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Continental Shelf Research 27 (2007) 1233–1248

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A numerical study of island wakes in theSouthern California Bight

Changming Dong�, James C. McWilliams

IGPP, University of California, Los Angeles, CA 90095-1567, USA

Available online 2 February 2007

Abstract

With the existence of eight substantial islands in the Southern California Bight, the oceanic circulation is significantly

affected by island wakes. In this paper a high-resolution numerical model (on a 1 km grid), forced by a high-resolution

wind (2 km), is used to study the wakes. Island wakes arise due both to currents moving past islands and to wind wakes

that force lee currents in response. A comparison between simulations with and without islands shows the surface

enstrophy (i.e., area-integrated square of the vertical component of vorticity at the surface) decreases substantially when

the islands in the oceanic model are removed, and the enstrophy decrease mainly takes place in the areas around the

islands. Three cases of wake formation and evolution are analyzed for the Channel Islands, San Nicolas Island, and Santa

Catalina Island. When flows squeeze through gaps between the Channel Islands, current shears arise, and the bottom drag

makes a significant contribution to the vorticity generation. Downstream the vorticity rolls up into submesoscale eddies.

When the California Current passes San Nicolas Island from the northwest, a relatively strong flow forms over the shelf

break on the northeastern coast and gives rise to a locally large bottom stress that generates anticyclonic vorticity, while on

the southwestern side, with an adverse flow pushing the main wake current away from the island, positive vorticity has

been generated and a cyclonic eddy detaches into the wake. When the northward Southern California Countercurrent

passes the irregular shape of Santa Catalina Island, cyclonic eddies form on the southeastern coast of the island, due

primarily to lateral stress rather than bottom stress; they remain coherent as they detach and propagate downstream, and

thus they are plausible candidates for the submesoscale ‘‘spirals on the sea’’ seen in many satellite images. Finally, the

oceanic response to wind wakes is analyzed in a spin-up experiment with a time-invariant wind that exhibits strips of both

positive and negative curl in the island lee. Corresponding vorticity strips in the ocean develop through the mechanism of

Ekman pumping.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Southern California Bight; Islands; Wakes; Submesoscale eddies; Vorticity; Circulation

1. Introduction

In the past decade physical processes have beenextensively investigated in the Southern CaliforniaBight (SCB), an oceanic region south of Point

front matter r 2007 Elsevier Ltd. All rights reserved

.2007.01.016

ng author. Tel.: +1310 825 5402.

ss: cdong@atmos.ucla.edu (C. Dong).

Conception, north of San Diego, and east of theSanta Rosa Ridge; studies focused on bight- andmesoscale currents are Hickey (1991, 1992, 1993,1998), Hickey et al. (2003), Wang (1997), Harmsand Winnant (1998), Oey (1999), Bray et al. (1999),DiLorenzo (2003), Bograd and Lynn (2003), Oeyet al. (2004), and Dong and Oey (2005). With high-resolution, remotely sensed ERS-1 and ERS-2 SAR

.

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–12481234

images, many small eddies, most less than 30 km indiameter, are observed on the sea surface in the SCB(DiGiacomo and Holt, 2001). In high-frequencyDoppler radar data, many fine structures in thesurface currents near the coasts are exposed(Beckenbach and Washburn, 2004). These lattertypes of small-scale flows are submesoscale (i.e.,smaller than the first baroclinic deformationradius). Fundamental questions about their origin,evolution, and material transport still need answers.

Based on in situ and remotely sensed measure-ments and numerical modeling, Caldeira et al.(2005) suggests that island wakes are a candidatefor generation of the submesoscale eddies. In theSCB there are eight substantial islands (Fig. 1). Theislands of San Miguel, Santa Rosa, Santa Cruz andAnacapa (collectively called the Channel Islands)form the outer edge of the Santa Barbara Channeleast of Point Conception in the northern SCB.Santa Catalina Island is located southwest of thePalos Verdes Peninsula with San Nicolas, SantaBarbara, and San Clemente Islands farther offshoreto the west and south. The total area of these islandsoccupies less than 5% of the SCB.

Much research has been done to understand thephysical processes in the wakes of islands andheadlands (e.g., Barkley, 1972; Pattiaratchi et al.,1987; Wolanski and Hamner, 1988; Aristegui et al.,1994; Heywood et al., 1996; Dietrich et al., 1996;

Fig. 1. SCB model domain. Co

Barton et al., 2000; Aiken et al., 2002; Coutis andMiddleton, 2002; Harlan et al., 2002, Neill andElliott, 2004; Caldeira et al., 2005; Sangra et al.,2005). An enhancement in the productivity andbiomass around islands and the general biologicalimpact of wakes have received much attention (e.g.,Hamner and Hauri, 1981; Hernandez-Leon, 1991;Dower et al., 1992;Martinez andMaamaatuaiahutapu,2004; Hasegawa et al., 2004). The vertical transportassociated with the eddies in the wake and theirimplication in the biological consequence have beennoticed (Wolanski and Hamner, 1988; Deleersnijderet al., 1992; Wolanski et al., 1996). Environmen-tal effects have also been studied since the watersare trapped, and particulates accumulate aroundislands (Rissik et al., 1997).

