporally, making any analytical representation of the wind stress
field extremely difficult.
4
There is positive wind stress curl at the coast during all months of the year
with the strongest curl occurring from May to September (Nelson, 1977; Halpern,
1976). The wind stress curl plots for the summer months are shown in Figures 1.4
through 1.6. Bakun (1987) found that anticyclonic wind stress curl dominated the
offshore region giving convergent Ekman transport, Ekman pumping downward from
the surface and equatorward Sverdrup flow. Conversely, at the coast he found cyclonic
wind stress curl, i.e., divergent surface Ekman transport, upward Ekman pumping,
oceanic upwelling, and poleward Sverdrup flow. A zero wind stress curl line occurs
parallel to the coast approximately 200-300 km offshore in the spring and summer
upwelling seasons coincident with the offshore wind stress maximum (Nelson, 1977;
Chelton, 1984).
The importance of the wind stress and wind stress curl in the current
dynamics and upwelling of the CCS is well documented (e.g., Huyer, 1983; Nelson,
1977; Chelton, 1984; Hickey, 1979; Kelly, 1985). Wind stress data has been correlated
with satellite infrared imagery of eddies and filaments, illustrating the possible
importance of wind stress in these mesoscale processes (Kelly, 1985; Wickham et al.,
1987). However, the roles of the wind stress and wind stress curl in eddy and jet
generation is not clearly understood. It is this phenomena which is the thrust of this
research.
3. Numerical Model Studies
The complexity of the CCS has led to tremendous diversity in numerical
model studies of this region over the last two decades. This section makes no attempt
to review all past studies, but rather will concentrate on those modeling experiments
5
with direct application to this research. More extensive reviews are included in Allen
(1980), Chelton (1984), and O'Brien et al. (1977). The primary thrust of this thesis
is wind forcing of the CCS. Within this area, however, classification can be made as
to whether the wind forcing is steady or transient and whether the forcing contains a
curl component or is curl-free. Further divisions are possible, but will be avoided here
for simplicity.
Initial studies primarily concentrated on the application of steady wind stress
forcing on a modelled current system. Chief amongst these studies was Pedlosky
(1974). He found that steady equatorward wind stress drives a baroclinic equatorward
jet, and that an undercurrent is not necessarily formed. If positive wind stress curl is
introduced at the coast, a barotropic poleward coastal flow develops. If the stress is
strong enough at the coast, the baroclinic jet may override the poleward flow and an
equatorward jet may result in addition to an undercurrent.
One of the first transient wind forcing numerical model experiments was
done by Philander and Yoon (1982). Their periodic forcing was meridionally restricted
but otherwise constant in the cross-shore and alongshore direction. The particular
response of the model depended on the frequency of the wind forcing. At low
frequencies the response spreads offshore, while at high frequencies the response is
coastally trapped. It should be emphasized that there was no positive wind stress curl
at the coast in Philander and Yoon's study.
The response of reduced-gravity models to realistic coastal winds was
investigated by Carton (1984) and Carton and Philander (1984). They utilized
temporally varying one degree resolution geostrophic winds to force their model and
6
found a time dependency in their results. At periods of less than 50 days the coastal
current was trapped within a Rossby radius of deformation of the coast and the
alongshore flow was well correlated with the alongshore stress. At periods longer than
50 days, wind stress curl became important, and at 100 days the alongshore currents
began to weaken and disperse, becoming a series of alternating jets.
The remaining three studies are most directly applicable to the
experimentation of this thesis. McCreary et al. (1987) did a series of experiments
utilizing a linear model with both transient and steady wind forcing. The wind forcing
included stress functions both with and without curl. Steady, equatorward, curl-free
wind forcing resulted in an equatorward surface jet and an undercurrent. If steady,
positive wind curl was used to force the model, a broad, deep, poleward surface current
developed near the coast. In addition to this poleward current, the positive curl also
forced equatorward flow offshore. Similar results were obtained from the periodic wind
forcing. An additional experiment was done by McCreary et al. in which an idealized
representation of the wind field was varied over an annual cycle to force the model.
This idealized forcing included both a wind stress and wind stress curl component. In
this experiment, the curl accounted for both the Davidson current and the equatorward
flow offshore. Only during those times in the forcing cycle when stress was strong
compared to the curl component was the equatorward jet and undercurrent seen. In all
of these experiments no eddies or filaments were developed.
Tielking (1988) extended this work by conducting numerical simulations
utilizing a full primitive equation model. His forcing was derived from meridionally
averaged summer climatological data for the region of central California. The forcing
7
varied only in the cross-shore direction, had a positive curl at the coast and was steady
throughout the experiment. Tielking obtained results similar to those of McCreary et
al., i.e., strong broad poleward flow at the coast, equatorward flow offshore, no
undercurrent, and no eddies or filaments.
The final study was done by Batteen et al. (1989). Again a primitive
equation model was used and the forcing took two forms, steady forcing constant
throughout the domain and forcing which varied meridionally. The constant stress
forcing resulted in an equatorward jet and an undercurrent. Additionally, the shear
between the jet and undercurrent led to instability and the production of eddies in the
coastal region. Similar results were seen when the model was forced by wind stress
which varied in y only. In neither case was there any curl at the coast in the cross-
shore direction.
It appears from these studies that equatorward wind stress is dominant in
forcing the coastal jet and undercurrent, and further, is instrumental in the instability
processes which lead to eddy production in the CCS. Conversely, positive wind stress
curl at the coast develops poleward surface flow with no eddies or filaments.
Interaction of these two components can lead to a mixed current structure at the coast,
but eddies and filaments not necessarily develop. Finally, there seems to be a time
scale to the relative importance of the stress and curl components.
B. OBJECTIVES FOR THESIS
The preceding two sections highlight a problem in the study of upwelling off the
California coast. Clearly, the prevailing surface wind pattern during the summer
upwelling season is one of strong equatorward wind stress, oriented predominantly in
8
the alongshore direction. Additionally, there is strong positive climatological wind
stress curl at the coast during this same season. It is these two characteristics,
alongshore equatorward stress and positive wind stress curl at the coast, that are
dominant during the summer. However, when numerical studies are conducted to study
the contributions of the wind stress and wind stress curl to the mesoscale processes of
the region, conflicting results are found. When wind stress alone is utilized as a
forcing mechanism, an equatorward jet and undercurrent are seen and eddies result.
When wind stress curl is applied, a poleward surface flow is generated at the coast and
no eddies are formed. Simply put, what is seen in model results does not agree with
what is seen observationally.
Two logical paths arise at this stage towards the further study and resolution of
the aforementioned paradox. First, it is possible that transient forcing is required to
produce more realistic results. McCreary et al. (1987) applied a transient wind stress
forcing function to CCS numerical simulations, but utilized a linear model in his
studies. A first objective of this thesis research is to apply an annually periodic wind
forcing function, with both a stress and curl component, to a fully nonlinear primitive
equation numerical model of the CCS and study the resultant mesoscale events.
The second possibility for continued research lies in the area of the exact
formulation of the wind stress forcing itself. Most studies to date have utilized forcing
which was either constant throughout the domain or which varied in only one direction.
Possibly it is not the relative weight of stress versus curl that is important in forcing
instability, but rather full two dimensional variability in the forcing field. With this
in mind, a second objective is to study the effects of climatological winds varying in
9
the cross-shore and the alongshore direction on eddy formation in the CCS. A final
objective will be to apply various energy analysis techniques to the above studies to
characterize the energetics of the CCS under the applied conditions of these numerical
model experiments.
The thesis is organized as follows. Section II discusses the numerical model used
in the research as well as the conditions unique to each experiment. Experimental
results with the associated energy analyses are presented in Section I1. A comparison
with observations is made in Section VI, and a summary and recommendations are
presented in Section V.
10
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140
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160
II. NUMERICAL MODEL OF THE CALIFORNIA CURRENT SYSTEM
A. MODEL DESCRIPTION
1. Model Equations
The numerical model used in this research was developed by Haney (1974,
1985) and modified by Batteen (1989). Most recently, the model, including specific
modifications applicable to this study, has been thoroughly detailed in Batteen et al.
(1989) and that discussion has been summarized here for the convenience of the reader.
The model is a multilevel, primitive equation (PE) model which uses hydrostatic, rigid
lid, and P-plane approximations. While the model also has a topographic capability,
a flat-bottom is used in this study to ensure separation of the wind forcing role from
the possible coupled role of wind forcing with bottom topography. The governing
equations are as follows:
a. Momentum Equations:
du -1 D~VA VUK ,i+dU (2.1)d.. .1 + fv -Am V'u + K. Lu.-u + 8d(11)(21
dt P" ax aZ2
dy -_1 v - fu A. Vu +K. .v + ,d(V) (2.2)dt p, DY aZy
b. Continuity Equation:
W r(Du + D dr) (2.3)f_1 a.x Dyj
17
c. Vertically Integrated Hydrostatic Equation:
PJ pgd-J[J pgd ] dz (2.4)
d. Equation of State:
p = p (1 - C (T - T)) (2.5)
e. Thermodynamic Equation:
dT = -A V4T + K, H + Q+ 8 (T) (2.6)dt ail
In the above equations, t is time, (x,y,z) is a right-handed cartesian coordinate system
with x pointing towards the shore, y alongshore, and z upward, with (u,v,w) being the
corresponding velocity components. Temperature is denoted by T, density by p, and
the departure of the pressure from the vertically averaged pressure by p'. In equations
(2.3) and (2.4), is a dummy variable of integration. Equation (2.4) includes the
assumption that the depth-averaged pressure is a constant (assumed zero); i.e., the
barotropic mode is ignored in this study. Equation (2.5) assumes that density is a
function of temperature only. This assumption is consistent with the region being
modeled (Lynn et al., 1982). Salinity may be a good water mass tracer in the CCS
(Huyer and Kosro, 1987; Lynn and Simpson, 1987), but inclusion of salinity in the
calculations is not essential for a zero-order description of the CCS because there are
no major sinks or sources of salinity in the model area.
In (2.6), Q, = aS / (p0 C az) is the heating due to solar radiation, with
S = S, (Rel ' + (I - R)ej zl) (2.7)
18
Here S, is the downward flux of solar radiation at the surface, R = .62 is the fraction
of solar radiation absorbed in the upper few meters (z, = 1.5 m) and (1 - r) = .038 is
the fraction that penetrates to somewhat deeper levels (z, = 20 m) as given by Paulson
and Simpson (1977) . The terms Sd(U), 8d(v), and 5d(T) represent the vertical turbulent
mixing of heat and momentum by a dynamic adjustment mechanism. This adjustment,
a generalization of the convective adjustment mechanism, is based on the assumption
of a critical Richardson number, and it serves to maintain dynamic stability in the
water column (Adamec et al., 1981).
The boundary conditions at the top (z=0) of the model ocean are:
K au = 0 (2.8a)az
K. av = t/p, (2.8b)az
K11 aT = (2.8c)
az
w = 0, (2.8d)
and at the bottom (z = - H) they areK,, u = C, (u + v2) (u cos y - v sin y) (2.9a)
K. = CD (u2 + v2)1, (v cos y- u sin y) (2.9b)
KH T = 0 (2.9c)
w = 0 (2.9d)
In (2.8b), T is the alongshore component of the surface stress which is varied in
accordance with the experimental conditions as noted. In (2.8c), Q is the net upward
19
flux of longwave radiation, sensible and latent heat across the sea surface which is
described below. In (2.9a,b), y = 100 is a geostrophic inflow angle (Weatherly, 1972).
The bottom stress in (2.9a,b) represents one of the simplest possible parameterizations
of a bottom Ekman layer. Table I provides definitions for other symbols used in the
model equations. This table also provides values for the constants used throughout the
study.
2. Model Domain and Resolution
The domain of the model is rectangular in shape covering an area of 60 of
latitude by 60 of longitude. The area of interest extends from 124' to 130'W and
from 36.5' to 42.5)N (Figure 2.1). Extending off the coast of central California
approximately 512 km, the model extends from Pt. Sur in the south to Cape Blanco
in the north (640 km). The horizontal model grid is comprised of 65 by 65 points
with 8 km resolution in the cross-shore direction and 10 km resolution in the
alongshore direction. This horizontal resolution is adequate for resolving mesoscale
features in the CCS whose scales are approximately 100 to 300 km (Bernstein et al.,
1977; Breaker and Mooers, 1986; Freitag and Halpern, 1981). The California coast is
approximated with a straight line and topography is ignored. Both of these
approximations are necessary to allow for the isolation of wind forcing effects from
other contributing factors.
20
Table I Constants used in the model.
VALUE DEFINITION
C 0.958 cal gm(K)1 specific heat of sea water
CD 1.225 x 10 drag coefficient
T. 278.2 0K constant reference temperature
p. 1.23 x I0. gm cm 3 density of air
P. 1.20276 gm cm 3 density of sea water at T
cx 2.01 x 10A(OK) 1 thermal expansion coefficient
K 10 number of levels in vertical
Ax 8 x 10' cm cross-shore grid spacing
Ay I X 106 cm alongshore grid spacing
D 4.5 x 10' cm total ocean depth
At 800 s time step
f. 0.93 x 10' s' mean Coriolis parameter
g 980 cm s acceleration of gravity
AM 2 x 107 cm4 s2 biharmonic momentum diffusioncoefficient
AH 2 x 10 17 cm 4 S- biharmonic heat diffusion coefficient
K.M 0.5 cm 2 s1 vertical eddy viscosity
Kl 0.5 cm2 s vertical eddy conductivity
Ps 1013.25 mb surface air pressure
0 2 7 day -' earth rotation rate
3. Finite Difference Scheme
A space-staggered B-scheme is utilized for differencing in the horizontal
(Arakawa and Lamb, 1977; Batteen and Han, 1981). A sigma coordinate system is
incorporated in the model giving 10 layers in the vertical. Since bottom topography
is ignored, these layers are separated by constant z-levels at depths of 13, 46, 98, 182,
21
316, 529, 870, 1416, 2283 and 3656 m. This vertical spacing is advantageous in that
it allows more layers to be concentrated in the upper, more dynamically active surface
region.
4. Heat and Momentum Diffusion
Biharmonic lateral momentum and heat diffusion are used in the model to
allow for less restriction of baroclinic and barotropic instability processes. Laplacian
lateral heat diffusion can decrease baroclinic signals associated with eddy generation
(Holland and Batteen, 1986). Further, biharmonic diffusion is selective for scales
smaller than those of eddies (Holland, 1978), therefore allowing eddy generation as a
result of ba 3clinic and barotropic instability mechanisms.
