The Role of Wind Stress Curl in Jet Separation at a...

The Role of Wind Stress Curl in Jet Separation at a Cape

RENATO M. CASTELAO* AND JOHN A. BARTH

College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

(Manuscript received 4 August 2006, in final form 14 February 2007)

ABSTRACT

A high-resolution numerical model is used to study the importance of spatial variability in the windforcing to the separation of a coastal upwelling jet at a cape. An idealized topography and wind field basedon observations from the Cape Blanco (Oregon) region are used. Several simulations are investigated, withboth the intensity and the spatial structure of the wind forcing varied to isolate the importance of theobserved intensification in the wind stress and wind stress curl magnitudes to the separation process. Asimulation using a straight coast confirms that the presence of the cape is crucial for separation. Wind stressintensification by itself, with zero curl, does not aid separation. The wind stress curl intensification south ofthe cape, on the other hand, is important for controlling details of the process. Because the positive windstress curl drives upwelling, isotherms in the offshore region tilt upward, creating a pressure gradient thatsustains an intensification of the southward velocities via the thermal wind balance. This aids jet separationvia continuity and by creating potential vorticity contours that track far offshore of the cape. The timing ofthe separation is dependent on the intensity of the wind stress curl (stronger curl leads to earlier separation),while how far offshore the jet is deflected depends on the offshore extent of the region of positive curl closeto the coast (increasing the extent increases the deflection).

1. Introduction

The seasonally varying wind stress is the primaryforcing mechanism for the circulation along much ofthe California Current System (CCS). Prevailing equa-torward, upwelling-favorable winds during spring andsummer off the Oregon coast, for example, lead to theformation of a strong along-shelf coastal jet that is ingeostrophic balance with the upwelled isopycnals. Inregions of along-shelf uniform topography (both bot-tom bathymetry and coastline orientation), the up-welling circulation is well described by standard two-dimensional models (e.g., Allen 1980).

The presence of along-shelf variations in topographysubstantially influences the coastal circulation. Studiesover the last decade or so have established that theupwelling jet often separates from the coast near Cape

Blanco, Oregon, to become an oceanic jet to the south(Barth and Smith 1998; Barth et al. 2000, 2005b). OffNewport (upstream of the cape), the summer-averagedupwelling jet lies about 20–30 km offshore, over theshelf. South of the cape, however, the jet is located farfrom shore (�120 km from the coast), with a weaksecondary jet near the shelf break (Huyer et al. 2005).Jet separation at Cape Blanco is further confirmed bysatellite observations (Strub and James 1995, 2000;Barth et al. 2000; Castelao et al. 2006; among others),which frequently show a broader area influenced by theupwelling circulation to the south of the cape whencompared with regions to the north.

The seasonal evolution of the flow in the CapeBlanco region was depicted during the Global OceanEcosystems Dynamics (GLOBEC) Northeast PacificProgram, which provided some of the few mesoscale-resolving, in situ, large-area surveys of the circulationand hydrographic structure in this area. Those obser-vations revealed an upwelling front and jet that waslocated close to the coast, south of the cape early in theupwelling season (late May–early June 2000), but dis-placed about 80 km offshore 2 months later (late July–early August 2000; Barth et al. 2005b). The seasonalevolution of the upwelling front and jet from satelliteobservations is also consistent with that observation.

* Current affiliation: Institute of Marine and Coastal Sciences,Rutgers, The State University of New Jersey, New Brunswick,New Jersey.

Corresponding author address: Renato M. Castelao, Institute ofMarine and Coastal Sciences, Rutgers, The State University ofNew Jersey, 71 Dudley Road, New Brunswick, NJ 08901-8521.E-mail: [email protected]

2652 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 37

DOI: 10.1175/2007JPO3679.1

© 2007 American Meteorological Society

JPO3141

Using 6 yr of altimeter and tide gauge data, Strub andJames (2000) found a concentrated equatorward flowclose to the coast during May and June. The jet remainscloser to the coast off Oregon and Washington, butmeanders far offshore (�100 km) off the Californiacoast during July and August.