The study of the physical processes related to thewake behind an obstacle has a very long history influid dynamics (e.g., Batchelor, 1967). In theclassical problem with horizontal flow and uniformdensity in a non-rotating frame, a viscous horizontalboundary layer is formed along the solid boundarywhere vertical vorticity, z, is generated. As the flowpasses the obstacle, it accelerates and the pressuredecreases according to Bernoulli’s rule. An adversepressure gradient may develop at the downstreamedge of the boundary layer that can then support aflow reversal and detachment of the boundary layerfrom the solid wall into the interior where eddies are

lors indicate water depth.

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–1248 1235

generated by wake instability. Laboratory experi-ments (Batchelor, 1967; Gerrard, 1978) indicate thata two-dimensional flow around a cylinder is wellcharacterized by the Reynolds number, Re ¼ UD=n,where U is the unperturbed upstream velocity, D thediameter of the cylinder, and n the molecularkinematic viscosity. A series of photographs of theflow regimes obtained at different Re values ispresented in Van Dyke (1982). If Reo1, flowseparation does not occur, and the flow is symmetricupstream and downstream. If Reo40, a laminarseparation is obtained with two steady vorticesdownstream from the obstacle. At moderateReynolds numbers, 40oReo103, the steady vor-tices are replaced by a periodic ‘‘von Karman vortexstreet’’, and finally for Re4103, the separated flowbecomes increasingly turbulent and temporallyirregular.

In the presence of stable density stratification androtation, and with an extremely large Re value,oceanic and atmospheric wakes can differ signifi-cantly from homogeneous, non-rotating wakes withrelative low Re values (Boyer and Davies, 2000).With Re large, the flow is expected a priori to befully turbulent. The common use of an eddyviscosity, ne ðbnÞ, in a numerical model allows apossible comparison with the classical wake, but itentails the important issue of how to estimate anappropriate value for ne. A Reynolds number basedon the eddy viscosity, Ree ¼ UD=ne, is thus animportant non-dimensional parameter for modelinggeophysical wakes.

In a homogeneous, rotating fluid, both theReynolds number and Rossby number (Ro) deter-mine the eddy shedding. Ro is defined by Ro ¼

U=fD, where f is the Coriolis parameter. Labora-tory experiments and theoretical and numericalstudies show that increasing the rotation rate tendsto inhibit the shedding of eddies (e.g., Boyer andDavies, 1982; Walker and Stewartson, 1972; Page,1985; Heywood et al., 1996). In these papers the

Ekman number, defined by Ek ¼ n=fD2, is intro-duced as a parameter characterizing the eddyshedding. Note that Ek ¼ Ro=Re is not an inde-pendent parameter. With a differential backgroundrotation frequency (i.e., ba0), the flow separationand eddy formation are affected by the direction ofthe incident current with respect to that of thepropagation of the Rossby waves (e.g., Merkin,1980; Johnson and Page, 1993; Tansley andMarshall, 2001). For eastward flow past an island,the b effect inhibits the separation and formation of

an attached eddy, while in a westward flow it doesnot have a significant influence.

For wakes in a stratified flow, the baroclinicFroude number, Fr ¼ U=NH, represents the ratioof inertial and buoyancy forces. H is the verticalscale (e.g., set by the upstream flow and densitystratification profiles), and N is a characteristicmagnitude for the Brunt-Vaisala frequency, N ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ðg=r0Þðqr=qzÞ

p(g is the gravitational accelera-

tion, r is the upstream density profile, r0 is a meandensity, and z is the upward vertical coordinate).Lin and Pao (1979) reviewed stratified, non-rotatingwakes with the distinctive behaviors of wakecollapse (i.e., a reduction of the vertical extent ofthe wake behind the obstacle), internal waveradiation, and downstream emergence of verticallythin (pancake) vortices when Fro1.

When both rotation and stratification are dyna-mically influential, the scenario differs from theabove. For a flow past a submerged solid obstaclewith moderate values of Re, laboratory experimentsby Boyer and Chen (1987) indicate that increasingdensity stratification (decreasing Fr) suppressesvertical motion, inhibits flow over the obstacle,and causes recurrent vortex shedding to occurbehind the obstacle at smaller values of Re than inmore weakly stratified flows. Their data indicatethat the Strouhal number, St ¼ D=TU , associatedwith recurrent eddy shedding at a time interval, T, isnot affected significantly by changes in the Burger

number, Bu ¼ ðRo=FrÞ2 ¼ ðRd=DÞ2, where Rd is thebaroclinic deformation radius, Rd ¼ NH=f .

An oceanographically geophysically importantdistinction is between shallow- and deep-waterwakes, depending upon whether the dominantboundary stress is associated with the nearshorebottom or the lateral side of the island (Tomczak,1988). In the shallow-water case, bottom drag is theprimary source of vorticity generation. In deep-water case, the influence of bottom drag is notimportant. This circumstance can be obtained in amodel (e.g., in this paper) by the combination ofvertical island sides and a surface-intensified up-stream flow.