5. Surface Thermal Forcing
The solar radiation at the sea surface, S., was specified to be the summer-
and CCS-mean value from Nelson and Husby (1983). The sum of the net longwave
radiation, latent and sensible heat fluxes, Q, was computed during the model
experiments from standard bulk formulas (Haney et al., 1978) using the summer- and
CCS-mean value of alongshore wind, cloud cover, relative humidity, air temperature
and model-predicted sea surface temperature. The sea surface temperature for the
experiments of this study was chosen so that the total heat flux across the sea surface,
S, - Q, was zero at the initial time. The only surface heat flux forcing, therefore, was
that which developed as a result of sea surface temperature variation being forced by
the wind. This highly simplified formulation of the surface thermal forcing in the
model was utilized to focus the study on wind forced variation of the thermal structure
22
in the CCS. Further discussions concerning both the necessity and applicability of this
formulation are found in Batteen et al. (1989) and Haney (1985).
6. Boundary Conditions
The California coastline is modeled as a straight, vertical wall and represents
the eastern boundary of the model. A no-slip condition is imposed on the tangential
velocity at the coastline.
The northern, southern, and western boundaries are open (Camerlengo and
O'Brien, 1980). The application of open boundary conditions can lead to unrealistic
results in studies utilizing wind forcing if the forcing is applied to the entire domain
including the open northern and southern boundaries. Uniform wind forcing of this
form will result in a steady alongshore current which is both too strong and too deep,
and is also equatorward with no undercurrent (McCreary, 1981). Following the work
of Batteen et al. (1989) and McCreary et al. (1987) wind band forcing of the form
t = To Y(y) (2.10)
is used in all model runs to generate a more realistic current structure. The wind stress
forcing at a location is represented by ;o and will vary in these experiments in either
x alone, or in both x and y depending on the specific experimental conditions. Y(y)
is the imposed latitudinal variation in the stress given by the following equation:1 100 km < y < 600 km
Y(y) = (2.11)1. 0 otherwise.
This form for Y(y) results in the imposition of wind forcing in the interior of the
model domain only and allows for the propagation of coastal trapped Kelvin waves.
23
It is these Kelvin waves which produce the alongshore pressure gradient and the
resultant surface trapped coastal jet and undercurrent (Batteen et al., 1989).
7. Initial Conditions
The model has the option of being spun up from rest by surface winds or
heat flux, or being initiated with a specific current field. All experiments conducted
in this study were started from rest and forced using wind stress alone. The specific
wind forcing conditions of each experiment are discussed in the following section.
An exponential temperature profile was used in all experiments to give the
mean stratification. This profile had a length scale of h = 450 m and took the form
T(z) = TB + AT ez , (2.12)
where TB = 2 'C is the temperature at great depth and AT = 13 °C is the temperature
change from the bottom of the ocean to the surface. This temperature profile is
considered to be representative of the long-term, mean climatological temperature
stratification of the CCS and was developed by Blumberg and Mellor (1987) for use
in the Dynalysis of Princeton model.
B. SPECIFIC EXPERIMENTAL CONDITIONS
1. Transient Wind Forcing (Exps. 1-2)
a. Experiment 1
Transient wind forcing as a mechanism for baroclinic / barotropic
instability is a poorly understood phenomenon. McCreary et al. (1987) have laid a
strong foundation for the study of transient wind forcing in their work and it is the
24
purpose of the first two experiments to expand on this previous study. They utilized
a viscid linearized model to investigate the effects of annually periodic wind stress
forcing on the dynamics of the CCS. The forcing used is as shown below in Equation
2.13 (McCreary et al., 1987, Equation 11).
' y = to Y(y) (.5 + .4 e-ial) + to X(x) Y(y) (.45 + .15 e-i ) (2.13)
In this equation rY represents the meridional stress; to is an initial stress value set
equal to -1 dyne / cm2; a is an oscillatory annual period equal to 2n / year; t
represents time, with June 1 set equal to zero; Y(y) is a meridional weighing function;
and X(x) represents the zonal distribution of the stress. McCreary et al. used a cosine
function to taper the meridional distribution of the stress at the northern and southern
boundaries. In this study Y(y) was formulated as previously described. The X(x)
weighing function acts to modify the wind stress component of Equation 2.13 and
produces wind stress curl in the model domain. The exact formulation of X(x) is given
by
sin 7 IxI -A < x <0X(x) 2 A (2.14)
1, x _-A
where x is equal to zero at the coast and A is equal to 200 km.
Equation 2.13 represents two distinct forcing terms. The left half of
the right hand side (RHS) of the equation, r, Y(y) (.5 + .4 e-ia), represents the
meridionally constant wind stress portion of the forcing function, while the other half
of the RHS, t, X(x) Y(y) (.45 + .15 e-im), acts to produce the wind stress curl part of
the idealized wind field. This formulation gives a maximum positive curl at the coast
and non-zero means for both the stress and curl components of the wind field. These
25
two characteristics correlate well with observations of the CCS (Nelson, 1977; Hickey,
1979). Additionally, this formulation allows the relative contributions of each
component to vary over the annual cycle.
Experiment 1 is forced throughout the domain with Equation 2.13. The
experiment was initialized with a t value equal to December 1 and the equation utilized
the same time step as found in the model, 800 seconds, with t being reset to 0 on June
1 in a cyclic manner. December is a minimum in the strength of the forcing function,
but is also the month when the ratio of wind stress to wind stress curl is the smallest
so that the curl makes its largest relative contribution. The December starting point
was chosen to allow the model sufficient time to spin up and establish a proper current
structure before the upwelling season begins (usually around March). Figure 2.2 shows
a graph of the initial forcing function compared to the climatological values of Nelson
(1977). Although the full wind stress / curl formulation of McCreary et al. (1987)
does follow the trend of the climatological data, it is seen that the climatological values
are more positive (less intense) throughout the region.
b. Experiment 2
Experiment 2 was the same as Experiment 1 except for the starting
date. A time value of June 1 was used to initialize the experiment to allow the
two extremes (i.e., December and June) of the forcing function to be tested. June
represents the maximum forcing values from Equation 2.13 and the largest ratio of
wind stress to wind stress curl. This maximum correlates well with observations for
the month of June (Nelson, 1977), a major upwelling month. Starting at this time also
more closely resembles Experiments 3 through 6 which were initialized with the strong
26
climatological wind stress values seen in the summer months. A plot of Equation 2.13
for June 1 with comparisons to climatological data is given in Figure 2.3 and again
it is seen that the Equation 2.13 solutions of McCreary et al. (1987) are stronger than
climatology. All other factors remained the same as in the above experiment.
2. One Degree Climatological Wind Forcing (Exps. 3-5)
a. Experiment 3
The wind stress field for Experiment 3 was derived from Nelson (1977).
Nelson utilized historic ship reports covering a time period from the mid-19th century
to 1972 to compile monthly wind stress and wind stress curl averages for one degree
boxes along the west coast of the United States.
The north-south component of the monthly stress averages of each one
degree block for the months of June, July and August were averaged giving a mean
summer stress value for each block. (Refer to Figures 1.1 through 1.6 for the
appropriate monthly plots.) These one degree summer stress averages were then
utilized to initiate the model. The cross shore (east-west) wind stress component is
much less then the alongshore component and can be ignored for a first order
approximation (Nelson, 1977; Chelton et al., 1987). The six degree by seven degree
(six by seven points) climatological stress domain was fit to the 65 by 65 model grid
utilizing a bivariate interpolation scheme after Akima (1978).
The original one degree stress values were computed such that the
average was valid in the middle of a one degree box. As a result, the first stress value
available for the interpolation was actually 42.5 km (one half of a degree of latitude)
27
offshore. The interpolation scheme had a closed boundary to interpolate to except at
the coast. This inconsistency led to the necessity of some form of artificiality in the
coastal wind field. The nearshore region is possibly the most dynamically important
area in the coastal upwelling region (Philander and Yoon, 1982; Allen, 1980) and as
such, the treatment of this region becomes of major importance.
In Experiment 3 the wind stress in the nearshore region, within 48 km
of the coast throughout the north-south extent of the model, was set constant to an
equatorward stress of 1 dyne cm2 . This value for wind stress is a good approximation
of the summer climatological mean for the area of the model domain (Nelson, 1977).
This treatment of the wind stress eliminates all spatial variability in the nearshore
region, reducing the total wind stress curl to zero. Neglecting wind stress curl in the
nearshore region can be justified via a scaling argument (Allen, 1980), but again, the
effects of this neglect are not clearly understood.
b. Experiment 4
Experiment 4 utilized wind stress fields developed in a manner similar
to that of Experiment 3, again using data from Nelson (1977). The difference in the
two experiments lies in the treatment of the wind field next to the coast. In
Experiment 4, the wind stress was set constant in the east-west direction in the region
within 48 km of the coast. This method of portraying the nearshore wind stress field
has the advantages of using real wind stress values, i.e., ones obtained from a closed
boundary interpolation, in the data poor region near the coast, and it also allows for
change in the meridional wind field in the coastal region. However, setting the wind
stress zonally constant does result in zero curl in this region. The curl in the coastal
28
region of the west coast of California has been shown to be climatologically positive
(Nelson, 1977). Even though spatial diversity in y has been introduced in the
nearshore region, it still does not accurately represent climatology.
c. Experiment 5
Experiment 5 represents the first simulation utilizing full two
dimensional surface wind stress forcing throughout the entire model domain. As in the
previous 2 experiments, one degree climatological wind stress data was used for forcing
(Nelson, 1977). In Experiment 5, the interpolation routine is allowed to extrapolate the
trend established just offshore to obtain values for the nearshore wind stress field. The
resultant model wind stress field, varying in both x and y, is shown in Figure 2.4. It
was this interpolated wind stress field that was used to initialize the model. As will
be seen later, the interpolated wind stress field compares well with finer resolution
data. There is a zero curl line off the coast at - 128 km and positive curl at the coast
throughout the model. However, the stress maximum does reach the coast at y - 280
km, lower than is actually seen climatologically.
3. Two Tenths Degree Climatological Wind Forcing (Exp. 6)
a. Experiment 6
Experiment 6 was initiated utilizing a wind stress field derived from
monthly stress averages calculated for two tenths degree boxes along the western coast
of California (Nelson, Unpublished Data). The data was compiled in a manner similar
to the two tenths degree data above (Nelson, 1977; Parrish et al., 1983; Nelson,
Personal Communication). The stress values were based on approximately two million
29
historical ship observations in the Tape Data Family II (National Climatic Center,
NOAA/EDIS/NCC, Asheville, N.C.) accumulated from the mid-1800's up to 1979. The
observations were biased towards the coastlines and transoceanic shipping lanes, making
the data sparse nearshore region of Experiments 3, 4 and 5 the most heavily sampled
area. A single pass editor was used to remove gross errors in the data, including
erroneous position reports and observations which exceeded extreme value limits. Upon
completion of editing, independent monthly averages were calculated for each two
tenths degree square. A summer mean for each block was computed by averaging the
monthly means for June, July and August. Since the original block values were
calculated independently of each other, several areas of erroneous data developed in the
averaged field. To smooth out these isolated discontinuities, the summer mean data
was run through a three by three median filter (Rabiner et al., 1975).
The averaged, smoothed two tenths degree data covered an area from the
coast to 255 km offshore, and 640 km alongshore, from 36.550 to 42.55' N. The data
was sampled as depicted in Figure 2.5, paralleling the coast as closely as possible.
The fine resolution of the data enabled the acquisition of wind stress values right at
the coast, i.e., there is now a closed boundary at the coast. No artificiality is
introduced by the interpolation scheme. The 16 X 31 two tenths degree data grid was
interpolated to fit the model grid of 8 km X 10 km resolution (Akima, 1978). The
area offshore where two tenths degree data was unavailable was filled utilizing
interpolated one degree data from above. The resultant wind stress field used in this
experiment is shown in Figure 2.6.
30
The two tenths degree data has several advantages over the one degree data
used in the previous experiments. First, interpolation was possible right up to the coast
eliminating the artificiality and approximations required in Experiments 3, 4, and 5.
The complexity of the wind field in the nearshore region was greatly enhanced giving
a much more realistic portrayal of actual conditions. Secondly, even in the offshore
region more detail in the wind stress field is noted. Of particular interest is the jet
extending up across the domain from 260 km to 440 km in the alongshore direction,
and from 160 km offshore to the coast at the top of its extent. The upper maximum
of this jet is roughly coincident with Cape Mendocino, an area of climatologically
strong wind stress (Nelson, 1977). In contrast, the maximum value found for the
interpolated one degree data (Figure 2.4) is not as large, it covers a much wider, less
concentrated area, and it reaches the coast at y - 280 km, much lower in the domain.
Specific conditions for all experiments in this thesis are summarized in Table II.
31
o U--. _ o.2
-o
z z
ciZ
a E4
z z z z
zr
E - - U - U ;S> E E > E9 A'
EE
i r. S-4E
S- o a ' -
32
0
00
0 C\1
0 Slz0
4z)4
0 ;,
toCV2
-4
0
CD2
0N
0) L 0(1 CO
Figure& 0. td oan h etnl ereet h rmtvqain(Emoe doan atyer i ees
z3
Q ~C
OD
It
DtLO
M 00
f- Zn - (3
C0_ = 7 'r -: - ::
.)_ - .,
Z 2z 'CE) ,
CLO - - ;ED 1, , CfD
.--.
LD ro Z71fM
LOnLU Z Z (CD ':: j
0 :,
m LI
Li C-
LiiIL CIL I I I ,# 1
.. . 0 'a 0 0 0
Ift)
CDCD I
44
oO CO/CD "1 '41- C i)
Figure 2.2 Wind stress versus offshore distance for December. The climatologicalwind stress data is an alongshore average with the seasonal averagebeing comprised of December, January, and February (Nelson, 1977).McCreary's Equation 11 (McCreary et al., 1987) is given in Equation
2.8 of this thesis. Solution of this equation was made for December1.
34
CD
CrnLi C:)
Vf) .4 ~L)
zcrco
LL.1 x CD, C
. "r .,
F- z r rO
N r. : \3I"1 CD r, ,: , CD• c , , C7 :
z z'M. U
LDC) L : (\3
Z o 6Cr-4 t' 0 )
cy-- to Ir-
CD
.4" to
Cc r)
l | I I I I I I
I I I I I I I
Figure 2.3 Wind stress versus offshore distance for June. The climatological windstress data is an alongshore average with the seasonal average beingcomprised of June, July, and August (Nelson, 1977). McCreary'sEquation 11 (McCreary et al., 1987) is given in Equation 2.8 of thispaper. Solution of this equation was made for June 1.