The offshore displacement of the upwelling jet pro-vides an important mechanism for exporting materialfrom the highly productive continental shelf toward thedeep ocean (e.g., Barth et al. 2002), and thus has im-portant consequences for both the coastal and adjacentdeep-ocean ecosystems. In situ observations show thatthe domain to the south of the cape has a more saline,cooler, denser, and thicker surface mixed layer, a widercoastal zone inshore of the upwelling front and jet,higher nutrient concentrations in the photic zone, andhigher phytoplankton biomass when compared with theregion north of the cape (Huyer et al. 2005). Huyer etal. attributed these differences to stronger mean north-erly wind stress in the south, strong small-scale windstress curl in the lee of Cape Blanco, and the reducedinfluence of the Columbia River discharge in thecoastal region south of the cape. The different charac-teristics in the south are consistent with more vigorouswinds and enhanced upwelling there. Enhanced up-welling in the lee of topographic perturbations can beattributed to several factors, including intensification inthe wind stress resulting from orographic effects [e.g.,airflow accelerating within an expansion fan; Dormanet al. (2000)], variations in bottom bathymetry (Peffleyand O’Brien 1976; Castelao and Barth 2006) and coast-line orientation (Gan and Allen 2002), and variations invorticity resulting from curvature of the trajectory asthe flow passes the cape (Arthur 1965).

The dynamics of the separation process at CapeBlanco are still not understood. Numerical (e.g., Haid-vogel et al. 1991; Batteen 1997) and laboratory (e.g.,Narimousa and Maxworthy 1987) modeling studieshave shown that irregularities in the coastline geometryare important in the formation of meanders and fila-ments. Previous studies have shown that bottom topog-raphy and coastline curvature are important in theseparation process (Barth and Smith 1998; Barth et al.2000). Using an analytic 1.5-layer model of coastal hy-draulics with constant potential vorticity in each layer,Dale and Barth (2001) found time-dependent solutionspredicting the flow field at critical transitions, in thesense of hydraulic control, consisting of a narrow up-welling jet upstream of the cape that moves offshoreand broadens at the cape.

More recently, Samelson et al. (2002) suggested thatthe wind intensification south of the cape could alsoinfluence the local circulation. Because the stress mag-

nitude south of Cape Blanco is 3–4 times that along thenorthern Oregon coast (see also Perlin et al. 2004; Chel-ton et al. 2007), Samelson et al. conclude that coastalupwelling must be similarly intensified toward thesouth, consistent with the observed offshore displace-ment of the jet and the observed presence of system-atically colder ocean temperatures in that region (Barthet al. 2000; Huyer et al. 2005). Samelson et al. also pointout that the wind stress curl evident in both atmo-spheric models and scatterometer data could also bedynamically significant, by causing local Ekman trans-port divergences and convergences. Using the U.S. Na-vy’s high-resolution atmospheric model [CoupledOcean–Atmosphere Mesoscale Prediction System(COAMPS)], Pickett and Paduan (2003) showed thatthe vertical transport resulting from Ekman pumpingfrom wind stress curl is as important as the verticaltransport resulting from coastal divergence in the Ek-man transport in causing upwelling in the central CCS.The main goal of the present study is, therefore, toexplore the importance of spatial variability in the windforcing in the separation of a coastal upwelling jet at anidealized cape. We are particularly interested in iden-tifying the specific roles of the wind intensification byitself, which enhances vertical transport very near thecoast, and the associated wind stress curl, which drivesweaker upwelling velocities that are spread over amuch larger offshore extent.

Although this study is motivated by jet separation atCape Blanco, results should be relevant for other re-gions where jet separation occurs at a cape. Off Chile,for example, the upwelling jet frequently separatesfrom the coast at Punta Lavapie (e.g., Mesias et al.2001, 2003). Off the Iberian Peninsula, jet separationand filament formation occurs associated with CapeFinisterre and Cabo Roca (e.g., Haynes et al. 1993),while in the southern Benguela upwelling system, jetseparation frequently occurs at Cape Columbine (e.g.,Penven et al. 2000). The wind stress curl downstream ofthese major capes is intensified (positive in the North-ern Hemisphere, negative in the Southern Hemi-sphere), favoring offshore upwelling (see Chelton et al.2004), which is a situation analogous to that of CapeBlanco.