For a shallow-water wake, Pingree and Maddock(1979) proposed that the vorticity near a headlandis primarily generated by bottom frictionaltorque rather than the no-slip lateral boundarycondition. Signell (1989) suggests two vorticityproduction mechanisms associated with shallowwater: ‘‘slope torque’’ (i.e., flow in shallower waterhas a greater depth-distributed drag force than that

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–12481236

in deeper water, resulting in a torque on the fluidcolumn) and ‘‘speed torque’’ (i.e., stronger flow isrelatively more retarded than weaker flow due to thequadratic velocity dependence of bottom stress). Aneffective Reynolds number, the ratio betweenadvective and bottom-frictional rates, is a non-dimensional parameter controlling the flow separa-tion and eddy shedding. Wolanski et al. (1984)called the effective Reynolds number the ‘‘islandwake parameter’’. The parameter has since beenapplied to a number of numerical studies with two-or three-dimensional (homogeneous) models (Sign-ell and Geyer, 1991; Furukawa and Wolanski, 1998;Wolanski et al., 1996; Alaee et al., 2004; Neill andElliott, 2004). Edwards et al. (2004) argue that thewake can also be affected by inviscid lateral stressfrom bottom pressure, i.e., form drag. Smolarkie-wicz and Rotunno (1989) propose an inviscidmechanism for vertical vorticity generation whenhorizontal vorticity is baroclinically generated andthen tilted into the vertical direction. In a rotatingfluid vorticity can be generated in the absence ofviscosity by potential vorticity conservation andvortex stretching when the fluid moves overshallower water near an island; however, as longas there is no net change in the depth betweenupstream and downstream, no net vorticity isgenerated this way. For the deep-water island wake(our subject), the vertical-tilted vorticity generationis trivial due to the negligible vortex-stretching.Kolyshini and Ghidaoui (2003) analyze the wakeinstability using the shallow-water equation (withno rotation).

For a deep-water island wake, bottom frictioncan be neglected. Using a rotating, reduced-gravitymodel, Heywood et al. (1996) show eddy sheddingthat is inhibited by an increase in the rotation rate(i.e., decrease in Ro). Coutis and Middleton (2002)numerically investigate a three-dimensional wakearound an isolated island. With a realistic islandgeometry and a strong incident current (0:7m s�1 atthe surface and decaying linearly to zero within a3 km water column), vortex shedding occurs in thewake. Focusing on the wake instability andmesoscale and sub-mesoscale eddy activity with anidealized island, Dong et al. (2007a) find the threeinstabilities are evident: centrifugal, barotropic, andbaroclinic. Sensitivities are shown to three non-dimensional parameters: the Reynolds number (Re),Rossby number (Ro), and Burger number (Bu). Thedependence on Re is similar to the classical wake inits transition to turbulence, but in contrast the

island wake contains coherent eddies no matter howlarge the Re value. When Re is large enough,the shear layer at the island is so narrow that thevertical component of vorticity is larger than theCoriolis frequency in the near wake, leading tocentrifugal instability on the anticyclonic side. AsBu decreases the eddy size shrinks from the islandbreadth to the baroclinic deformation radius, andthe eddy generation process shifts from barotropicto baroclinic instability. For small Ro values, thewake dynamics is symmetric with respect to cyclonicand anticyclonic eddies. At intermediate Ro and Bu

values, the anticyclonic eddies are increasingly morerobust than cyclonic ones as Ro=Bu increases, butfor large Re and Ro values, centrifugal instabilityweakens the anticyclonic eddies while cycloniceddies remain coherent.

In the present study, a high-resolution oceaniccirculation model forced by a fine-resolution windanalysis is utilized to make a phenomenologicalexploration of island wakes in the SCB. The fineresolution in both the oceanic model and wind datamakes it possible for the model to resolve both thevorticity generation process and the ensuing sub-mesoscale eddies shed from islands. The paper isorganized as follows: Section 2 is the introduction ofthe numerical model configuration; in Section 3 theeffect of islands is examined; in Section 4 threeexamples of the island wakes are analyzed; Section 5examines the oceanic response to wind wakes; andSection 6 is the summary and discussion.

2. The model

The Regional Oceanic Modeling System (ROMS)solves the rotating Primitive Equations (Shchepetkinand McWilliams, 2005). This model uses a general-ized sigma-coordinate system in the vertical direc-tion and curvilinear grid in the horizontal plane. Itis a split-explicit, free-surface oceanic model, whereshort time steps are used to advance the surfaceelevation and barotropic momentum equations,with a larger time step used for tempera-ture, salinity, and baroclinic momentum. A third-order, upstream-biased advection operator allowsthe generation of steep gradients in the solution,enhancing the effective resolution of the solution fora given grid size when the explicit viscosity is small.The numerical diffusion implicit in the third-orderupstream-biased operator allows the explicit hor-izontal viscosity to be set to zero without excessivecomputational noise or instability (The impact of