35
C) ' I
a.) -- • s r
(0
- I
-.. . . . . - , , O
- - - - - CD_
I / S
CD C,
CD
L I
LU~)
(L44
/ , \.
t sI \
L,2s" ,'1' ",'(o,
N \C.9 , C., " t-
/_ ,, ,
/ I •
77 C ,'
ri i) U C W
C) I'* I" I " I " 1 !
II I1 ' I " II " ' 1
-I r) ) (C - . r-J) ) a IC) 0",IU Ci (tI () V I') Cn t t ) r" (J (NI I -i
L I 'I NICE OFF 51 URE (KM)
Figure 2.4 Wind stress isopleths for one degree resolution climatological data overthe model domain. Contour interval is .2 dyne / cm2.
36
3 3 3 3 I 3 3 3 1 1 3 3i i
I I I 3 3 I 3 3 I 3 3 3
3 3 3 3 3 3 I 3 3 3
3 3 I 3 3
42 0 30 ' N .' ' " ''-' L ''
3 3 3 3 3 3 3 I 3 I 3 3
I3 I 3 3 3 3 3 3 3 3
41-30N -- r- -------- - - -I I 3 3 3 3 3 3 3 3 I 3i 3 3 I I 3 3 3 3 I I I I
3 I 3 3 3 3 3 3 3 3
Si 3 3 3 I I 3 33 3 3 I 3 3 I I 3 340'30' N . . . . . .T
3 8 3- 2 - - - - , -, - - - - - - - - - - , - - -,- - -
3 I 3 I I I I 3 I I
3 I 3 3 3 I 3 3 3 3 3 I
- .- _L- - --.-.--.--- . _. _
3 5' 3 3 3 3 3 3 3 3
1 I I V I 1 2 I 1 i 3 I
380 30' N -- -- -- - -, ---- , -, -3-, - -- ---- 3 ----3I3 3 I3 I 3 I I 3 I
3 3 I 3 3 1 I 3 3 3 3 3 3
^~ .J '., . .. , --- -,. ...- L,-- L.... .,- -.- ,- -- - 4 -
I 3 3 3 3 3 3 I 3 I I I I 3 3 ,
3 2 S d fr t7 0w h I c a t a w30N-------------------------- '--------------K"
3& '30' N -- , ... . . . , , . . . . . . . )
i I I 3 3 I 3 3 3 3 3 3 3 I 3 I I 3 \
3 3 I 3 3 3 I 3 3 3 r 3 3 3 I--- -- -- -- -- "_,, ,------ ,--- -------- ,--,-----,, ,, ',,, ',
35 030 ,'N1310 W; 1290 XV 1270 XV 1250 XV i23 ° X,'" 1210 "XV
Figure 2.5 Sampling domain for the two tenths degree climatological wind stress
forcing. Sampled area is outlined.
37
( 0
CI)
S- - - - - -;
CO
|I
it
,- , , ,,.o, , ,
.V C. W, .0
a ] q - cx l " ut 1) I cc) u ) ( 'J a ) I li C :
4 .4
-I t-) I - I
LJ: I 5 1 1 C O F 51 -O R K I
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,
.
38- .4 -
.4 ,/,
I, .1 -' ,4I4
I .#4 l
S lt
t • I
- , '4
0 '""I'I l I " €
.4. ,\*.-I'I .4 j l 4 4
-I • " 4)( J ( 0 U 4 .4LD ( 0 1 4
,1[5'f'' 4O F 5 10R.4lrt
Fiue26 Wn4tesioltsfroedge w tetsdge reouto
clmaolgca dtaoerth m~eldonan Cntu inerali
.2 dyne,/-crn, .
c~) 4I ,38
HI. EXPERIMENT RESULTS
A. TRANSIENT WIND FORCING
1. Experiment 1
The transient wind forcing experiments, numbers 1 and 2, were designed to
replicate work done by McCreary et al. (1987) using a primitive equation model.
McCreary et al. forced a linearized model with equation 2.13 and were able to produce
a model current system which varied in a manner similar to that of the CCS.
However, the results of McCreary et al. did not include the formation of eddies and
filaments. It was hoped that inclusion of the nonlinear terms would allow for eddy
development. The sensitivity of the model to the starting date of the wind forcing
was not known so the model was initiated with two different times.
Experiment I was initiated with a starting time of December 1, representing
the minimum forcing values for wind stress and curl. Unlike the rest of the
experiments, the model was extremely slow. For example, on day 20 (December 20)
an alongshore current was still not established, there was negligible offshore Ekman
transport, and there were no perturbations in the temperature field.
A poleward alongshore surface current finally developed in the nearshore
region on day 25 (December 25). The poleward nature of this surface current is
consistent with the dominance of the curl component over the stress in the wind
forcing function with a December 1 start date. As will be seen in later experiments,
39
all run in the summertime, the initial reaction in the model is usually driven
predominately by the equatorward wind stress. In this experiment, however, the stress
is completely overwhelmed from the very beginning by the curl portion of the forcing
function. Ekman transport throughout the model domain on day 25 (December 25) is
still extremely weak and calculations of dynamic heights with reference to 2400 m
show no perturbations at the surface. If upwelling of cold water was ongoing, it would
appear as a negative pressure perturbation due to the denser nature of the cold
upwelled water. Conversely, downwelling can be characterized as positive pressure
perturbations. The lack of any pressure structure in the dynamic height plots serves
to illustrate the quiescent nature of this experiment.
Development continues in this weak manner throughout the experiment. A
equatorward coastal flow is first seen in the northern portion of the model domain on
day 40 (January 10). Experiment 1 was concluded after 60 days (February 1). Figure
3.1 shows the zonal (u) and meridional (v) velocities, temperature (T) and pressure
(p) fields for day 60 of Experiment 1. Poleward flow is dominant in the nearshore
region and has reached a maximum velocity of 4 cm s 1 (Fig. 3.1b). Equatorward
coastal flow is evident in the northern reaches of the model, but has reached a velocity
of only 2 cm s-. The southern extent of this equatorward jet has slowly increased
throughout the experiment and extends to y - 448 km. Equatorward flow is also
evident offshore of 100 km. The temperature field (Fig. 3.1c) shows downwelling
coincident with the poleward surface current and weak upwelling coincident with the
equatorward flow at y - 550 km. In later experiments it will be seen that Ekman
transport is most strongly influenced by the direction of the wind stress. Here,
40
however, it appears that the poleward current flow due to the curl dominates
equatorward wind stress.
Overall, these results compare favorably with McCreary et al. (1987). They
found that when wind stress curl dominated in relation to wind stress, as was the case
in this experiment, a broad poleward surface current developed in the nearshore region
with equatorward flow offshore at approximately 100 km. Both these features were
seen in Experiment 1. Furthermore, neither McCreary et al. nor Experiment 1 showed
any signs of instability or concurrent mesoscale processes. Additionally, McCreary et
al. observed that as the strength of the stress forcing component increased in proportion
to the wind stress curl component, an equatorward coastal jet became discernible. This
phenomenon was seen in this experiment. As the model simulation time progressed
through January, the equatorward flow increased in width and in southern extent.
Theoretically, if computer resources had allowed for the extension of this experiment,
the equatorward jet should continue to grow and develop in a manner similar to a
summer regime. These results support the concept that positive wind stress curl can
generate both a poleward surface current at the coast and an equatorward flow offshore
which are seen in the winter season (McCreary et al., 1987).
2. Experiment 2
Experiment 2 was initiated with a forcing function representing the wind
stress of June. As previously mentioned, June has the maximum wind stress forcing
of the yearly cycle, and is the month which depicts the greatest ratio of wind stress
to wind stress curl seen throughout the year (Nelson, 1977).
41
As expected, the equatorward coastal jet sets up early in the model run. On
day 5 (June 5) a coastal jet has developed (Fig. 3.2b) extending from the northern
boundary to the southern extent of the forcing (y = 100 kn). The velocity of this jet
is 12 cm s1 , a relatively large value when compared to Experiment 1. Offshore Ekman
flow is also strong at this time (Fig. 3.2a) and upwelling as denoted by the closed 140
isotherm (Fig. 3.2c) is evident along the coast.
The cross-shore plot of the alongshore averaged velocity field for day 10
(June 10, Fig. 3.3) shows the current field to be characterized by an equatorward jet
extending to a depth of 100 m with an undercurrent from 100 m to 320 m. The width
of this jet is at a maximum early in the run and does not exceed - 40 km. The
associated vertical temperature plot for day 10 (Fig. 3.4) shows a bending up of the
isotherms in the nearshore region down to a depth of 100 m, just above the
undercurrent. This bending is indicative of the upwelling in the region. What is not
seen is a bending down of the isotherms below the undercurrent as would be expected
as a result of the undercurrent forced Ekman flow.
This pattern of development continues to day 25 (June 25, Fig. 3.5) when
the nearshore poleward flow becomes dominant and offshore equatorward flow
develops. The coastal jet still exists with a velocity of 10 cm s-, but it is steadily
being overwhelmed by the poleward flow (Fig. 3.5b). Although the northern areas of
the model domain still show an equatorward jet overlaying an undercurrent, the average
alongshore flow in the model (shown for day 30 in Figure 3.6) has become poleward
in the nearshore region with only a very thin band of equatorward flow evident at the
surface. The temperature signature at the coast has developed a core of 13 'C (Fig.
42
3.5c). The pressure field for this day (Fig. 3.5d) shows little structure, with only one
large meridionally oriented negative perturbation indicative of coastal upwelling.
By day 80 (July 20) the coastal equatorward jet (Fig. 3.7b) has been nearly
eliminated. The poleward surface flow dominates the nearshore region out to
approximately 100 km and has reached a velocity of 8 cm s-. The predominant
feature in the offshore region is a weak equatorward surface flow, of - 4 cm s'.
Offshore Ekman transport is still evident (Fig. 3.7a), but onshore Ekman forcing by the
poleward surface current is also exhibited. The upwelling temperature signature has
been reduced in both area and strength and downwelling is also seen in the southern
coastal region.
The features noted above continue to develop until the completion of the
model run at day 120 (October 1). The nearshore poleward flow maintains a velocity
of 8 cm sl , and extends out to 128 km from shore (Fig. 3.8b). The equatorward
offshore flow has maintained the same intensity, but has become better defined. The
Ekman induced upwelling has been greatly weakened and is now confined to the
northernmost region of the model domain (Fig. 3.8c). While it appears that the
poleward flow is causing a downwelling regime, this downwelling is extremely weak
as seen in the vertical cross-shore plot of temperature (Fig. 3.9). The isotherms bend
up slightly in the middle of the domain at y - 290 km, but cross-sections south of this
point show no isotherm deformation. The alongshore averaged velocity plot (Fig. 3.10)
clearly shows the prevailing current structure of this model run. There is a poleward
surface current well defined to a depth of 520 m and extending offshore to
approximately 120 km, with an average maximum velocity of 6 cm s'. The offshore
43
region contains a broader, shallower, weaker equatorward flow, with a maximum
velocity 4 cm s-'.
McCreary et al. (1987) had similar model results for their transient wind
forcing experiment. In general, their velocities for both the surface and undercurrent
were comparable with those of this study. Neither experiment showed any signs of
eddy or filament development. However, several inconsistencies do exist between the
two simulations. While the coastal jet of McCreary et al. extended well offshore
(greater than 200 km) and persisted in this form well into late fall, the jet of
Experiment 2 did not exceed more than 40 km in width and as documented, showed
rapid decline by late July. In addition, the growth of the poleward surface flow
progressed at a faster rate than in McCreary et al. (1987). These differences in results
are most likely due to differences in nonlinear versus linear models and to different
treatments of the boundary conditions at the coast.
If computing resources had not been restricted to 120 days for this
experiment, this experiment would have been continued for a full multi-year long
simulation. This would have given continuity over the seasonal changes, and would
have allowed for observations of the effects of continued periodic forcing.
B. ONE DEGREE CLIMATOLOGICAL WIND FORCING
1. Experiment 3
Extensive literature has documented the effects of one dimensional wind
stress forcing both with and without curl components (e.g., McCreary et al., 1987;
Batteen et al., 1989; Tielking, 1988). If in fact the nearshore region is the primary
44
area of eddy and filament developments in the CCS, then how we treat this specific
area should play an important role in the mesoscale activity of the model. Experiments
3 and 4 use constant and meridionally varying forcing in the nearshore region to
examine the role of these forms of forcing.
The coastal equatorward jet dominated the surface flow throughout the entire
experiment run. By day 40 (Fig. 3.11) the surface meridional velocity contours (Fig.
3.11 b) exhibited a surface equatorward jet - 64 km wide with a velocity of
35 cm s'. The width of this current agrees well with the results of Batteen et al.
(1989) in their constant stress, P-plane simulation, but the speed in this experiment is
considerably larger. Batteen et al. found a maximum speed for the jet of only - 15-
20 cm s'. (For a summary of comparisons of the instantaneous results of Batteen et
al. (1989) and Experiments 2, 3, 4, and 6, refer to Table III of Section IV.) The
offshore region of Experiment 3 shows the development of equatorward flow, another
feature absent from the model results of Batteen et al.. A vertical cross section of the
alongshore average of the meridional velocity for day 40 (Fig. 3.12) shows the presence
of a large undercurrent with a vertical extent of over 1000 m (z - -1520 m). While
the speed of the undercurrent (4 cm s-l) correlates well with the work of Batteen et al.,
the size of the undercurrent is nearly twice as large as the one seen at the end of their
experimentation. Strong upwelling is exhibited in the surface temperature plot (Fig.
3.1 Ic), with a core temperature in the coastal region of 11.5 'C, the coldest of any of
the 6 experiments. Isotherm deformation is seen throughout the water column for day
40 (Fig. 3.13). Nearshore, the upward bending of the isotherms is seen from - 320
m to surface, while the downward bending of the isotherms due to effects of the
45
undercurrent is seen all the way to - -1520 m. The extent of this downward
deformation exceeds that of all other experiments run in this thesis as well as similar
numerical model studies.
The zonal velocity time sequence shown in Figure 3.14 illustrates the eddy
development over this experiment run. Day 40 (Fig. 3.14a) shows two eddies in the
coastal region at y - 256 km and 320 km. These eddies enlarge, intensify and move
southwest over the time sequence shown. Three additional eddies are seen forming on
day 70 (Fig. 3.14c), including one in the offshore region (x - 208 km, y - 480 km).
Figure 3.14d, day 80, completes the sequence showing the continued development of
the eddies, with velocities of - 10-15 cm s'. These eddies differ from those in
Batteen et al. (1989) in several respects. The eddies of Experiment 3 are larger, less
densely populated and form further offshore. However, the zonal velocities of the two
sets of eddies do correlate well.
The development of Experiment 3 continued as outlined above until the
completion of the model run on day 95 (not shown). The meridional speed has
continued to increase and is now at 45 cm s'. The upwelling region has also
intensified extending offshore to - 320 km with a core temperature of 10 *C.