2. Methods

The Regional Ocean Modeling System (ROMS) usedhere is a hydrostatic primitive-equation numerical cir-culation model with terrain-following vertical coordi-nates (Shchepetkin and McWilliams 2005), based onthe S-Coordinate Rutgers University Model (SCRUM)described by Song and Haidvogel (1994). The modelincorporates the Mellor and Yamada (1982) 2.5-level

NOVEMBER 2007 C A S T E L A O A N D B A R T H 2653

turbulence closure scheme as modified in Galperin etal. (1988). The pressure gradient scheme is a spline den-sity Jacobian (Shchepetkin and McWilliams 2003),which minimizes the errors associated with computinghorizontal pressure gradients with terrain-following co-ordinates.

The model domain extends 300 km offshore and 600km in the along-shelf direction (Fig. 1). The grid reso-lution is 2 km in the along-shelf direction, and between1.3 and 4.4 km in the cross-shelf direction, with thehighest resolution near the coast. In the vertical, 30 slevels, where s denotes a generalized vertical coordi-nate, are utilized with grid spacing that varies so thatthere is higher resolution both near the surface and thebottom in order to resolve the respective boundary lay-

ers. The horizontal velocity v has components (u, �)corresponding to the cross- and along-shelf velocities inthe (x, y) directions, so that u is positive onshore and �is positive toward the north. The depth average of thevelocity components are denoted by V and (U, V). Weuse the notation � for the surface elevation above theundisturbed free surface, T for temperature, S for sa-linity, t for time, and D for the water depth.

To simplify the complexity of the problem an ideal-ized bottom topography is used, consisting of a conti-nental shelf/slope with no variations in the along-shelfdirection, except where a perturbation in the form of acape is imposed (Fig. 1). The coastline curvature andcape dimensions are similar to Cape Blanco. The coast-line coordinates (xc, yc) from the center of the cape tothe north are given by

xc � x0 �tanh ��yc � y0 1.5�

2.3, �1

where x0 � �124.57° and y0 � 42.84° are the longitudeand latitude of Cape Blanco, and yc � y0. After trans-forming xc and yc to kilometers, their values are pro-jected symmetrically to the south of the cape. Note that,although the topography is a close fit to the coastline inthe Cape Blanco region, it is sharper than the actualbathymetric contours. Tests were also pursued usingmore rounded topographies, which better fit thebathymetry in the region. As the radius of curvature ofthe topography increases (i.e., the cape becomes morerounded), jet separation takes longer to occur. How-ever, the effects of the wind stress and wind stress curlintensification on the time and spatial scales of separa-tion remain identical to when the topography is sharp.Therefore, the description of the role of the wind in-tensification in jet separation that follows remains validfor rounded capes, although with separation occurringat later times. A second domain, in which no along-shelf variations is imposed, was also used in order toverify whether, with the setup used, separation can beobtained without the cape. The Coriolis parameter f �9.92 10�5 s�1 is constant, matching the value nearCape Blanco. The horizontal viscosity coefficient isconstant and chosen to be small (5 m2 s�1). The modelis initialized with zero velocities and with horizontallyuniform stratification. The vertical stratification, ob-tained from in situ observations, and the bottom slopeare representative of the Oregon coastal ocean.

The model has three open boundaries. In the north,we use a zero-gradient condition for �, and the condi-tion proposed by Gan and Allen (2005a) for the re-maining variables. The local solution is obtained fromcalculations utilizing a local two-dimensional (x, s, t)submodel at the boundary. At the southern boundary,

FIG. 1. Idealized bottom topography used in the simulations.Gray contours are isobaths from 100 to 900 m, with 100-m incre-ments. The black contour is a line of constant near-surface along-shelf transport. The definition of Sx is also shown.


� satisfies an implicit gravity wave radiation condition(Chapman 1985), while the depth-averaged velocitiessatisfy a Flather radiation scheme (Flather 1976). Thespecified values needed in the Flather condition areobtained from a local two-dimensional solution. For thedepth-dependent variables, an oblique radiation condi-tion (Marchesiello et al. 2001) is used. At the offshoreboundary, �x � Vx � Tx � Sx � 0, and we use a radia-tion condition for U, u, and �. Shelf wave tests, likethose performed by Gan and Allen (2005a), producedresults nearly identical to theirs, giving us confidence inthe set of the open boundary conditions used. Tests,using a domain doubled in size, produce results verysimilar to those obtained with the basic domain, includ-ing the time and spatial scales of jet separation at thecape, further increasing our confidence in the boundaryconditions used. No surface heat flux was used in thesimulations presented here. Tests with a surface heatflux showed no significant difference regarding jet sepa-ration.