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Table 1

Numerical experiments

Exps. Topography Wind forcing

Exp. 1 ETOP2 2 km MM5 wind

Exp. 2 Sunken Islands 2 km MM5 wind

Exp. 3 Flat bottom Steady wind

C. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–1248 1237

different forms of the horizontal viscosity onnumerical solutions can be found in Shchepetkinand O’Brien, 1996). The vertical viscosity is para-meterized using a K-profile parameterization (KPP)scheme (Large et al., 1994). The bottom stress iscalculated with ~tb ¼ Cdr0~uj~uj, where tb is thebottom frictional stress, r0 the water density, Cd

the drag coefficient (Cd ¼ 2:5� 10�3 in this study),and ~u the bottom current. The no-slip lateralboundary condition is also imposed through themomentum advection operator and yields animplicit lateral stress (see Dong et al., 2007a, for afull discussion).

The model domain is plotted in Fig. 1 with a gridspacing of 1 km horizontally and 40 levels vertically.The fine resolution resolves all eight islands in SCB.Mixed boundary conditions are used along the openboundaries, i.e., the Orlanski radiation condition inthe tangential direction and the Flather conditionwith adaptive restoration of material properties toimposed data under inflow conditions (Marchesielloet al., 2001). The restoring data for the lateral open-boundary conditions and the initial conditions areextracted from a 1996–2003 ROMS solutionin a larger U.S. West Coast domain (Dong et al.,2007a,b, using procedures similar to those inMarchesiello et al., 2003). The solid boundaryaround the island and land has zero-normal andno-slip flow implemented through a standard land-mask algorithm (Shchepetkin and O’Brien, 1996).(The solutions presented here have insignificantinternal gravity wave energy or open-boundaryreflection.)

A reanalyzed wind with a horizontal resolution of2 km is used as the surface forcing, along withclimatological heat and fresh-water flux (of lesserimportance than the wind stress in the relativelyshort-time integrations used in this paper.) The dataset is generated by a mesoscale meteorologicalmodel MM5 through a down-scaling reanalysisprocedure on successive embedded grids of 54, 18, 6,and 2 km. This wind product and its observationalcalibration are described in Conil and Hall (2006)except that it does not include a 2-km domain. Thewind speed is converted to the stress using theformula of Large and Pond (1981). The tidal forcingin SCB is relatively weak (Munchow, 1998) and isnot included in the current paper.

In the present study a series of numericalexperiments is performed (Table 1). A primaryexperiment with realistic topography (ETOP2 with2-min horizontal resolution) and the 2 km MM5

wind is implemented for Year 2002 (Exp. 1). In analternative experiment directly examining the islandeffects in SCB, all islands are sunk to a minimumdepth of 50m (leaving the mainland shallowbathymetry unaltered) but still forced by the 2 kmMM5 wind (Exp. 2). A time-invariant wind with astrong wind curl behind the islands is used to studythe influence of the wind wake on the oceaniccurrent (Exp. 3), where the bathymetry is modifiedby both removing the islands and setting theminimum depth 1000m everywhere to exclude anycurrent-topography interaction.

3. Island effects

Prior to analyzing particular island-wake cases,we first examine the impact of the existence of theeight islands on the physical processes in the SCB.Two parallel experiments (Exps. 1 and 2) areperformed: the ETOP2 bathymetry is used in bothof experiments, but in Exp. 2, all islands arereplaced with water 50m in depth. The forcing,boundary conditions, and initial conditions in thetwo experiments are identical. The model isintegrated for three months (January–March,2002) for both experiments. To avoid any effectfrom the initial condition, only the results in Marchare analyzed.

Fig. 2 shows the surface vorticity on March 15 forExps. 1 and 2. The vorticity distributions in the twoexperiments are similar but the eddies aroundislands are much stronger in Exp. 1 than those inExp. 2. Within the gaps of the Channel Islands andsouth of these islands, cyclonic and anticycloniceddies are presented in Exp. 1. Eddies are also foundaround Santa Catalina Island, San Nicolas Island,and even the smaller Santa Barbara Island. Thediameter of these eddies is less than 20 km, aboutthe same size as the islands. For Exp. 2 with sunkenislands, the vorticity around most island areas ismuch weaker than that in Exp. 1 except around SanNicolas Island, where a pair of strong cyclonic and

ARTICLE IN PRESS

121°W 120°W 119°W 118°W 117°W30’

33°N

30’

34°N

30’

121°W 120°W 119°W 118°W 117°W30’

33°N

30’

34°N

30’

0.4

0.2

0

0.2

0.4

0.6

Fig. 2. Comparison of surface vorticity (normalized by the Coriolis frequency f ) on March 12, 2002 with islands (Exp. 1; upper panel) and

with sunk islands (Exp. 2; lower panel).

0 5 10 15 20 25 304

6

8

10

12

14

16

18

Date (March, 2002)

Enstr

ophy (

m2s

−2)

Fig. 3. Time series of surface enstrophy for Exp. 1 (islands, solid

line) and Exp. 2 (sunken islands, dashed line).

C. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–12481238

anticyclonic eddies occurs on March 15, likelycaused by the wind wake (Section 4).