Clearly the inclusion of spatial variability in the far field has allowed for
more development than was seen in constant wind stress forcing. This fact is primarily
seen in the offshore equatorward and poleward flows, which were absent from Batteen
et al. (1989). The greater extent and intensity of the undercurrent than that seen in
Batteen et al. can be explained by the much stronger coastal jet which occurred in this
46
experiment and the compensatory increase in the intensity of the processes which drive
the undercurrent.
2. Experiment 4
Experiment 4 utilized a wind stress forcing which was zonally constant but
varied meridionally within 48 km of the coast. The offshore forcing still varied in x
and y. As previously mentioned, this gives a variation in the alongshore stress, but
causes the curl to equal zero in the critical nearshore region. This forcing is very
similar to that of Batteen et al. (1989) of utilizing a meridionally varying stress
function for the wind forcing throughout the domain.
The results of Experiment 4 were as expected. The curl-free stress in the
nearshore region led to the establishment of a coastal jet, which extended offshore to
the limits of the zonally constant forcing, - 48 km. Additionally, a narrow poleward
surface current was formed offshore ( - 48-96 km), and even further offshore ( - 96-
208 km) another equatorward current developed. All three of these alternating currents
were relatively strong compared to the previous experiments. Day 40 (Fig. 3.15)
clearly shows these strong well defined surface currents (Fig. 3.15b). The vertical
alongshore averaged velocity plot (Fig. 3.16) shows the offshore currents extending to
- 300 m, while the nearshore equatorward jet is surface trapped, less than 100 m deep
with a weak undercurrent below it. The undercurrent may actually be contiguous with
the poleward surface flow offshore. Upwelling is extremely strong, as seen in the
temperature plot (Fig. 3.15c), having already reached a core temperature of 12 'C. As
expected, the upwelling is preferentially developed in the region of maximum wind
stress at the coast and has adopted a filamentous form which, a time sequence of
47
temperature fields (not shown) shows, is advected southwest. A vertical temperature
cross section taken in the middle of the domain (Fig. 3.17) illustrates the breadth of
the upwelling, with the upward deformation of the isotherms extending more than 150
km offshore. Like the coastal jet, the upwelling is relatively shallow, extending to only
- 100 m, and shows no concomitant downwelling in the vicinity of the undercurrent.
The first manifestation of mesoscale eddies is seen in the u field (Fig. 3.15a) near the
coast at y - 360 km and 450 km at day 40. These eddies continue to develop until,
by day 85, the u (Fig. 3.18a) field shows three distinct eddies formed in the coastal
region between y - 384 km to 512 km.
The experiment was terminated on day 110 (Fig. 3.19) of the model run.
Little change has actually occurred in the gross structure of the domain since day 85.
While the offshore flows have strengthened, the equatorward jet has weakened.
However, the eddies are still present and exhibit a strong effect on the upwelling
signature as the cold water is advected by the cyclonic and anticyclonic circulation of
the eddies. This advection gives the temperature front a distinctive wave-like
appearance. The alongshore vertical cross section (Fig. 3.20) for this day shows the
coastal jet to still be relatively shallow, but shows the offshore flows to have deepened
to 520 m. Current vector plots for days 40 and 110 (Fig. 3.21) illustrate the surface
flow pattern. On day 40 (Fig. 3.21a), the current structure was strongly equatorward
at the coast, with westward flow throughout the offshore region. By day 110 (Fig.
3.21b), the nearshore flow is both equatorward and poleward but is predominantly
poleward. The offshore flow is strongest in the middle of the domain and is
48
equatorward. The appearance of two gyre-like circulations at the southern and northern
regions of the model can also be seen.
These results can be compared to those obtained by Batteen et al. (1989).
Although the eddies were more densely grouped and more numerous in Batteen et al,
they otherwise compare closely to those generated in this experiment. The primary
difference in the two experiments lies in the offshore region. While Batteen et al had
a simplistic quiescent region offshore, Experiment 4 developed a strong, well-defined
equatorward flow, with poleward flow further out. This difference is primarily due
to the increased diversity of the offshore wind forcing of Experiment 4. Consistent
with Batteen et al. (1989), both Experiments 3 and 4 reinforce the conclusion that curl-
free wind stress forcing in the nearshore region leads to the development of a coastal
jet and undercurrent and eddies.
3. Experiment 5
Experiment 5 is the first of the climatological wind stress forcing
experiments with two dimensional forcing throughout the entire model domain. The
structure in the nearshore region varies in both x and y, and there is a positive wind
stress curl along the coast.
Day 10 of the model run (Fig. 3.22) is in many respects similar to day 5
of Experiment 2 (Fig. 3.2). The equatorward coastal jet is well developed, extending
southward to y - 200 km, and has a maximum speed of 10 cm s-. The poleward
surface flow at the coast is already evident with a speed of 4 cm s'. The alongshore
averaged velocity plot (Fig. 3.23) depicts an equatorward jet overlaying a poleward
undercurrent in the nearshore region. The undercurrent is weak (- 2 cm s1) and
49
relatively small. Offshore Ekman transport due to the wind stress is seen on day 10
(Fig. 3.22a) and a cold water region is present in the coastal region (Fig. 3.22c). The
position of maximum upwelling at y - 300 km coincides with the region of maximum
wind stress near the coast (refer to Fig. 2.4). The pressure field similarly exhibits a
negative perturbation in this same region (Fig. 3.22d). The vertical cross shore plot
of temperature (Fig. 3.24) exhibits the upward bending of isotherms in the coastal
region, consistent with upwelling. However, a noticeable bending downwards of the
isotherms in the region of the undercurrent is not seen, indicative of the weakness of
this current.
By day 20 (Fig. 3.25), the poleward surface flow (Fig. 3.25b) is well
established and has moved up the coast to y - 300 km. Additionally, the speed of the
flow has increased to 8 cm s1. The equatorward jet shows the opposite trend, having
been pushed back up the domain decreasing to 4 cm st The offshore equatorward
flow is beginning to develop in the region - 100 km to 190 km off the coast. The
coolest temperature (Fig. 3.25c), indicative of upwelling develops in the area of
maximum coastal wind stress and develops a meandering filamentous form. The strong
poleward flow in the southeastern corner of the domain has begun to drive offshore
Ekman flow (Fig. 3.25a) and warmer temperatures indicating downwelling are seen in
this area. A cross shore averaged velocity plot for this day (Fig. 3.26) and shows the
poleward current dominating the coastal region. This coastal flow is well defined in
the average to 520 km.
The filament continues to grow and to be advected in a southwesterly
manner so that by day 40 (Fig. 3.27) it extends off the coast out to 190 km (Fig.
50
3.27c). The filament continues to develop in the high wind stress region nearshore as
seen by the small core of 13 'C at y - 384 (Fig. 3.27c). Offshore Ekman flow (Fig.
3.27a) is found throughout the model except for the downwelling region in the south
where relatively strong onshore flow is discernible. The poleward coastal flow now
dominates the nearshore region and has reached a speed of 14 cm s'. The equatorward
flow offshore has also become more defined with a speed of 12 cm s' in the northern
region.
Development of this form continues with the filament reaching its maximum
extent of 240 km on day 55 (Fig. 3.28) before starting to dissipate. By day 80 (Fig.
3.29), the filament has completely disappeared and in its place is a broad band of
upwelled water, as seen in the northern part of the model domain (Fig. 3.29b). The
downwelling region in the south now extends to y - 320 km and has a core of 16 'C.
The coastal flow is poleward at 16 cm s' (Fig. 3.29b), while the offshore equatorward
flow is much better defined than at day 40 with a core of 20 cm s'. The alongshore
averaged velocity (Fig. 3.30) shows the poleward flow extending down to 720 m depth,
while the equatorward current offshore is very broad and descends to 520 m depth.
A temperature section in the middle of the domain (Fig. 3.31) upward bending of
isotherms in the nearshore upwelling region as well as a clearly defined temperature
anomaly offshore where the cross section cuts through an offshore protrusion of the
upwelling region. This figure illustrates the strong frontal nature of the filaments in the
surface region.
The simulation was run to day 110 (Fig. 3.32). The downwelling signal has
advanced to y - 350 and has a strong northward propagation. The upwelling has
51
decreased in intensity to 13 °C and has become confined to the coast. There is a
protrusion of cold water from the north which appears to be advected southward by the
mean alongshore flow, but this cold water does not show signs of intensification over
the last few days of the model run. A cross-sectional temperature plot (Fig. 3.33)
again shows the characteristic isotherm bending in several locations in the domain.
The pressure field (Fig. 3.32d) shows a small eddy starting to develop at x - 256 km
and y - 512 km. This location is coincident with the boundaries of the offshore
equatorward flow and a poleward flow forming further offshore. This would seem to
indicate that the eddy generation is a result of the strong horizontal shear, and
subsequent barotropic instability, in this region. The alongshore averaged velocity
(Fig. 3.34) still shows the same pattern as on day 80 with a deepening of the poleward
flow to 820 m and the offshore flow to 720 m.
The current vector sequence of Figure 3.35 shows the progression in the
surface current flow. The shift from equatorward flow dominating at the coast on day
20 (Fig. 3.35a), to the strong poleward surface flow in the coastal flow with
equatorward flow offshore on day 110 (Fig. 3.35d), is clearly seen. It is interesting
to note the offshore flow and the development of the gyre-like circulation, which is
shown to be clockwise in the bottom right portion of the model domain and
counterclockwise in the upper left.
The additional diversity in the nearshore wind field of Experiment 5 has led
to a cessation of cyclonic / anticyclonic eddy generation in the nearshore region, but
a filament was formed. The lack of eddies is probably a result of no strong coastal
jet / undercurrent structure. The equatorward wind st- is not strong enough to
52
maintain a coastal jet in face of the strong positive wind stress curl at the coast. The
filament formation seems to be a consequence of upwelling occurring preferentially in
the area of maximum equatorward wind stress at the coast with a subsequent advection
of this cold water offshore.
C. TWO TENTHS DEGREE CLIMATOLOGICAL WIND FORCING
1. Experiment 6
Experiment 6 utilized two tenths degree resolution climatological wind stress
forcing. This fine-scale resolution added a great deal of structure to the wind field,
specifically in the nearshore region. Of particular note is the region of maximum
southerly stress and negative wind stress curl at approximately 400 km (Fig. 2.6).
Experiment 6 was by far the most dynamically active and realistic simulation
of the six experiments. By day 5 (Fig. 3.36), a strong equatorward jet in the nearshore
region had set up (Fig. 3.36b), and an offshore Ekman transport has been established
(Fig. 3.36a). The peak velocities of the equatorward surface jet, of - -22 cm s-,
coincided with the location of maximum southward stress values at the coast, which
resulted in a negative wind stress curl region. It is interesting to note that while at day
5 in Experiments 2 through 5 the core of the equatorward jet extended along the entire
alongshore extent of the model domain, Experiment 6 showed a preferential
development and confinement of the equatorward current core to the north. As
previously highlighted in the wind field description (Section I.A.3), this area is located
at the climatologically maximum wind stress values found at Cape Mendocino (Nelson,
1977). As expected, examination of the u (Fig. 3.36a) field also shows a maximum
53
offshore transport at the coast at y - 400 km. The temperature field for day 5 (Fig.
3.36c) depicts the first development of a cold core filament at y - 400 km, just south
of the equatorward flow maximum.
Day 10 (Fig. 3.37) delineates the continued development of offshore
transport (Fig. 3.37a) and a strengthening of the equatorward jet to -26 cm s' (Fig.
3.37b). The jet is confined to a region within approximately 40 km of the coast, while
the core is located only a few kilometers from the shore. As seen in previous
experiments, a coastal surface poleward flow has developed and has progressed
southward in the southern portion of the domain. An alongshore average of the v field
(Fig. 3.38) shows that the dominant flow pattern is that of an equatorward jet overlying
a weak but well defined undercurrent. These locations represent areas of potential
baroclinic instability due to the vertical shear exhibited. A filament has also developed
and has a core temperature at day 10 of -13 'C, with an offshore extent of 48 km
(Fig. 3.37c). Two opposing surface currents have formed as a result of the diversity
in the wind field and the resulting convergence has advected the cold upwelled water
offshore. Figure 3.39 shows a vertical cross section of the instantaneous temperature
contours for a location approximately equal to the filament core (y - 390 km). The
bending upward of the temperature contours is clearly indicative of an upwelling
regime. The upwelling is confined to a region within 150 meters of the surface which
agrees well with the vertical extent and influence of the equatorward jet at this time
and location (Fig. 3.40). Day 10 marks the beginning of strong, observable eddy
development in the nearshore region. The pressure field (Fig. 3.37d), shows a cyclonic
eddy forming at approximately 420 km. By day 10, there is both poleward and
54
equatorward flow at the surface in the nearshore region, with some manifestation of an
undercurrent at various locations throughout the domain. Additionally, there is strong
evidence of both filament and eddy developments. By day 20, the alongshore averaged
velocity field (Fig. 3.41) shows no evidence of an undercurrent. A poleward surface
flow dominates the nearshore region. Although some evidence can be found for a
weak undercurrent in the northern portion of the model domain (Fig. 3.42), the model
as a whole is developing predominantly surface intensified features.
The pressure field of day 25 (Fig. 3.43d) shows four eddies. There is a
dipole eddy with an axis at y - 384 km, an anticyclonic eddy at y - 176 km offshore,
and a cyclonic eddy at y - 448 km. These offshore eddies have been formed in areas
of strong horizontal shear between opposing surface currents, as seen in a comparison
of the pressure (Fig. 3.43d) and meridional velocity (Fig. 3.43b) fields for day 25. The
cold core filament (Fig. 3.43c) now extends to 160 km offshore and is exhibits a
hammerhead shape coincident with the axis of the dipole eddies.
By day 40 (Fig. 3.44) the nearshore poleward flow extends along the entire
coast (Fig 3.44b) Equatorward flow is still manifested in the alongshore region from
y - 384 km to 520 km. The equatorward jet is clearly defined, extending offshore to
-60 km and having a peak velocity of 25 cm s-1. An undercurrent is very weakly seen
in the region under the equatorward jet, but strong poleward surface flow is seen in
the nearshore region (Fig. 3.45). The filament now extends offshore to 192 km as a
result of advection a southwest direction (Fig. 3.44c). The core temperature of the
filament remains at 13 'C with a location at y - 400 km in the alongshore direction.
A vertical temperature section (Fig. 3.46) still shows shallow upwelling at the coast,
55
but offshore there is evidence of the filament at x - 125 and 210 km. The eddies that
developed earlier are still present, but an additional cyclonic eddy has formed just north
of the anticyclonic eddy that formed at y - 176 km offshore (Fig. 3.44d).