With the objective of minimizing the span of the pa-rameter space investigated in this study, the model isforced by winds constant in time, after being ramped upover 2 days. In all experiments, the cross-shelf compo-nent of the wind stress is set equal to zero, and thealong-shelf component is always upwelling (southward)favorable. A background wind stress of �0.04 Pa isimposed, with a slight decrease in magnitude withinabout 100 km from the coast, establishing an along-shelf band of weak, positive wind stress curl followingobservations north of Cape Blanco (Perlin et al. 2004).The wind forcing differs among the simulations by themagnitude and spatial structure of the wind intensifica-tion south of the cape, so as to explore how the windintensification itself and the associated wind stress curlfield affect jet separation. In the basic case (Fig. 2), thewind stress (N m�2) is given by

�sy � ��0.04 �

110

e��Ae�Aw�Ans� tanh ��x

25� 1.55�,

�2

where x ranges from �300 to 0,

A �x � 80

80,

Ae � � |A| � A

2 �2

,

Aw � � 1

�3

|A| � A

2 �2

,

Ans � �y � 29060 �2

, �3

and y ranges from 0 to 600. The coefficients in (2) and(3) are chosen so that the wind fields (stress magnitudeand curl) resemble the averaged fields over the up-welling season off Oregon (see Perlin et al. 2004). Be-cause the cross-shore component of the wind stress iszero, the wind stress curl is simply given by �y

s/ x. Notethat satellite observations (Perlin et al. 2004) indicatethat the cross-shore component of the wind stress is, ingeneral, one order of magnitude smaller than the along-shore component in the Cape Blanco region. Over theupwelling season, the contribution from the cross-shorecomponent of the wind stress to the wind stress curlsouth of the cape is about 15%. Other wind patternsrepresent variations around the basic case (Table 1).

The axis of the wind intensification used in the simu-lations has an east–west orientation (e.g., Fig. 2). Inreality, the axis of the wind intensification off CapeBlanco is tilted by approximately 45° toward the south-west, away from the cape (Perlin et al. 2004). Simula-tions forced by winds similar to the wind fields usedhere, but with the axis of the wind intensification tiltedby 45°, produce results consistent with those describedin this study. We choose not to use the rotated winds,however, because the interpretation of the results be-comes more difficult, because more parameters varyamong the different cases shown in Table 1. For ex-ample, if the wind intensification axis is rotated by 45°,moving the location of the intensification offshore (asin the “curl far” experiment, Table 1) not only increasesthe width of the region of positive wind stress curl closeto the coast, but also changes the north–south extent ofthe region with positive curl.

To isolate the effects of the wind fields from topo-graphic effects, simulations were also run using a two-dimensional model (x, s, t), with the same bottom slopeas that of the regular domain.

Coastal jet separation is quantified by measuring theoffshore displacement experienced by a line of constantnear-surface along-shelf transport (�jet

coast �0�5m � dz dx,

where z is the vertical coordinate and “jet” is the jetcore) in the vicinity of the cape. We first choose a trans-port isoline that is located along the core of the jetupstream of the cape. The offshore jet displacement Sx

is determined by differencing the maximum offshoredistance reached by the isoline south of the cape andthe offshore distance of the isobath over which the iso-line lies upstream of the cape (Fig. 1). Note that similarresults are obtained if an isotherm, instead of a line ofconstant near-surface along-shelf transport, is used inthe calculation.

For some simulations, we found it useful to analyzethermal balances. Details of the computation are givenin the appendix.