The intensification of eddy activity by islands canalso seen in the time series of the surface enstrophy(i.e., area-integrated square of the vertical compo-nent of vorticity at the surface) during March 2002in Exps. 1 and 2 (Fig. 3). It is found that the sinkingof the islands results in a 29% decrease in theenstrophy, which is much larger than the portion ofthe area of islands in the SCB, viz., less than 5%.Even with 50m depth, the sunken islands are a(reduced) source of wake vorticity through bottomdrag (Section 4), and no doubt further sinkingwould further diminish the surface enstrophy intheir vicinity. Thus, probably one-third or more ofthe eddy activity in the SCB is directly caused by theislands.

ARTICLE IN PRESS

30’ 15’ 120°W 45’ 30’30’

40’

50’

34°N

10’

0.2m/s

A

A

Fig. 4. Channel Island wake: surface velocity on March 12, 2002.

Section AA is indicated by the solid line.

Fig. 5. Channel Islands wake: time sequence of maps for surface vorticit

C. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–1248 1239

4. Current wakes

In this section, three illustrative island wakes areanalyzed: a wake southwest of the Channel Islandswith flow squeezed through the narrow gaps, a wakearound San Nicolas Island with flow from thenorthwest, and a wake around the Santa CatalinaIsland with flow from the southeast.

4.1. Case 1: Channel Islands

As shown in Fig. 4, when a flow squeezes throughthe gaps between the Channel Islands, a largecurrent shear is generated. This gives rise to positive(cyclonic) and negative (anticyclonic) vorticity,respectively, on the right and left sides of the island

y (normalized by f) during March 12–17, 2002. March 12 ¼ day 0.

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–12481240

facing downstream. These vorticity sheets thenseparate from the islands and are advected down-stream along the main current (Fig. 5). We cantrack several anticyclonic eddies shed from the rightside of Santa Rosa Island during a period of 5.5days presented in the figure: a first anticyclonic eddyis formed at the beginning and separated from theisland at day 1.5. The shed eddy is advectedsouthwest along the main flow. Its intensitydecreases as it is advected downstream. On day4.0, another anticyclonic eddy is shed from theisland. The period for eddy shedding is roughly 2.5days (d), which gives a Strouhal numberSt ¼ D=TU � 0:23. St is a non-dimensional para-

0 2 4 6 8 10 12 14

−60

−50

−40

−30

−20

−10

Distance from the left end of Section AA (km)

Wate

r D

epth

(m

)

Fig. 6. Channel Islands wake: velocity ðms�1Þ normal to Section

AA (see Fig. 4) on Day 0 (March 12, 2002). Negative values

denote southeastward flow (see Fig. 4).

A

30’ 15’ 120°W30’

40’

50’

34°N

10’

SM

SR

Day 0: Botto

Fig. 7. Channel Islands wake: bottom stress on day 0 ðNm�2Þ. SM, SR

meter describing the eddy shedding frequency,where D, T, and U are the island width (20 km),the shedding period (2.5 d), and the current speedð0:4m s�1Þ. The Strouhal number from laboratoryexperiments is about 0.2 (Boyer and Chen, 1987); itis not too sensitive to stratification and rotation(Dong et al., 2007a).

The vertical profile of current normal to SectionAA, located between Santa Rosa and Santa CruzIslands, is plotted in Fig. 6 (see Fig. 4 for theposition of Section AA). The maximum speedoccurs about 2 km from Santa Rosa and about5 km from Santa Cruz in this section. The maximumcurrent shear forms within a lateral layer of highstress along the Santa Rosa side of the gap, which isresponsible for the generation of the anticyclonicvorticity within the gap at this time.

Fig. 7 shows the bottom stress on March 12(day 0), where significantly large values are foundwithin gaps between Santa Rosa, Santa Cruz, andSan Miguel Islands—much larger than the con-temporaneous surface wind stress (Fig. 12). Whenthe vorticity generation is dominated by the bottomstress, vortex stretching above the bottom boundarylayer yields the following vorticity balance:

qzqt¼ �5� tb

r0H, (1)

where z is the vorticity, t the time, and H is thestretching-layer thickness. Thus, positive bottomstress curl (as in Fig. 7) generates negative (antic-yclonic) vorticity (as in Fig. 5 on day 0). Assumingthe relevant time for vorticity advection is dt ¼

A

45’ 30’

SC

m Stress (Nm−2

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

, and SC denote San Miguel, Santa Rosa and Santa Cruz Islands.