By day 45 (not shown) there is no evidence of an undercurrent below the
equatorward jet. The model flow field exhibits strong alternating poleward /
equatorward surface flow. This pattern persists through the remainder of the 120 days
of the model run. The anticyclonic nearshore eddy remains stationary and well-
defined. The cyclonic eddy in the nearshore region is slowly absorbed by the
nearshore large scale pattern and has lost its identity by day 55 (not shown). The
nearshore region has two large cyclonic gyres with anticyclonic eddy located near the
shore at y - 440 km. The offshore eddies are advected to the southwest. Their size
and structure, as well as the structure in the nearshore region, is seen in the pressure
field of day 80 (Fig. 3.47d). Day 80 (Fig. 3.47) also illustrates the flow pattern that
is characteristic of the remainder of the model run. From the coast to approximately
128 km offshore, poleward surface flow dominates (Fig. 3.47b). However, within this
poleward current is a pocket of strong equatorward with speeds of 25 cm s- from 128
km to 190 km. The offshore equatorward flow has a speed of 20 cm s1. The filament
has reached an offshore extent of 288 km (Fig. 3.47c).
The pressure field at day 100 (Fig. 3.48d) shows another anticyclonic eddy
developing at y - 512 km and approximately 320 km offshore. Again this is an area
of strong horizontal shear between two opposing surface currents (Fig. 3.48b).
The model was run to day 120 (Fig. 3.49). The equatorward coastal flow
has increased in speed to 40 cm ', but is confined to - 45 km from the coast (Fig.
56
3.49b). The poleward surface flow near shore is relatively weak with only isolated
pockets exceeding 20 cm s1 . The offshore equatorward flow has also weakened to less
than 15 cm s 1 throughout most of its extent. The extremities of the cold core filament
have fragmented and been absorbed, while the offshore limit of the filament (Fig.
3.49c) has regressed to 256 km from its maximum extent of 320 km at day 95. Six
eddies are present in the domain, three cyclonic and three anticyclonic, in an area
extending from the coast to 320 km offshore (Fig. 3.49d). These eddies continue to
develop in areas of strong horizontal shear.
In summary, the development of a confined equatorward jet with an
undercurrent is initially seen in Experiment 6. The remaining nearshore region has
poleward surface flow. The offshore region is primarily equatorward, with various
regions of poleward surface flows. Eddies develop first in the area of the negative
curl near the coast and later in the areas of horizontal shear offshore. The temperature
structure exhibits a cold core filament which develops at the convergence of negative
and positive curl near the coast. Throughout the experiment the eddies continue to
develop, the filament continues to grow, and the surface currents become more defined.
The undercurrent disappears so that the current regime has surface currents only.
Whereas in Experiment 5 the filament appeared to be the result of preferential
upwelling and strong offshore advection, in Experiment 6 the filament forms and grows
as a result of a surface current convergence. The diversity of the wind structure
causes the formation of these opposing surface currents. These currents converge and
advect the cold, upwelled water offshore in a plume. Once offshore the plume is
advected southwesterly by the mean flow. The strong filament formation emphasizes
57
the importance of fine scale diversity in the wind field for the development of both
current and mesoscale features in the CCS.
D. STABILITY ANALYSIS
One of the primary motivations of this research was to investigate the energetics
of eddy formation in the CCS. Both baroclinic and barotropic instability mechanisms
have been shown to be instrumental in the production of eddies (Robinson, 1983).
Evidence for both baroclinic and barotropic instability has been given for the northeast
Pacific (Wright, 1980). Evidence for baroclinic instability alone has been given for the
northern portion of the CCS (Emery and Mysak, 1980; Thomson, 1984; Freitag and
Halpern, 1981). The baroclinic instability which occurs as a result of the equatorward
jet over the undercurrent has been hypothesized by Ikeda and Emery (1984) to be the
primary mechanism for meander growth and eddy development. The importance of
barotropic instability is less clearly documented with only a few studies showing
evidence in support of this mechanism operating in the CCS (Robinson et al., 1985;
Thomson, 1984).
There are many ways to both qualitatively and quantitatively describe the energy
transfer processes which lead to the development and growth of mesoscale phenomena.
On the most basic level, the velocity shear in the region of development is indicative
of the form of instability occurring. As a first approximation, areas of strong
horizontal shear are considered to have the potential for barotropic instability, while
areas of strong vertical shear are considered to have the potential for baroclinic
instability (Pond and Pickard, 1983). Beyond the simple qualitative shear observations,
instability is also characterized in the potential vorticity patterns of the flow fields.
58
Watts (1983) and Watts and John (1982) were able to characterize the instability of the
Gulf Stream region through analysis of the potential vorticity fields of the area. Two
necessary conditions of baroclinic instability are that the cross stream derivative of
potential vorticity change sign in the domain and that the mean velocity times the
potential vorticity gradient be positive somewhere in the model field. A final method
of analysis involves actual computation of the energy transfer terms. This method has
been used extensively by Semtner and Mintz (1977) in their Gulf Stream study and by
Han (1975) in his study of mesoscale eddies. This latter technique is particularly
helpful in quantifying the relative contributions of the two instability processes.
Of the four experiments (Exps. 3-6) which showed eddy development,
Experiments 5 and 6 were chosen for more in-depth energy analyses. Since
Experiments 3 and 4 closely followed the energy analyses as discussed by Batteen et
al. (1989), they will not be discussed here.
1. Experiment 5
Eddy development occurred very late in Experiment 5 at - day 110. These
eddies developed far offshore and were relatively small. Horizontal shear was prevalent
in the area of the initial development leading to the hypothesis that a barotropic
instability process was the dominant mechanism.
In accordance with the work done by Watts (1983), potential vorticity was
computed in the cross shore direction using the following equation:
q f + C) aT aTDv (3.1)az ax az
59
where = v au (3.2)ax ay
Utilizing the above formulations, the time-averaged cross-stream derivative of potential
vorticity (D / ax) was calculated and plotted for the period 90 to 99 days (Fig. 3.50).
This time period was chosen as the period during which generation occurred. From
the plot, one can see that sign changes occur both in the vertical in the nearshore
region and in the horizontal in the offshore region. Although this shows that eddy
generation is possible in the coastal region due to baroclinic instability, no such eddies
are seen in that area. The forcing is not strong enough to produce the eddies which
are seen in Experiments 3 and 4. In the region of offshore eddy generation, barotropic
instability is in evidence (Fig. 3.50).
2. Experiment 6
Eddy development in this experiment appears to fall into more than one
spatial and temporal frame. Initially, the nearshore eddies in the location of the
equatorward jet occurred at day 10, early in the model run. Somewhat later in the
model development at day 25 and much later at day 100, offshore eddies developed.
For simplicity, these two classes of nearshore and offshore eddies will be addressed
separately.
As described previously (Section III.C.1), strong vertical shear persists in the
region of the equatorward jet up until day 45. This vertical shear is located in a
region coincident with the formation of the first anticyclonic eddy ( y - 420 km). This
characterizes the nearshore eddy generation during the early portion of the experiment
as being due to baroclinic instability.
60
The time-averaged cross-stream derivative of potential vorticity (D / ax) was
calculated and plotted for the period 5 to 15 days (Fig. 3.51). This time frame was
chosen to coincide with the period of initial nearshore eddy development. Examination
of Figure 3.51 clearly reveals a vertical sign change of the potential vorticity gradient
in the region of the nearshore coastal jet and the underlying undercurrent (z - 75 m).
A sign change is also seen in the horizontal in the boundary region between opposing
currents just offshore (x - 75 km). Visual comparison of the potential vorticity
gradient with the average alongshore velocity (Fig. 3.24), shows several areas in both
the nearshore and offshore regions noted above where the product of the two fields is
greater then zero. It should be noted that the vertical v field in Experiment 6 is
extremely diverse so that different instantaneous cross sections of v varied tremendously
throughout the domain. In particular, there are many areas of positive products of the
fields of v and vorticity which fail to show up when alongshore averaged velocity
fields are used. Nonetheless, based on this method of analysis, the necessary
cC.iditions for baroclinic instability are well satisfied. Barotropic instability as denoted
by the horizontal sign change in vorticity gradient is also evident, but to a lesser
extent.
A time series of kinetic energy for Experiment 6 is shown in Figure 3.52.
It is seen from this figure that there are three phases to the kinetic energy development
in the model. There is an initial period of change in the kinetic energy from the start
of the experiment to day 12. This period coincides with the development of the initial
eddies in the nearshore region. A second period of change in the kinetic energy occurs
between 12 and 100 days. This period is demarcated by a strong near linear increase
61
in kinetic energy throughout the model domain. A final period is illustrated in the
leveling off of kinetic energy after day 100 until the completion of the experiment on
day 120. If it is assumed that the level periods at the start and end of the experiment
represent quasi-steady state situations, actual values for the energy transfer process can
be computed (Semtner and Mintz, 1977; Han, 1975).
Utilizing analysis techniques formulated by Rutherford (1989) based on Han
(1975) and Semtner and Mintz (1977), the energetics were computed for the period of
1 to 12 days. The computed values along with the directions of energy transfer are
shown in Figure 3.53. Transfer of energy from eddy potential energy (EPE) to eddy
kinetic energy (EKE) represents baroclinic instability, while mean kinetic energy
(MKE) transfer to EKE indicates a barotropically unstable process (Semtner and Mintz,
1977). While both processes are illustrated in Figure 3.53, the baroclinic instability
term is nearly twice as large as the barotropic term so that it is the dominate instability
mechanism over the first 12 days. It should be noted that these calculations were
made over the entire model domain, including the relatively inactive offshore region,
which account for the seemingly low energy and transfer values in Figure 3.53.
It is clearly seen that the initial period of Experiment 6 is dominated by
baroclinic instability. This is shown by the vertical shear in the velocity field, by the
sign change in the cross shore potential vorticity derivative, and by these energy
calculations. All of these indicators are strongest in the area of eddy generation in
the nearshore region. Barotropic instability is also seen, but it does not appear to be
as strong as baroclinic instability during the beginning phases of the experiment.
62
The offshore eddies which appear later in the experiment at - days 25 and
100 exhibit different instability characteristics. As mentioned in the results section
(Section III.C.1), these eddies initially appeared in areas of strong horizontal shear,
specifically at the boundary between the offshore equatorward flow and the poleward
surface currents. Horizontal shear indicates a barotropic instability process. Figure
3.54, Dq / ax, shows a horizontal change in the potential vorticity gradient. However,
a vertical sign change seen is not discernible. An energy analysis was made for this
quasi-steady period of 100 to 120 days, and the results are shown in Figure 3.55. It
is seen in this figure that not only has the barotropic instability component increased,
but the baroclinic component has decreased by a whole order of magnitude. Clearly
a change in instability processes has occurred with a shift to the dominance of
barotropic instability.
63
U o doy 60 dkp) 0 V n' qyg An d'pI-Pi
940640
76 I
........... ... .. ... ..
s12 512
448 448
384
E E
C V,,
7:s
3706-U
428 7,3 28
* 64
042 44FI 3A4 3,0 ; 6 142 428 q, A 512 .18 394 370 V-1 ''I 4
I1 ,nyn, (1 pt,,i
veocity) (cPs),an1() epeatre(°) o Expeimet1a)a
60.Cotorlntrvl s .0cms 1 fo c(a) an (b, and~I 0. °Cfo ()
C
512
.448
64
12
627 4;m 484 370 25 1402 17- 64 0
Figure 3.1 Surface isopleths of (a) zonal (u) velocity (cm s-'), (b) meridional (v)velocity (cm s'), and (c) temperature ('C) for Experiment I at day60. Contour interval is 2.0 cm s-' for (a) and (b), and 0.5 *C for (c).Dashed contours denote offshore velocities in (a) and equatorwardvelocities in (b).
(4
U at da y5 depthO0 V at day 5 depth 0
a - --- -- - -- - -- - - -- - -576 7
---- --- -- -
384 E --- - - - - - - - - - - - - - - - 9
% --- -- - - - - - - - - - - - -
-- - -- --- - -- - -- - -- -
258- 3 oe
12 --- 120
64 6
312 446 384 320 256 192 128 64 0 512 448 384 320 258 192 126 64 0Distance (kmn) Distance (kin)
contour interval 2.0 contour interval 2.0
T at doy 5 depth 0
640
C576
512
448
384
320
25e
28
128
84
512 44 3164 320 2;6 9i2 128 64 0Distance (kmn)
contour interval - 0.5
Figure 3.2 Surface isopleths of (a) zonal (u) velocity (cm s-'), (b) meridional (v)velocity (cm s'), and (c) temperature ('C) for Experiment 2 at day 5.Contour interval is 2.0 cm s' for (a) and (b), and 0.5 'C for (c).Dashed contours denote offshore velocities in (a) and equatorwardvelocities in (b).
65
(W) L ('
0 0 0 0 0 0 0 0 0 00 (N 0' 0
",( r f C fj (,j
0 1 - j o c .c_ r~' ' N '~ ~ -
0
CD C
CA6
CD
C J
0
0)74
CI
Figure 3.3 Vertical cross-shore section of meridional (v) velocity (cm s- ) forExperiment 2 at day 10. Contour interval is 2.0 cm s' . Dashed
contours denote equatorward velocities. The vertical cross section wasalongshore-averaged.
66
(u.i) nvi >rj
0 0 0 0 0 000)0 0DC 0
(A "l (Ij in crC) Cl
Q . I J ' 1 I 1. I , 1 , 1 I I
CD0)
0
U ) (D
DI'
0
Figure 3.4 Vertical cross-shore section of teniperature (°C) for Experilent 2 at day|10. Contour interval is 1.0 'C. The vertical cross-section was takenat y = 290 ki.
67
U at day 25 depth0 V ot day25 drth0
640 .
-----------...-- .......... 578 ." ''" 76
-- - - --- -7 53,* 2 ,j 2
-- - - - - - - - - -- 446
.4
/ 1364E 24 E' ' , 120"
- o30 a
"". .. ................. .. ' " 2 T
ISO- 250
.-- 192 36
---------- - ----. - 32 ------ ii~iii 326
64 4
532 440 564 520 2 2 3 44I -- 0 312 448 364 320 256 192 128 64 a512 446 3i4 ,]i0 256 192 128 64 O0i~c kn Osoc kn
Distance (krn) O'Stance (k M)
contour interval= 2.0 contour ;ntervol - 2.0
T at day 25 deph 0 P at day 25 depth 034f0 4
I'll
$76
512 -.12
446 4,49
3E4 304
20 .520 3.,
302 392
326 326
f4 44
532 446 384 220 24 39I2 129 64 0 512 448 384 320 2 6 15 3 2 9 35 10 0Dstonce (krn) U,1StJ3ce (k"")
COntour interval 0 5 contour intervol 2 0
Figure 3.5 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s'), (c) temperature (°C), and (d) dynamic height (cm)relative to 2400 m for Experiment 2 at day 25. Contour interval is 2.0cm s' for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 24() m in (d).