3. Two-dimensional results

To more clearly isolate the effects of the wind inten-sification and associated wind stress curl from topo-graphic effects, two-dimensional (x, s, t) simulationswere pursued. Three different wind scenarios are con-sidered. In the first run, the wind stress is consideredconstant in the cross-shelf direction and is equal to�0.04 Pa (upwelling favorable), except very near thecoast, where a slight decrease in the southward windmagnitude occurs. This is close to the Quick Scatter-ometer (QuikSCAT) summer-averaged wind stressmagnitude north of Cape Blanco (Perlin et al. 2004).Note that QuikSCAT observations are not available ina thin band (�30 km) close to the coast. In the secondexperiment, the intensity of the along-shelf component

of the wind stress is increased to �0.1 Pa, again withonly a weak cross-shelf variation close to the coast (Fig.3a). Because in both cases there is only a thin, weakband of positive curl close to the coast, these winds willbe referred to as having no curl. The goal is to identifythe effects of the wind intensification by itself. In thethird experiment, the maximum in the southward windstress (�0.14 Pa) is imposed at about 120 km from thecoast. The wind intensity decreases toward the coast (toabout �0.05 Pa) and in the offshore direction. There-fore, the region close to the coast is characterized bypositive wind stress curl, while the region farther off-shore has negative wind curl (Fig. 3b). This cross-shelfwind profile is similar to a profile through the center ofthe wind intensification in the observed summer-averaged wind stress field south of Cape Blanco (Perlin

FIG. 2. Along-shelf component of the (left) wind stress (Pa) and (right) associated wind stress curl ( 10�7 Nm�3) for the basic-case experiment.


et al. 2004), with the exception that the maximum in thewind stress magnitude (and hence the curl pattern) isshifted slightly offshore. By comparing results from thissimulation with the other two, the effect of the windcurl can be assessed. Only results after 80 days of simu-lation are shown (Fig. 3). Although 80 days of constantwinds is not realistic for the region, long runs areneeded to differentiate clearly between the simulations.In addition, the wind magnitudes used are similar to theobservations averaged over the upwelling season,which is considerably longer than 80 days.

Results from the second experiment (�0.10 Pa, nocurl; Fig. 3a) are very similar to those from the firstexperiment (�0.04 Pa, no curl; not shown here), withthe obvious exception that upwelling is enhanced in thecase forced by stronger winds. The upwelling front andjet are found farther from the coast (by about 15 km),and along-shelf velocities are stronger. In both cases,the circulation is consistent with two-dimensional mod-els of coastal upwelling (e.g., Allen 1980). The south-ward wind stress drives an offshore flow in the surfaceEkman layer, which is balanced by the upwelling ofcold water from below. A vertically sheared along-shelfjet develops in geostrophic balance with the tiltedisopycnals. Upwelling, in this case, is restricted to re-gions close to the coast. At distances greater than �60–65 km from the coast, outside the surface mixed layer,isotherms are nearly flat in both experiments 1 and 2,presenting no significant depth changes from the initialcondition.

In the third experiment (with curl; Fig. 3b), there isstill upwelling within the first tens of kilometers fromthe coast resulting from coastal divergence of the Ek-man transport, as with the zero-curl wind. The regionoffshore, however, differs dramatically from the previ-ous experiments. Within �120–130 km from the coast,

isotherms are uplifted as compared with the simulationsforced by winds with no curl, while isotherms arepushed downward offshore of that. This is consistentwith the wind stress curl field, which is positive (up-welling favorable) close to the coast, and negative(downwelling favorable) offshore. At 80 km from thecoast, for example,

wcurl � k̂ · �� s

�f� � 0.7 m day�1, �4

where k̂ is a unit vector in the local vertical direction,�s � (0, �y

s) is the wind stress vector, � is the waterdensity, and wcurl is the curl-driven vertical velocity.This vertical velocity would result in a vertical displace-ment of the isotherms of approximately 55 m over 80days, consistent with results presented in Fig. 3b. In acomparison of the upwelling response to different windproducts off Point Sur (central California), Capet et al.(2004) also observed significant differences betweenthe results of a simulation forced by a product withweaker southward winds close to the coast and strongpositive wind stress curl, and another one with strongerwinds close to the coast and weaker curl. The differ-ences were qualitatively similar to those presentedhere.