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–1248 1241

L=U , where L and U are the length and velocityscales associated with the high-stress region, then

z�tb

r0UH� 10�4 s�1 ð�f Þ. (2)

If tb�0:5Nm�2, r0 ¼ 1025 kgm�3, U�0:1m s�1

and H�50m, the same magnitude as that of vorti-city shown in Fig. 5, which indicates that the

40’ 30’ 20’ 10’ 119°W

4’

8’

33°N12.00’

16’

20’

24’

0d

40’ 30’ 20’ 10’ 119°W

4’

8’

33°N12.00’

16’

20’

24’

1d

40’ 30’ 20’ 10’ 119°W

4’

8’

33°N12.00’

16’

20’

24’

2d

40’ 30’ 20’ 10’ 119°W

4’

8’

33°N12.00’

16’

20’

24’

3d

40’

4’

8’

33°N12.00’

16’

20’

24’

40’

4’

8’

33°N12.00’

16’

20’

24’

40’

4’

8’

33°N12.00’

16’

20’

24’

40’

4’

8’

33°N12.00’

16’

20’

24’

Fig. 8. San Nicolas Island wake: sequence of normalized surface

bottom friction contributes significantly to wakevorticity generation in this case.

4.2. Case 2: San Nicolas Island

When current passes San Nicolas Island from thenorthwest, an island wake forms. A time series of 8days for the surface vorticity is plotted in Fig. 8,

30’ 20’ 10’

4d

30’ 20’ 10’

5d

30’ 20’ 10’

6d

30’ 20’ 10’ 119°W

7d

−1

−0.5

0

0.5

1

119°W

119°W

119°W

vorticity maps from March 21–28, 2002. March 21 ¼ day 0.

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–12481242

showing the formation and detachment of a cyclo-nic eddy and the decaying progression of an anti-cyclonic eddy in the wake. While the cyclonic eddyremains coherent, the anticyclonic eddy becomesweaker and weaker as it is advected downstream.Asymmetry in the robustness of cyclonic andanticyclonic wake eddies can be due to the weak-ening effect of centrifugal instability on the latterwhen z is smaller than �f (Dong et al., 2007a), asoccasionally occurs in Fig. 8.

Fig. 9 plots the vertical profile of the currentnormal to Section BB (marked in Fig. 10). Thecurrent is characterized by the presence of a shallowshelf on the eastern side of the island, and a localmaximum in speed occurs over the shelf break,about 4 km away from the island, with a somewhatlarger speed maximum about 8 km offshore. These

0 5 10 15 20 25 30 35−300

−250

−200

−150

−100

−50

0

Distance from the left end of Section BB (km)

Wate

r D

epth

(m

)

Fig. 9. San Nicolas Island wake: velocity ðms�1Þ normal to

Section BB (see Fig. 10 for its position). Negative values indicate

flow to the southeast.

B

B

30’ 24’ 18’ 12’ 6’ 119°W

4’

8’

33°N12.00’

16’

20’

24’

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Fig. 10. San Nicolas Island wake: bottom stress ðNm�2Þ on day

0. Section BB is indicated by the solid line.

speed maxima imply inshore negative vorticity onthe northeastern side of the island. On the south-western side of the island, the maximum speedoccurs about 8 km from the island with an asso-ciated inshore positive vorticity, but the separationdistance of the speed maximum is related to a weakcounter-flow nearer the island, and its vorticitygeneration apparently occurs earlier and upstreamof the section. The mechanisms for generation ofpositive and negative vorticities are different fromeach other here and also distinct from the wakearound the Channel Islands.

The bottom stress on March 21 is plotted inFig. 10. Large values are found on the northeasterncoast of the island. Formula (2) again gives anestimated value of z�10�4 s�1, the same magnitudeas shown in Fig. 8. This suggests the bottom stressdominates the vorticity generation on the north-eastern coastal of the island. On the southwesterncoast of the island, the bottom frictional stress canbe neglected.

4.3. Case 3: Santa Catalina Island

An abundance of submesoscale eddies is observednorth and west of Santa Catalina Island (DiGiacomoand Holt, 2001), and most are cyclonic; they aresometimes called ‘‘spirals on the sea’’ because of thecurved radial-azimuthal surfactant lines seen in SARimages (Munk et al., 2000). When the SouthernCalifornia Countercurrent flows northward aroundthis island, wakes are formed. Fig. 11 shows anexample of the formation and evolution of a cycloniceddy around the island. On day 0 a vortex sheet withpositive vorticity is formed along the northeasterncoast of Santa Catalina, and a part of the sheet leavesfrom the northern tip of the island half a day later.On day 1 a separated cyclonic eddy forms and movesnorthwestward. The shape of the eddy is not circularyet since a weak anticyclonic eddy exists nearby.From day 1.5 and onward, the eddy preserves around shape after the anticyclonic eddy disappears; ithas a diameter of about 6 km, and it continues topropagates downstream with the main current. Theeddy can be tracked more than 4 days. On day 3another cyclonic eddy is formed at the northern tip ofthe island and repeats a similar cycle. A localupwelling is associated with the cyclonic eddy thatcarries along the cold water upwelled from below,primarily during the eddy generation phase. Thesurface temperature anomaly at the center of thecyclonic eddy drops up to 0.5 1C (not shown).

ARTICLE IN PRESS

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4d

−1

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0

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Fig. 11. Santa Catalina Island wake: normalized surface vorticity maps during March 14–18, 2002. March 14 ¼ day 0.

C. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–1248 1243

Partially due to the asymmetry in the islandshape, anticyclonic eddies generated on the south-western side of the island are much less developedand have a weaker magnitude than cyclonic eddies,and, as previously remarked, they may be furtherlimited by centrifugal instability. On the south-western coast, there is a small bay that may ensnarethe vorticity sheet formed and block the movementof the vorticity along the coast and into the wake.The local bottom stress (not shown) is very weak inassociation with these eddy formations due to thenarrow shelf; this indicates that the island wakearound Santa Catalina Island belongs to thecategory of deep-water wakes.

5. Wind wakes

When wind blows past and over an island, a windwake develops on the lee side where the windintensity is lessened due to island shielding. Because

of the sheltering, large wind-stress curl occurs on thelee side in parallel strips of opposite sign, and it mayeven develop into circular patterns if atmosphericwake eddies arise (e.g., Sun and Chern, 1993). Theoceanic response to the weak lee wind stresscan result in a weaker boundary-layer mixing anda warm sea surface temperature (Caldeiraand Marchesiello, 2002), and the wind-curl stripscan induce oceanic Ekman pumping and vortexstretching.

The MM5-reanalyzed wind with 2 km spatialresolution resolves island wind wakes rather well.Fig. 12 shows a snapshot of the generally north-westerly wind stress and its curl on March 13, 2002.Weaker wind stress occurs on the lee side of theislands, and positive and negative lee wind-curlstrips are evident and extend 50–100 km past theisland (Xie et al., 2001 shows that the wind wake onthe west of the Hawaiian chain islands can extendby 1000 km). Interestingly, the cyclonic curls are

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–12481244

larger, again possibly due to anticyclonic weakeningby centrifugal instability in the lower atmosphere.There is no sign of atmospheric lee vortices inFig. 12, and in any event, they would be less likelythan the curl strips to incite a strong oceanicresponse if they are rapidly propagating downwind.Winds from the northwest are common in thenorthwestern SCB region, although there is alsosignificant synoptic and (inshore) diurnal variabilityas well.

In nature wind-wake forcing and boundary-stressvorticity generation combine to cause oceanic islandwakes. Nevertheless, in Exp. 3 we examine how theocean responds to the island-influenced wind-curlpattern in Fig. 12, by holding it steady in time andstarting from a stratified state of rest on day 0 (usingthe mean SCB stratification). To further isolate the

121°W 120°W 119°W 118°W 117°W30’

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−0.5

0

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1

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Fig. 12. A snapshot of wind stress ðNm�2Þ (arrows) and its curl

ð10�5 Nm�3Þ (color) on March 13, 2002. The blue dot south of

San Nicolas Island is the location of the vorticity time series in

Fig. 14.

121°W 120°W 119°W30’

33°N

30’

34°N

30’

Fig. 13. Oceanic response in Exp. 3 to the steady wind sho

wind-curl response, we remove the islands and set aminimum topographic depth 1000m.

Fig. 13 is a snapshot of the normalized surfacevorticity on day 5, showing a pattern behind theislands that recognizably corresponds to the wind-curl pattern, as well as a coastline strip of vorticityassociated with the abrupt wind impulse on day 0.The temporal development of this response isillustrated in Fig. 14. There is an approximatelylinear spin-up in vorticity over a 7–9 d interval,after which the evolution changes. The eventualresponse at the surface is comparable to f inmagnitude, and the response at 50m is only about25% as large.

We can interpret this wind-curl response in termsof a linear vorticity balance involving vorticitytendency, vortex stretching, and turbulent transport(neglecting the b effect because of the relativelysmall scale of the forcing):

qzqt¼ f

qw

qzþ

1

rqpqzþ � � � , (3)

where w is the vertical velocity, p the turbulentReynolds stress curl, and z the vertical coordinate;the dots denote advective terms not explicitlywritten here. In relation to this balance, weanticipate three evolutionary stages starting fromrest with an impulsively applied wind:

(1)

wn i

When toOðf �1Þ, an Ekman layer circulationspins up within the layer where p is not small.The divergence of p causes the ageostrophicvorticity to grow within this layer proportional

118°W 117°W

−0.5−0.4−0.3−0.2−0.100.10.20.30.40.5

n Fig. 12: normalized surface vorticity on day 5.

ARTICLE IN PRESS

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

Days

Norm

aliz

ed V

ort

icity

Fig. 14. The evolution of normalized vorticity in Exp. 3 at a

point on the lee side of San Nicolas Island (as marked on Fig. 12).

The solid and dashed lines are for the surface and 50m in depth,

respectively.

C. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–1248 1245

to the wind curl, and an Ekman pumping wðzÞ

profile develops in space.

(2) When Oðf �1ÞotoOðL=UÞ, the Ekman layer

circulation has equilibrated within the boundarylayer, with vortex stretching balancing theturbulent transport and no further increase inageostrophic z. Beneath the Ekman layer, p issmall, an approximately steady wðzÞ decreasesfrom its Ekman-pumping extremum wek, andvortex stretching causes a geostrophic z to growlinearly with time (as in Fig. 14) with a verticalprofile determined by the profile of qw=qz. Thegeostrophic z field continues through the Ekmanlayer since there are no horizontal densitygradients to support its vertical shear. Sincewek is proportional to the wind curl curl½s�, so isthe geostrophic z.