68
(U ) LI IC) C ( O O C) C) ) C)0 000 C ) 00 0 )0
C4 ~ C4 C4. (4i (AJ (4A C r 4 . N r, - * 4-I , ,) , ,E) ,, 1- , 0n r, - b) 0 ,
0) 0
C4._ C'-C C) -'
C)a(A
U
(DU>
Cu
-q a
U
C-)
Figure 3.6 Vertical cross-shore section of meridional (v) velocity (cm s0) for
Experiment 2 at daly 30. Contour interval is 2.0 cm s . Dashedcontours denote equatorward velocities. The vertical cross section wasalongshore -averaged.
69
U ot doy8O depthO V at day B0 depth 0
040 640
.570 7
52 512
448 440
c *1
25. 256
- 'I. . C= 0"
1 . 92 192
040
128 - 26
64 14
512 448 304 320 256 12 120 64 0 212 44 3414 220 2i4 192 120 64 0Distance (krn) Distance (kn"-
contour interval = 2.0 contour interval - 2.0
T at daySO depthO P at day8O depthO
640 640
570 76
-4 -512 "5t2
448 448
.,2
CC
192 2
128 120
.1 4 4
0 0572 4 3M4 37, 20 712 2 7ill 0 ..2 - 3. 320 256 .2 720 04 0
D,tor, ce (k -) DiStance (k,,,)
contour intervol = 0 5 contour interval = 2 0
Figure 3.7 Surface isopleths of (a) zonal (u) velocity (cm s"), (b) meridional (v)velocity (cm s'), (c) temperature (C), and (d) dynamic height (cm)relative to 24() m for Experiment 2 at day 80. Contour interval is 2.0cID s-' for (a) and (b), 0.5 C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 m in (d).
7(0
U at day 120 depth0 V at day 120 depth 0
$40 4"o
512 i
,4444 .
,..4
12B >12,
512 448 384 320 256 192 129 64 0 12 448 A 4 3i0 2 6 192 125 64 0Distance (kn) Distance (kmn)
contour interval m 2.0 contour interval = 20O
T at "lay 120 depthO0 P at doy120 depthO0
'304 32
3202. 4.4
254 25
152 192
128
44044
512 440 354 320 256 112 128 64 0 512 445 34 2 5 192 128 644Distonc e (kin) C,stonce (k-)
contour ;niter-Ol 0 5 rntffvol = 2 0
Figure 3.8 Surface isoplethis of (a) zonal (u) velocity (cm s-'), (b) nieidional (v)velocity (cm s"), (c) temperature ('CQ, and (d) dynamic height (cm)relative to 24d e for Experiment 2 at day 120. Cotour interval is2.0 cm s- for (a) and (b), ).5 'C for (c) and 2.(0 c4 for (d). Dashedcontours denote offshore veloities in (a), equatorward velocities in (b)
and negative values relative to 24(X) ni in (d).
71
F4x f\!x r 4 (- C( O 0) Ln N (N (A (N (N r. (
CO
I' f V 0 - - - . ( .(N ( N [ ) i '
-.J
04
.) CC
0
('j
C)
C r I
Figure 3.9 Vertical cross-shore section of temperature (°C) for Experiment 2 at day12(0. Contour interval is 1.0 °C. I'he verticail cross-section was takenat y = 290 kn.
72
(Wu) (4 1 JI)(
0 0 0 C) 0 0 -C) C ) C) C ) 0 0 -. C 0') (1 n 0-(N , Ci , N (. ( I I ( '-J N (I , l I - -I l -I -4 , I _- n- Cl (> l F ) f - )) _ " )
(0 0
A)0) C
alnsoe averaged
3II
(1)
t t)
/0
(I)
0 0
Figure 3.10 Vertical cross-shore section of meridional (v) velocity (cm s") forE-xperiment 2 at day 120. Contour interval is 2.0 cm s'. Dashedcontours denote equatorward velocities. The vertical cross section wasalongshore- averaged.
73
U at day 40 depth 0 V at day 40 dept 0O
#40 m 640
576 7
S12
4446
4464
384 E. 8
320 U 7U
~925Oa o
1124
44$4
0 11112 44i 3i; 22 5442 2 6
012 446 384 32C 256 192 12864~ 0 stance (2in)i 250
Distonce (kmn)one(m
contour interval - 5. 0otu nera .
T a da 40deph 0P of day 40 der~h 0
6640
/44
1 .4 .,..,,30 .
19211
4262
_____________________________ o_ ; 12 -'8 36- 32 2 ' 02 125 64 c
512 446 364 320 2"G 192 128 6- 0 atne(o0,s.0ance (1,-)
contour4 interval = 0 5 c.o irt a = 2,
Figure 3. 11 Surface isopleths of (a) zonal (u) velocity (cm s'I), (b ' meridional (v)velocity (cm s'), (c) temperature ('C), and (d) dynamic height (cm)relative to 24(00 rn for Experiment 3 at day 40. Contour interval is 5.0cml S" for (a) and (b), 0.5 'C for (c) arid 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 24MK in in (d).
74
0 00 00 00000 00 0 0 00 00000CA~N (4 C) C,4 C)4 C) C) N4 CA CAr
aCo C A rj r
0-
00
C-)
I V
cn
Exe0
mn 3 tdy4. CnoritrvliC. m s. Dse
conous dnoe euaorwrdvelciies Te vrtcalcrss ecionwa
alongs hre-averged
75
(LU) q dap
o ~~~ 00 ~00 a 0 0 0 oCI N C,4 "N C(N r4 4
0 L0 - 0-
i9
L)
U)- 0
1Z.
U II
00
(c4O
0
Figure 3.13 Vertical cross-shore section of temperature ('C) for Experiment 3 at day40. Contour interval is 1.0 'C. The vertical cross-section was takenat y = 290 kn.
76
U at dioy 40 depth 0 U at day 50 depth 0
640 b 6~*%*.*.* 40
578
512 512
44844
565 2508*
19 192
. I ~ .. . .... ....------ ------ .. ......
512 448 304 310 256 'q2 128 6' 0 512 448 384 320 256 192 128 84 0DitnCe (k-,) Distance (kin)
Contour interval =5 0 contour inter wci =5.0
U at da y 70 depth 0
S640 U at day 80 depth0 4
576
576
-. 3 84
3 20 U
02
1522
.............. . .... 48
0512 446 384 320 254 182 126 64 8 0 26 82 18 6
Distance (kin) 1148 34 ,0 26 97 2 4 0Distance (km,)
contour interval - 5.0contour intervalI 5.0
Figure 3.14 Surface isopleths of zonal (u) velocity (cm s-') for Experiment 3 at (a)day 40, (b) day 50, (c) day 70 and (d) day 80. Contour interval is 5.0cm S". Dashed contours denote offshore velocities.
77
U at day 40 depth 0 V at dcy40 depth 0
4484
25.4-0
320 C
25 25 4484 2 0 2 8 2 2
522 48 24 22 25 292228 ' 00 stnce19inOrstane (kin
440 1 48 34 32 5 9 12.---y-- 6 4 0
312 4480 2 5 9 2 4 aDsac kn
520 '440 '
256 - 50
4458
0 10
522 448 284 220 258 292 228G 84 00 522 448 284 220 258 292 128 SCDistance (kin) Distance (kmn)
contour interval = C1 5 con~tour intervalI 2 0
Figure 3.15 Surface isopleths of (a) zonal (u) velocity (cm s-'), (b) i9,-riaionna (v)velocity (cm s"), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 4 at day 40. Contour interval is 5.0cm s*' for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400) m in (d).
78
(Lu) qlda U
C0 C) C) 0 0 ) C)C C 0 0 C) 0 C) C C) C) 0 CD( CN Cj C) C.JN r C) 4 rJ 'j CN ('4 C4 c C)N r4 C 4 C r Cr,) Ln 01 n ) ) tr0 -; n 0) - ) )00 - - - - - - - - -
~.
)CC.
a)
1l) (\J'ci-
I -0
C)
cciC:
If)0
Experiment 4 at day 40. Contour interval is 2.0 cm s . Dashed
contours denote equatorward velocities. The vertical cross section wasalon gs hore -averaged.
79
r.'J!
(w) t41d-:]0 000 0 0 0 0 0
o - *J....'.J. , . , I , t + , I , I I I , , !
0~
-0 to 'I
00%,
CC)0O
U
Figure 3. 17 Vertical cross-shore section of temperature (TC) for Experiment 4 at day4(0. Contour inlterval is 1.0 TC. The vertical cross-section was takenat y = 290 ki.
800
U~~~~~ ~ at day 85 depth 0V tdy5eph646440
-576
9' 51512
146
320 U
192 N 9
- - -- - - - - - - -- - -- - 2
0 7 12 448 384 320 256 192 129 54 0
i112 440 3i4 320 256 192 128 64 00 Distance (kin)Distance (krm)
contour interval = 5.0contour interval =5.0
T at day 85 depth 0 P at day 85 depth 0 46400
312512
449/445
384 E
4, 0
192
-1922
6464
512 448 35* 320 256 92 25 64 01I2 448 364 220 256 192 12864 0 Dis tance (krn)
Distance (krn)
qontour interval 2.0contour interval - 0.5
Figure 3.18 Surface isopleths of (a) zonal (u) velocity (cm s-), (b) meridional (v)velocity (cm s't ), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 4 at day 85. Contour interval is 5.0cm s" for (a) and (b), 0.5 TC for (c) arid 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 m in (d).
81
U at day 110 depth 0 V at day 110 depth 0~, ~ , *640 0
0 '312512
4486,1
:.-" ~ *'- 84~ 8
320 U 320 U.
2564 250
- -, 192 192
126 126
0
512 448 384 320tO254 (12 128 64 0 512 448 3a4 320 256 1692 125 84 0Digtance (n) Distance (kin)
cantour interval - 5.0 contour interal =5.0
T at da y 110 depth 0 P at day 110 depth 0640 440
512 512
30
7"565 25eo
\ 192 192
84 64
512 4;8 3j4 320 2;5 12 128 64 0 512 448 384 220 256 192 128 6- 00Distance (kin) Distance (krn)
contour interval =0 5 contour interval - 2.0
Figure 3.19 Surface isopleths of (a) zonal (u) velocity (cm s-'), (b) meridional (v)velocity (cmn s-'), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 4 at day 110. Contour interval is5.0 cm s-' for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 24(X) m in (d).
82
00000 0 0 0 00000000N (A C-j r'N (N C,4 ri (' 'J_ ~ L r, 0 Ia , P V4 C- C- C1 N P) II,
0-
CD
0
00
U
r- II
t) ""CU)
(I)
, 2C
-I.
0
Figure 3.20 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 4 at day 110. Contour interval is 2.0 cm s'. Dashedcontours denote equatorward velocities. The vertical cross section wasalongshore-averaged.
83
0 -U Co0
0 CL
. .. . . .... .
0.0
.... . . ...
C.)CO
. .0
Go w
...... .... . N
- * ,.~' ~ ** *..~.. .......
C-))
Fiur 3.1 SraecretvcosfrEpriet4a Na a 0 b a 0
84N
U at day 10 depth 0 V at doy O depthO
640_ 640
.A - _. ----- s,
. . . . . . . . .... .... ......... 5 7 6 ; '
* 512.- ~~---- ..............-
446
.o.- ....".......... "... s8 -
.......... ........... " i 256
1 2 - - - - - - - - - -- 192
126 ---- .,------- --- -- -- ------- - -
64 6
------3 12 44 314 320 254 92 12 64 0 ..-- , 15__ o12 46 3384 320 22i5 192 12 64
Distance (km) Distance (kin)
contour intervol - 2.0 contour ;ntervoal = 2.0
T ot day 10 dep'hO P o day5 depth0
C U64: _______________0______C d
546
512
446 446
64
34E
05 u
250 5 5
192l2
64 /
D12 446 t34 320 254 62 16 64 512 448 264 320 256 192 128 64 00
Dstonce (i) Distonce (kin)
contour interv l = 0.5 contojr intervol 2 0
Figure 3.22 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) meridional (v)velocity (cm s), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 5 at day 10. Contour interval is 2.0
cm s" for (a) and (b), 0.5 °C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 m in (d).
85
(wi) qla
c) 0 -- 0 0 " 0 0 0 0 0 0S N '('I ( C'4 .( . IN - C4 ,I ,I C
C' C4~ ) to r, ('4 LO - ) r) n r) -' (3) ff4 U
0
0
000
C)
C
U II
C 4~
C) U
I
.0
Oj
conour deoe0utradvlcte.Tevria rs eto a
¢1
('4
Figure 3.23 Vertical cross-shore section of meridional (v) velocity (cm sj) forExperiment 5 at 'Jay 10. Contour interval is 2.0 cm s1. Dashedcontours denote equatorward velocities. The vertical cross section was
alongshore-averaged.
86
(, ) ( 100a 0 do0 ' 0 0 0 (N0o o o 0 o o 0 o 0 0 o 1 0
(' N rj C'4 C4) N' "N " " "N (j C4 Ca) UO ( 7) t' If) ) ' -tI. n, I , , I .
0
0U2
NI fl O
L)C
_P_
C II2 ,~
0, N
.000>
V)0
V) 9
C)
iU
a)(NI
C)j
Figure 3.24 Vertical cross-shore section of temperature (°C) for Experiment 5 at day10. Contour interval is 1.0 IC. The vertical cross-section was takenat y = 290 km.
87
U of day 20 depth 0 V at djy 20 depth 0440
4
420 446
320320
------ 13
25192
128
644
512 448 384 370 250 0i2 12n 0 1 1 00,toc (I 1-28 5 12 448 384 320t,256 102 128 64 0Di~~0stance (k inc(in)
contour interval - 2.0 contour anteroal -2.0
T at day 20 d-roth 0 P at day 20 depth 0640 4
512
384 E 3, 84 E
3205' 3205
256 *, 256-
192 . 192
64 64
0 0512 448 3i4 320 2154 I02 128 44 0o '12 448 3i4 3i20 55 182 128614 0DrStonce (lam) Distance (lam)
cords.,, aa = O.5 contour interval = 2.0
Figure 3.25 Surface isopleths of (a) zonal (u) velocity (cm s"), (b) meridional (v)velocity (cm s"), (c) temperature ('C), and (d) dynamic height (cm)relative to 24(00 n for Experiment 5 at day 20. Contour interval is 2.0cm s" for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 24(X0 m in (d).