The offshore curl-driven upwelling in the third ex-periment creates a strong horizontal temperature (anddensity) gradient, which is enough to sustain a strongintensification of the along-shelf velocities offshore viathe thermal wind balance. By computing the differencebetween the along-shelf velocities in the third (withcurl; Fig. 3b) and second (no curl; Fig. 3a) experiments,we verify that the presence of the positive wind curl andweaker winds near the coast strongly intensifies thesouthward velocities in the offshore region (greaterthan 80 km from the coast), and strongly weakens thesouthward velocities in the region close to the coast(30–70 km offshore) (Fig. 3c). There is yet another re-gion of intensified southward flow over the shelf atabout 25 km from the coast. Because the winds close tothe coast are weaker relative to the no-curl scenario,the cross-shore advection of the upwelling front close tothe coast is reduced, and the inshore jet remains closerto the coast when compared with the upwelling jet inthe no-curl simulation. Curl-driven upwelling near theshelf break may also contribute to the intensification.

Other simulations (not shown here) reveal that de-creasing the offshore extent of the region with positivewind stress curl causes the offshore jet to occur closer tothe coast, while increasing the width with positive curlleads to the formation of the offshore jet farther fromthe coast. In a consistent manner, increasing the mag-nitude of the positive curl (i.e., increasing the curl-

TABLE 1. Summary of experiments.

Index(see

Fig. 8) Short nameMax � y

s

(hPa)

Positive curlmagnitude

( 10�7 N m�3)Zero-curlline (km)

a Basic case �0.14 12 80b Half curl �0.08 6 80c One and one-half

curl�0.21 18 80

d No curl �0.09 — —e Uniform �0.04 — —f Half strength �0.08 12 80g One and one-half

strength�0.21 12 80

h Curl near �0.14 8 30i Curl far �0.14 12 130j Curl very far �0.14 12 200


FIG. 3. Along-shelf component of the (top) wind stress (black) and wind stress curl (gray), (middle) temperature, and (bottom)along-shelf velocity at day 80 for two-dimensional simulations forced by winds (a) with no curl (except in a thin band close to the coast)and (b) with positive curl within 120 km from the coast. The dashed line in (b) shows the wind stress used in the simulation forced bywinds with no curl, for comparison. In temperature plots, the 6°, 8°, and 10°C contours are thick, and the contour interval is 0.5°C. Solidlines in velocity plots are the �0.7 and �0.4 m s�1 contours. (c) The difference in the along-shelf velocities between the two cases (�curl

� �no curl). Positive (negative) contours are solid (dashed). Thick is zero, and the contour interval is 0.05 m s�1.


driven upwelling) causes the offshore jet to be estab-lished earlier, while decreasing the magnitude of thepositive curl leads to a delay in the formation of theoffshore jet.

The effect of the wind stress curl is further illustratedby comparing terms in the temperature equation (seethe appendix for details) between the second and thirdexperiments (Fig. 4), averaged over the first 80 days of

FIG. 4. Time-averaged values of terms (°C s�1) in the temperature equation calculated as described in theappendix for 2D simulations forced by winds (a) with no curl and (b) with positive curl close to the coast. See Figs.3a,b for the cross-shelf profile of the wind. Terms are (from top to bottom) the time rate of temperature change,horizontal advection, vertical advection, horizontal diffusion, and vertical diffusion. The time-averaged period isfrom day 0 to 80. (c) The difference between the cases (curl � no curl).


Fig 4 live 4/C

simulation. In the no-curl scenario, the temperaturecooling ( T/ t � 0) is primarily balanced by cross-shelfadvection (here, horizontal advection is synonymous ofcross-shelf advection, because the simulation is two-dimensional). Positive vertical advection is only signifi-cant within a few kilometers from the coast. Verticaldiffusion is most important in the surface and bottomboundary layers, and particularly within 20–30 km fromthe coast. Away from the coast, T/ t �0, except in thesurface layer, where the cooling is due to Ekman trans-port advecting upwelled waters offshore.

In the wind stress curl scenario, the results are con-siderably different. Cross-shelf advection is reduced(see difference panel) as a consequence of reducedwinds close to the coast. Vertical advection, on theother hand, is now important within 120 km from thecoast, which is the same region where the wind stresscurl is positive. A local intensification is also found overthe shelf. This leads to a significantly larger area with T/ t � 0, consistent with Fig. 3b. Offshore of 120 kmfrom the coast, the deep water actually warms over theperiod simulated as surface water is downwelled (nega-tive vertical advection). As in the constant wind case,vertical diffusion of temperature is most important inthe boundary layers.