(3)

When t4OðL=UÞ, advective effects modify thegeostrophic spin-up.

During the middle period we can therefore estimatethe surface vorticity by the scaling formula,

z�curl½s�t

rH� 10�4 s�1, (4)

when curl½s��10�5 Nm�3, H�40m, and t ¼ 5 d.This is of the same order as seen in Figs. 13 and14. It indicates that the wind-wake forcing can be asignificant influence on the oceanic island wake,although temporal variability in the winds andboundary-stress vorticity generation are also sig-nificant and, in combination with eddy variability,

make the simulated SCB circulation in the upperpanel of Fig. 2 appear quite different from Fig. 13.A correlation map between wind curl and surfacevorticity averaged over the month of March 2002(not shown) shows statistically significant butmodest correlation values around the islands.

6. Summary and way forward

Using a high-resolution numerical oceanic modelforced by a high-resolution wind for the SCB, wehave investigated island wakes, vorticity generation,and submesoscale eddy formation and evolution. Bycomparison of the standard simulation with onewhere the islands are sunk to a minimum depth of50m, we conclude that much of the enstrophy in theSCB is generated in island wakes. Wakes around theChannel Islands, San Nicolas Island, and SantaCatalina Island are analyzed. When flows squeezethrough gaps between the Channel Islands, largelateral current shear and bottom stress curl occurand generate vorticity comparable to f. After theeddies are shed from the islands, they are advecteddownstream. When a California Current flow passesSan Nicolas Island from the northwest, a surface jetover the shelf break is formed on the northeasternside of the island and gives rise to a locally largebottom stress that dominates the vorticity genera-tion. On the southwestern side of the island with itsmore concave shape, a return flow forms and givesrise to the positive vorticity. The asymmetry in theevolutions of cyclonic and anticyclonic eddies in thewake suggests that centrifugal instability takes placein the wake. When the northward SouthernCalifornia Countercurrent passes by the irregularlyshaped Santa Catalina Island, a sequence ofcyclonic eddies are formed on the eastern side, andan anticyclonic eddy is generated from recirculationin an indented bay. The cyclonic and anticycloniceddies carry cold and warm surface water anoma-lies, respectively, northwestward along the mainstream. The cyclonic eddies downstream of SantaCatalina Island, among other islands’ wake eddies,are plausible candidates for the observed spirals onthe sea. Finally, parallel strips of positive andnegative wind-stress curl occur in wind wakesbehind the islands and generate a similar patternof oceanic response through Ekman pumping andvortex stretching.

The ability to unambiguously track the evolutionof an island wake can be hampered by thecomplexity in the oceanic circulation pattern,

ARTICLE IN PRESSC. Dong, J.C. McWilliams / Continental Shelf Research 27 (2007) 1233–12481246

whether real or simulated. For example, the flowupstream of an island may vary with time and evencontain eddy structures generated elsewhere, andthe downstream wake may also interact with otherflow features. Coastline irregularity, especially apeninsula or headland, can also be a source of awake and submesoscale eddy generation, somewhatsimilar to an island (n.b., the eddies from headlandwakes can be seen in Fig. 2). Even away fromboundaries mesoscale eddies may generate densityfronts that are subsequently unstable to submesos-cale eddies. Nevertheless, the present study demon-strates the efficacy of island wakes in generatingsubmesoscale vortices.

As addressed in the Introduction, the currentpaper is focused on phenomenological explorationof island wakes in the SCB. To better understandphysical processes occurring in an real oceanicisland wake and the mechanisms in the wakegeneration and evolution, more idealized islandwakes should be examined. For example, theincoming flow can be spatially non-uniform (e.g.,an eddy approaching an island and multiple islandsSimmons and Nof, 2000; Cenedese et al., 2005) ortime-varying (e.g., tidal oscillations, where anadditional new time scale is introduced; Lloydet al., 2001; Stansby and Lloyd, 2001). When ashelf slope is associated with an island, potentialvorticity conservation may restrain the flow frommoving too close to the shoreline (Schar andDurran, 1997) and the effective island radiuscan be larger than island size. The shape of anisland can influence the wake structure. Thethermal flux change due to the presence ofeddies in the island wake can have certain feedbackon the wind structure, which may require the air–seacoupling model. Much remains for further investi-gation.

Acknowledgments

We appreciate support from the National ScienceFoundation (OCE 06-23011) and the Office ofNaval Research (Grants N00014-02-1-0236 andN00014-05-10293). We thank Alex Hall and hiscolleagues for providing the MM5 reanalyzedproduct, and Yi Chao for his aid in making JPLsupercomputers available. We thank our colleaguesat UCLA (Alexander Shchepetkin), IRD of Fran-ce(Pierrick Penven, Patrick Marchesiello), JPL(Hongchun Zhang) and Delft Hydraulics of theNetherlands (Meinte Blaas) for aiding in many

aspects of this work, and anonymous reviewers forthe comments on the manuscripts. Computationswere performed on both JPL and NCSA super-computers.

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