88
C) C) r(u) (ld A J 0
Sin r- a, rj ,-j J rj C j I r " 1) ,-f _j
CD
CC)
(-
F ) e(
-longs ho aeagd
U)89
/((1
C1C
C) Cr'U
t=.gur 3.6 ertcalcros-hor setin o meidina (v veociy crn s ) f)
ExeieC tdy2. Cnor nevli . m s . Dse.otusdnt4qaowr eoiie.Tevria rs eto a
alnsoe-vrgd
C89
U at day 40 depth 0 V at day 40 depth 0
5-1 '- 40 1Vo640
------ 576
55,6
448 i 7
Distance38 Ek)6
contour'2 .0e~a .
c.nt.... 0tro 252
040 4
264 384
320 44 8 320 25 18 4
640 40
0 57
572 44 6 2 5 72 76 6 7246 242025 2 16 6Distnce(ti) Dstace t~r)
co44o8 inevl 05 otu4ntra 8.
Figure 3.27 SufcEspeh f()znl()vlct c 1 ,()mrdoa v
9()
o at (lay 55 d111 t(I
64 0
5 7
14 1 517,
4 413R
320u
256
/ 192
1283
64
5 1? 4 1 -1 .1 3 .2( 2". 6 192 12(R 6.1 0
corutomu i1tel Vol -:0"
Figure 3.28 Surface isopleths temperature ('C) Experiment 5 at day 55. Contourinterval is 0.5 'C.
91
U at day 80 depth 0 V at doy 80 de~pth 0---
64
5)6 b
SX J
32a 3. 20 .
69 26
6444
312 448 364 320 25f692 U26 64 o1 2466 3;4 0 2 ''6 Ill 12a6. 6 0
Distance (k-n) Distance (1,M)
contour intervalI - 5.0 contour interval =5 0
T at day SO depth0
640 P at day 80 d~pth0
C 640
382
364 E
32o u.
64 '6
5:2 466 3e6 3 2361 26 6ie 64 Do
Distonce (1,n) 512 448 364 320 361 2 1:8 66 0
contour interval = 0 5contour interval -2.0
Figure 3.29 Surface isopleths of (a) zonal (u) velocity (cmn s-'), (b) meridional (v)velocity (cin s-'), (c) temperature ('C), arid (d) dynamic height (cm)relative to 240X) m for Experiment 5 at day 80. Contour interval is 5.0cmr s" for (a) arid (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 mn in (d).
92
0~~u 0 0 d 00 0 0 0 0 0 0 0DC 0 000 0 0I 0 UJ
01~ ~ ~ t-j A 4
o- o o o o a N ' ( o o ' (N ') ( N (o
A
0)
1113
CO
I C
Fiur 3.3 Vetia crs-hr etino eii._ v eoi cns' o
)¢, /, '
C)
C'C)
IDJ
Figure 3.30 Vertical cross-shore section of meridional (v) velocity (cm s) for
Experiment 5 at day 80. Contour interval is 2.0 cm s'. Dashedcontours denote equatorward velocities. The vertical cross section wasalongshore-averaged.
93
(u J) Ld t1
I I , , , , I , I , IC I
0t
C) -
T0)
C-) II
94-
C--)
Ciur 3.1 V ria rs-hr scino e prtr °C o xeiet5a a
80 onorinevl s10 C hevriclcos-etinws aeat y-290km
94)
U at day 110 depth 0 V at day 110 depth 0$404v
512
448
-- - 2484 E*f34
320 u5~
2540( 0
12128
44
0 512 448 344 320 5412 12a 64 0312 44a 384 320 254 192 128 S. 0 Distance (kin)
Distance (krn)
contour interval - 5.0 cnori~ra .
T at day 110 depth 0 P at day 110 depth 0
640 d 40
.5,46
512 0 *''- 512
4,a8
4484
320
-10 82
121 126
4 64
(1 054 483432 5 1218 4 0512 448 380 320 258 M8 128 44 0
Distance (kin) tne(k)
contour interval =0.5 contnw, interval 2.0
Figure 3.32 Surface isopleths of (a) zonal (u) velocity (cmi s"), (b) meridional (v)velocity (cm s'), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 5 at day 110. Contour interval is5.0 cm s' for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 ni in (d).
95
(LU) tlldntl
oOC)0C)0COo) o oo°OooooC) o oC) a
1, 0
co
lr j
3)
U)C-C00UU
at y = 290km
96L
C)C
(-I
Figure 3.33 Vertical cross-shore section of temperature (°C) for Experiment 5 at day110. Contour interval is 1.0 0C. The vertical cross-section was takenat y = 290 km.
96
C, C, ~ C) C o C)00 0 0 C) - C- 0 ) C~) 0 :
Cl (N (> C 4 ('N (N 4NL) (A i0, L
.- \
/a -. b
CO
) ('5
ED-
cotusdnt qaow elcte.Tevria rs s cinwa(no gsoe-aergd
SI 0
/' / ,
0Ci
/4
0
Figure 3.34 Vertical cross-shore section of meridional (v) velocity (cm s') forExperiment 5 at day 110. Contour interval is 2.0 cm s'. Dashedcontours denote equatorward velocities. The vertical cross section wasalongshore-averaged.
97
a 40Cd'fC 4 b1 "*i • 0 |p 8= 'l
. \'
a • - .
... . . . . . . .I , . . . . . . . " 3
. ... . .... .. .
" " ..... VI 40- .
21 .'6 w2.026
doy 0 yfI
da , an (d 0 daC10.
"21' d II'l -(1 ' ' "-V/",/I9'i # 71',,.,o,,,,o . . ' /' { ,. ...
"0'. . -/ ....- : / :
. ... . . . .• - . ~-, . \". .
3 6 - .- . . ,
12 8 W 12 6 W 12 4 W 12 2 * 12 60 ' 6 W 1'.w '2 w
doy 60da O
Figure 3.35 Surface current vectors for Expeiment 5 at (a) day 20, (b) day 40, (c)
day 80, and (d) day 110.
98
U at doy5 depth0 V at day5 depth 0
64004a bu.. ...... 576
576
,: ' '. :' 440 4
38 ...... 4" E " 8413 E- -. ,- - 55 51-
320 -6 -a25012 C
128 -128
64 6
1 4 0 102 512 448 304 320 254 192 128 14 0Ditonce (km) Distonce (kin)
contour interval w 5.0 contour intervol = 5.0
T at day5 depthO P at day5 depth0
640 040c "° dU 76 570
512 512
40 448
446 4.@2 2
Distonce (lain) Distance (kin)
contour ;ntervol = 0.5 contour interval 2.0
Figure 3.36 Surface isopleths of (a) zonal (u) velocity (cm s"), (b) meridional (v)velocity (cm st), (c) temperature (°C), and (d) dynamic heighlt (cm)relative to 2400) m for Experiment 6 at day 5. Contour interval is 5.0cm st'for (a) and (b), 0.5 °C for (c) and 2.0 cm for (d). DashedContours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 m in (d).
99
U at day 10 depth 0 V at day 10 depth 0
440
5512
, 448
3S4~ q3 84EoO.... .. ... .. 1,J
- ~ a* -\ -225 35.... . . ,, -8
02 159
--- 4----------'''" 126
£4
10 4Dista43 3 ki 512 448 304 320 256 192 126 64 0
nce (km) Distance (kin)
contour interval = 50 contour interval - 5.0
T at daylO depth0 P at dayl 0depth0£40 ________________________ 40
57£ d 7
512 512
.48 )3a4 E384 E
350 u 320 1."
25£
'20 12£
64 64
00S.:44838 2: 2:97 13£84 53 448 A8£ 320 21£ l95 12£ £4 0
Distance (kn) Distance (kn)
contour interval - 0.5 contour intervoI - 2.0
Figure 3.37 Surface isopleths of (a) zonal (u) velocity (cm s"), (b) meridional (v)velocity (cm s'), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 10. Contour interval is 5.0cm s" for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 m in (d).
100
(u il l 11
C n , n C) nI C) C), C)
V)
C'
ao
0F) 8 -cI t _
i o
!~
Experiment 6 at day 10. Contour interval is 2.0 cm s' . Dashed
contours denote equatorward velocities. The vertical cross section wasalongs hore- averaged.
(ll)
( "C) C)in
ri.
C)
0.c
Figure 3.39 Vertical cross-shore section of temperature (C) for Experiment 6 at day10. Contour interval is 1.0 'C. The vertical cross-section was takenat y = 390 kn.
102
00 C)0 00~ C) 0 ) C) 0 ~C'00oC) O0OOF? C C) rI C 4 (q '! r) 4 ('4~j ~ C) CC4 ) C 4 C) C1 n
. ,I . I I, I, ., .1 .1 I I I I . .
0
0
/
U',00 _-
or- II
It
0
) 0
Figure 3.40 Ve'rtical cross-shore section of meridiona] (N,) velocity (cm s-' ) for
Experiment 6 at day 10. Contour interval is 2.0 cm s-'. Dashed
contours denote equatorward velocities. The vertical cross section was
taken at y = 390 kn.
103
C C)
.)o C) I
o)
Figure 3.41 Vertical cross-shore section of meridional (v) velocity (cm s") forExperiment 6 at day 20. Contour interval is 2.0 cm s' . Dashedcontours denote equatorward velocities. The vertical cross section wasalongshore -averaged.
104
- ' C ' rC .,., Cl CI CS C)0 C, C) C)
V)-
105
U at day 25 depth 0 V at day 25 depth 0
%_ 40
5112
354 E 382
050
.... ... ... 110
1262
'512 448 3684 320la254 192 1286 4 0051 448 3a4 320 2i6 i2 2le 646 0
Distnce (kMm) Distance (km)
contour inera =5. contour interval - 5 0
T at day 25 depth 0 P at day 25 depthO0
6.0 III 40
C U512 5 12
446 446
304~ is,
320320
258 ?54-
64 64
0 o
512 446 3i4 320 2;6 i2 126 64 0 112 446 36. 3201 2;6 iz2 lie 6. 0
Ostlance (km) Distance (Mmn)
contour intervaol = 0.5 contourl inter vol =' 2 0
Figure 3.43 Surface isopleths of (a) zonal (u) velocity (cm s-'), (b) meridional (v)velocity (cm s"), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400) m for Experiment 6 at day 25. Contour interval is 5.0cm s' for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 24(00 m in (d).
106
U at day 40 depth 0 40V at day,40 depth 0 4
$12 512
446 446
*L e7- to
520 u32U
.... 256Q 250
1226
512 445 384 320 25i6 192 126 64 0 512 445 3i4 320 2i6 192 128 64 0Di3tonce (kmn) 0istance (kin)
contour interval = 5.0 contour interval = 5.0
T ot day 40 depth 0 P at day 4D depth 0
640 440
512 S
44864
320 Q t 201.
C 250
192 192
2 9
64 64
0 0512 444 86 3j 2 256 19'2 126 6- 0 512 448 386 3'5) 256 12 129 64 0
D i 1(once (kmn) Distance (kni)
contour interv~al = 0.5 contour interval = 2,0
Figure 3.44 Surface isopleths of (a) zonal (u) velocity (cm s-), (b) meridional (v)velocity (cm s*1), (c) temperature (0C), and (d) dynamic height (cm)relative to 2400 m for Expefiment 6 at day 40. Contour interval is 5.0cml s' for (a) and (b), 0.5 'C for (c) and 2.0 cmn for (d). Dashedcontours denote offshore velocities in (a), equatorwvard velocities inl (b)and negative values relative to 24(X mn in (d).
107
(u1) Lid !-
0 C ) C I a Cl C ) C) C ) C , 0 C) 0 0 f C) ) 0 ) I
j fj C) - 'VI r4i (J 4 4)
o
C
C,
- 0
(.3.t
r)
t-,
Figure 3.45 Vertical cross-shore section of meridional (v) velocity (cm s') for
Expefrment 6 at day 40. Contour interval is 2.0 cm s". Dashedcontours denote equatorward velocities. The vertical cross section was
alongshore -averaged.
108
(tu) (I)d@Gc
r4 C ,4) C ) C) C ) a~ C 4 rq (4 (4 "4 (4 (,1)C) C) C(N~~~t o) cj e Lr) rnc
94q i ,P c) j N qf -40 I i I , I , I . I I , I . I I I II , I . I ,I • I .
0
a)
atC y = 30 -ti
109
I II- o
aO0_)
0)
Uiur 3.6 Vria0rs-hr eto ftmeaue(C o xeiet6a a
010
U at day 80 depth 0 V at day 80 depth 0440 140
445 - 448
r 304 E 384E
Caa
............. 258 2-2
1212 192
12 I
12
0 0512 440 384 320 256 192 128 54012 448 384 320 250 192 128 84 0
Distance (kin) Distance (kin)
contou.r interval = 5.0 contou.r interval - 5.0
T at day 80 depth 0 40P at day 60 depth0
C 64
5124 J, .. a
,* 54304 E 8
220: u1
02 C3
0
"4 .44
512 4 i134 320 356 42? 128 0 64 0512 448 384 3.10 250 192 128 84 0Distance (kirn) Distance (kirn)
contour interval = 0.5 contour interval - 2.0
Figure 3.47 Surface isopleths of (a) zonal (u) velocity (cm s'), (b) menidional (v)velocity (cm s"), (c) temperature ('C), and (d) dynaimic height (cm)relative to 2400 mn for Experiment 6 at day 80. Contour interval is 5.0Cm1 S" for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 m in (d).
110
U at day 100 depth 0 V at dcylOO depth0440 640
- 446 (0 8
*384 34
-320 7 *,, 30C 32
126 - 26*
64 64
512 448 384 320 54 2128 54 0 512 448 384 320 '256 192 28 6 0DitanCe (k) Distance (kmn)
contour inter~al - 5.0 contour nter~al - 5.0
T at day 100 depth 0 p at day 10depth 0640 640
C -576 d 7
5t2 0 05124464
39 E -384 E
410 320
92
044
4
312 4;8 3i4 320 254 M8 128 64 0 $12 4485 2364 320 256 192 28 84 0Distance (kin) Distance (kin)
contour interval -0.5 contour intervol -2.0
Figure 3.48 Surface isopleths of (a) zonal (u) velocity (cm s-), (b) meridional (v)velocity (cm s"), (c) temperature ('C), and (d) dynamic height (cm)relative to 2400 mn for Experiment 6 at day 100. Contour interval is5.0 cm s" for (a) and (b), 0.5 'C for (c) and 2.0 cm for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 2400 m in (d).
U at day 120 depth 0 V at day 120 depth 0 * 54
644
382 E~)5445 ~ ~ ~ 2 u430 24 5 2
254Ei 54
42 44
3440 44
4.
384-
0 32 /0
X258 250
444
5 52 445 3i4 320 19 42 124 4 4 0 05Q2 44S 384 320 256 442 l2e i4 00
Distance tkrne Diii r )
contur iteral -0 5contour interval = 2.0
Figure 3.49 Surface isopleths of (a) zonal (u) velocity (cmn s'), (b) meridional (v)velocity (cmn s-), (c) temperature (0C), and (d) dynamic height (cm)relative to 2400 m for Experiment 6 at day 120. Contour interval is5.0 cm s-' for (a) and (b), 0.5 'C for (c) and 2.0 cmi for (d). Dashedcontours denote offshore velocities in (a), equatorward velocities in (b)and negative values relative to 24(X m in (d).
112
(w) tqjd Q
- '4r-~u CO L] 04 1)
00
006
T) tQ
V,)
0
0
CK)
12 ) 00
0
Figure 3.50 Vertical cross-section of the cross-stream derivative of potential vorticitymultiplied by the grid size ('C m"' s-') scaled by 10' for the time-averaged days 90-99 of Experiment 5. Contour interval is0.1 'C in' s". Dashed contours denote negative values. The verticalcross-section was alongshore -aver, ged.
113
00) ~d9
00.
Fiue351 Vrialcossc~no hecosstemdrvaieo ptnil otct
mutpidb h rdsz C -1s1 cldb 0 o h ie
avrgddy0-5 fEprmet6 otu nevli
0 .1" 's.D se otusdnt eaievle.T evria
Figue 3. 1 Vrti-sca i crsssction of the ross-steadervtv fpteta otc
114
0 -, 9*
• ,,
6s
1*J -,'
00
,,
0 U
* .
Figure 3.52 Kinetic energy (ergs cm ) time series for Experiment 6.
115
PE PEI
EIZK- I LIZZ.'Zo
KE KE I
Figure 3.53 Basin-averaged energy diagram for days I to 12 of Experiment 6.Energies are in ergs cm- and transfer rates are in 106 ergs c-3 sA.
116
(u J) tLdo(J
A r4 C'!j '" (4(0) 4 n Y ,4 n• •
0 ' 0.0.00 ~ @2 0)-
00
-
.0.
C II
1J117
ni -3
- ) C00
n"j
Figure 3.54 Vert~~~~~~ica. rs-eto ftecossra eiaieo oeta ofct
Fiur 354 Vetalcross-sectiwsaongofsheos-readervtv.fpteta otct
117
PE PE'
KE KE'
Figure 3.55 Basin-averaged energy diagram for days 100 to 120 of Experiment 6.Energies are in ergs cm- and transfer rates are in 106 ergs cm- s".
118
IV. COMPARISON OF MODEL RESULTS WITH OBSERVATIONS
Quantitative comparisons of model results with actual observations are not easily
done due to the diversity in the current field structure in the many experiments.
However, a few assumptions can be made to assist in this comparison. First,
equatorward flow exhibited anywhere in the nearshore region was considered a coastal
jet. Secondly, poleward flow beneath the equatorward jet was considered an
undercurrent even if this flow was contiguous with a northward surface current further
offshore. Finally, values for Experiment 2 were taken at day 30 (June 30) during
summer wind stress conditions. The resulting values are displayed in Table III with
comparisons from Batteen et al. (1989) and various observational studies. Experiments
1 and 5 are not included in the table due to the lack of a coastal jet in these
experiments.
As seen in Table Il, the model gave widely varying results over the different
experiments. No one experiment fit all the ranges of the observations, but several
important comparisons can be made. The coastal jet of Experiment 2 (transient wind
stress with a June 1 start) was weaker and narrower compared to observations.
Additionally, the undercurrent velocity was too small. The other features, listed in the
table, of both the coastal jet and undercurrent, do compare favorably with the
observations. It should be noted, however, that no eddies or filaments developed in
this experiment.
Experiment 3 (constant stress in the nearshore region) developed a reasonably
strong, well defined coastal jet, but the undercurrent was too deep and wide. This
119
overdevelopment of the undercurrent could be a product of the much stronger coastal
jet in this experiment. A stronger jet can lead to a larger alongshore pressure gradient
and, therefore, a stronger poleward undercurrent.
Experiment 4 (climatological wind stress, constant in the nearshore region)
exhibited the proper current structure except that the coastal jet was too weak.
Additionally, the undercurrent was too wide and located too far offshore.
The results of Experiment 6 (two tenths degree climatological wind stress)
showed a similar coastal jet structure as in Experiment 3, but a much shallower,
narrower undercurrent. In Experiment 6 the coastal jet was confined to a relatively
small region to the north at Cape Mendocino. Thus, the signal from the jet was
greatly reduced due to its limited size. The jet in Experiment 6 was also the result of
not only the strong stress in the region, but also the negative wind stress curl.
The results of Experiment 5 (not shown in the table) did show initial coastal jet
development but this jet did not persist. The 14 cm s' velocity of a poleward surface
current in Experiment 5, as well as the 4 cm s- velocity of this same current in
Experiment 1 were considerably smaller than the observed peak velocities of
25 cm s-1 (Hickey, 1979).
In all experiments which developed eddies (Exps. 3-6), the size of the eddies
compared well with the observations. There remained a discrepancy in zonal eddy
velocity, however. The maximum eddy velocity of 40 cm s- was seen in Experiment
6. This velocity was still less then typical velocities observed during the CODE
experiments (Kosro and Huyer, 1986). This can be attributed to the difference between
the steady climatological wind stress values in the experiments and the much stronger
120
transient wind stress seen during CODE. It is interesting to note that the zonal eddy
velocity obtained for Experiment 6 was at least twice as large as the other experiments
including Batteen et al. (1989). This shows the importance of using the more
representative, finer scale two tenths degree climatological wind forcing. The
differences exhibited between observed and modeled values may also be a result of
several modeling considerations: flat bottom rather than shelf / slope topography,
transient rather than steady wind forcing, neglect of salinity and / or the climatological
temperature profile used for the initial mean stratification (Batteen et al., 1989).
The offshore equatorward flow seen in all the climatological forcing experiments
(Exps. 3-6) also compares well to observations. The flow appears to be driven by the
negative wind stress curl offshore (McCreary et al., 1987).
The temperature fields of Experiment 6 exhibited filamentous structures which
closely resemble the cold water plumes seen in many recent satellite observations.
Kelly (1985) found that the plumes can extend offshore 200 km or more. Other
filaments have been observed as long as 400 km (Ikeda and Emery, 1984). The
filament of Experiment 6 extended to - 288 km before fragmenting, which compares
favorably with these observations. The characteristic T-shaped termination of the initial
modeled filament has also been observed in the field (Ikeda and Emery, 1984).
The variable current structure around Cape Mendocino in Experiment 6 correlates
well with recent work done by Magnell and Winant (1987). Current meter data taken
by them during the NCCCS program shows predominantly southward flow north of
Cape Mendocino (Fig. 4.1a) and predominantly northward flow south of the Cape
(Fig. 4.1b). (The placement of the current meters is shown in Figure 4.2.) This
121
opposing current pattern about Cape Mendocino is seen throughout Experiment 6 and
is clearly illustrated in Figure 3.48, the meridional velocity field for day 120. The
concept that spatial variations in wind stress leads to convergence of surface currents
and the formation of a cold filament is also consistent with the work of Kelly (1985).
Spatial variability in the wind field clearly has a significant effect on the oceanic
response of the CCS, particularly in the development of opposing surface currents.
As several studies have indicated, it is possible that poleward flow driven by the
positive curl at the coast is the normal flow in many regions of the CCS (Hickey,
1979; Chelton et al., 1987). It is only when equatorward wind stress of significant
intensity is present that the equatorward flow overcomes this poleward current with a
resulting coastal jet (Hickey, 1979; McCreary et al., 1987).
Overall the model results compare quite favorably with available observations,
particularly in the structure and form of the current systems that develop. Most notable
of these correlations is the opposing currents and cold filaments which develop in
Experiment 6.
122
00
-~ - R
- 0
CD~
< A5
E U"
CC
0
a.)E2 4 ir
0 0
a Cii N -cU'
EU
2 r
W~ I 0 >'
9) v gs
123~
T..,ro CT~rmta 1
'87 "87
Figure 4.1 Current vector time series for a station (a) north of Cape Mendocino
and a station (b) south of Cape Mendocino. Data from the NCCCSProgram (from Magnell and Winant, 1987).
12
-1124
0
00
00r-4 0
Figure 4.2 Pilot moored instrument station locations during NCCCS program.Station namne refers to water depth in meters (From Magnell andWinant, 1987).
125
V. SUMMARY AND RECOMMENDATIONS
A. SUMMARY
This study used a high-resolution primitive equation model to study the effects
both of transient and climatological wind forcing on eddy generation in the California
Current System. An annually periodic wind forcing function with zonal variability, was
used as transient forcing in an idealized, flat-bottom eastern boundary current model
in several experiments. One degree and two tenths degree steady wind stress data,
varying in x and y, were also used as climatological forcing in other experiments. In
addition, stability analyses were made to describe any types of instability that occurred.
Experiments 1 and 2 utilized a periodic wind stress function for their forcing.
In Experiment 1, since the curl component of the forcing was stronger than the stress,
a surface poleward flow developed in the nearshore region with an equatorward flow
offshore. This structure is similar to that of the Davidson Current during the winter
although the modelled current was weaker than observed. At the end of the simulation,
a coastal jet was beginning to form and move southward, denoting the beginning of the
upwelling season. In Experiment 2, due to the stronger stress compared to the curl,
a coastal jet developed with an undercurrent. Again, though, because the proportion
of wind stress to wind stress curl decreased in the forcing, a poleward surface flow
started to dominate and by late July, the coastal jet disappeared. No eddies were seen
in either of these experiments due to the lack of a lasting jet / undercurrent structure
and the resultant instability. These results support the findings of McCreary et at.
126
(1987), that wind stress curl is important in developing the Davidson Current in the
winter season as well as the poleward surface flow seen throughout the year. It is also
important in forming the equatorward offshore current. When the equatorward wind
stress is sufficiently strong, a baroclinic equatorward surface jet develops, which
overrides the poleward flow and forms an undercurrent.
Experiment 3 tested the application of a spatially varying steady climatological
wind stress forcing in the offshore region and constant stress in the nearshore region.
A strong coastal jet and a very large undercurrent developed. Large eddies formed,
but had sluggish velocities compared to observations. The nearshore forcing was
changed to be zonally constant in Experiment 4. In this case eddies developed near
the shore, but were smaller in diameter and slower than observations. The current
structure was more realistically sized, but still too slow compared to observed values.
In both of these experiments there was no curl at the coast. The offshore area, with
its spatially varying wind field and curl, did form well developed equatorward and
poleward surface currents which were not seen in other steady forcing studies, as in
Batteen et al. (1989).
The wind stress forcing of Experiment 5 was comprised exclusively of spatially
varying one degree climatological wind stress data with positive curl along the coast.
Although an equatorward jet was initially present, it was relatively weak and was soon
overwhelmed by poleward surface flow form the south. The offshore region again
exhibited the equatorward surface current. Some signs of eddy development were just
beginning to show when the Experiment was terminated at day 110. In this
experiment it would appear that the wind stress curl was strong relative to the stress
127
component and as such the curl was the dominant driving mechanism in the current
system. The results were similar to those of Experiment 6 in that the where curl
increased in strength in the fall season and overpowered the wind stress. However, the
resolution of the wind field was too coarse to allow for the forcing of opposing current
structures and the subsequent formation of filaments and eddies as a result of this
convergence.
The final experiment, Experiment 6, utilized one degree climatological wind stress
forcing in the offshore region and two tenths degree wind stress data in the region
within 255 km of the coast. Again there was a positive curl in the coastal region, but
the scale of the data was such that the forcing led to the formation of opposing
currents. In the area near Cape Mendocino, there was a convergence in the surface
flow which led to the development of a well defined cold filament. Additionally, the
current structure was stronger than Experiment 5, with velocity values more
representative of observations. The eddies formed during this experiment were of
moderate size with maximum zonal velocities which compared quite well with previous
observational studies. It is apparent from these results that spatial variability in the
wind field is important for obtaining realistic current and eddy structures in the CCS.
Energy analyses were made for both Experiments 5 and 6. Since the eddies of
Experiment 5 were still relatively weak at the time the experiment was completed, the
analysis was inconclusive as to the type of instability occurring. Qualitatively, it was
seen that analysis of the horizontal shear and potential vorticity showed that barotropic
instability could be important. There was a shift in energy mechanisms during the time
span of the Experiment 6. During the first 12 days, when the nearshore eddies were
128
forming, baroclinic instability was dominant. Later, as eddies began to be formed
offshore, barotropic instability was dominant. Thus, during the model runs of this
research both baroclinic and barotropic instability processes were present.
A final note can be made concerning the formulation of the forcing in the
nearshore region. It appears that the most important consideration in nearshore forcing
is the degree of complexity exhibited in this field. While the relative weights of stress
to curl play an important role in the gross structure of the current system, the
interaction of the diverse current structure driven by an equally diverse wind field can
play an important role in the production of cold filaments and eddies.
B. RECOMMENDATIONS
The importance of using high resolution wind stress data in the nearshore region
of a numerical model has been shown. The role of transient forcing, particularly in
relation to this spatially varying climatological wind stress field, has yet to be clarified.
A logical next step to this study is the use of a time series of climatological wind
stress data, preferably of two tenths degree resolution, to force the model. This form
of forcing would allow for not only a realistic wind field, but also an accurate seasonal
pattern. Both a spatially and temporally varying forcing of this type would greatly help
to clarify the role of wind forcing in the CCS. Once these wind forcing studies have
been completed, parameters such as bottom and coastline topography should be
incorporated into the model to study their effects on instability and mesoscale
processes.
Another area of importance is the study of sudden, strong wind signals in the
onset and intensification of upwelling. Wind events of this sort may also be of
129
importance in eddy generation (Carton, 1984; Carton and Philander, 1984). The
incorporation of an intense wind stress forcing on an already established current system
may be a simplistic but effective method of studying this phenomena.
Two additional projects are also recommended involving the model itself. First,
the resolution of the model should be modified to allow for detection of frontal
features. Fronts in the CCS have been observed with scales of 10 km or less (Mooers
et al., 1976). Reducing the model resolution to 1 km by 1 km vice the current 8 km
by 10 km would be required to completely resolve these features. Secondly, the many
regional models for the west coast of the United States should be coupled to derive a
"total" CCS numerical model, encompassing the area from Baja California to Canada.
Only by modeling the entire region can a true picture of the flow patterns in the CCS
be properly simulated.
130
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