4. Importance of geometry and the basic case

Before exploring the flow dependence on the spatialstructure and intensity of the wind forcing, we investi-gate if, with the setup used, jet separation can be ob-tained in the absence of the cape. Previous studies haveshown that the presence of a cape can play an impor-tant role in jet separation (Batteen 1997; Barth andSmith 1998; Barth et al. 2000; Dale and Barth 2001). Wecompare results from two simulations forced by thesame wind stress (and hence the same wind stress curl)representative of the Oregon coastal ocean during sum-mer (Fig. 2), differing only in the geometry of the to-pography. The basic case topography mimics the coast-line geometry in the Cape Blanco region (Fig. 1); that iscompared with a domain with a straight coast.

Surface velocity vectors overlain on the surface tem-perature field for the basic case at days 70, 85, and 110are shown in Fig. 5. Vertical sections of temperatureand alongshore velocity at days 70 and 110 are shown inFig. 6. Results at day 70 are consistent with the generalpicture of coastal upwelling, with isotherms tilting up-ward toward the coast leaving a band of cold water atthe surface close to shore, and the jet roughly followingthe topography. By day 85, the jet has significantlymoved offshore south of the cape, advecting large

amounts of cold, upwelled waters offshore. Around 80km south of the cape, the increase in the local waterdepth causes the flow to turn cyclonically back onshorein order to conserve potential vorticity, leading to re-attachment. By day 110, the temperature front and jetare further separated, reaching about 80–90 km fromthe coast south of the cape. Inshore of the separated jet,a strong recirculation region is established. The north-ward flow in this recirculation has weak vertical shear.Over the shelf, a secondary, weaker southward up-welling jet is formed, associated with the inshore tem-perature front. Although the present simulation ishighly idealized, results bear close resemblance to insitu observations just south of Cape Blanco (Barth et al.2000; Huyer et al. 2005). Temperature and alongshorevelocity observations along 41.9°N (south of CapeBlanco) during the summer of 1995, for example, arevery similar regarding scales, patterns, and direction ofthe flow to those at day 110, km 300 (see Fig. 6 of Barthet al. 2000).

Time series of Sx, a measure of separation (see sec-tion 2 for definition), for both the basic case and thestraight-coast simulation are shown in Fig. 7. As seen inFigs. 5 and 6, the jet in the basic case is still attacheduntil day 70, experiencing only a small (�15 km) off-shore deflection. From day 70 onward, the jet movesaway from the coast, being displaced about 50 km off-shore by the end of the simulation. Instabilities in thejet create smaller-scale oscillations around the meanposition of the jet, which are clearly seen in the timeseries of Sx. In the straight-coast case, the jet stays at-tached for the entire duration of the simulation. Thisshows that the presence of a cape plays an importantrole in jet separation, consistent with previous results(Haidvogel et al. 1991; Batteen 1997; Barth and Smith1998; Barth et al. 2000; Dale and Barth 2001). The windintensification with a strong positive curl is not enough,by itself, to lead to jet separation.

5. Response to different wind forcing

Several simulations were run using the cape geom-etry, but varying the intensity and/or spatial structure ofthe wind forcing. The wind patterns represent varia-tions about the basic case (Table 1; Fig. 2), which arechosen to highlight the relative importance, if any, ofthe wind intensification versus the wind stress curl inthe separation of the upwelling jet at the cape. Thealong-shelf component of the wind stress for all casesconsidered is shown on the upper panels of Fig. 8. Thecross-shelf component of the wind is set to zero. Thebasic case is repeated for reference. In the lower panels


of Fig. 8, the associated wind stress curl ( �ys/ x) field

for each case is shown. As described in section 2, allcases considered here have a thin band of weak, posi-tive curl close to the coast. Therefore, when a simula-tion is referred to as being forced by a spatially uniformwind, or by a wind field with no curl, what is reallymeant is that there is no intensification in the windstress and/or wind stress curl south of the cape. Windpatterns only differ in the region of the intensification,being identical in the northern and southern parts ofthe domain. Time series of Sx are then compared be-tween different wind scenarios (Figs. 9–12). In allgroups of comparisons, the time series of Sx from thebasic case is shown as the solid black line.

Results from the basic case (Fig. 8a) are first com-pared with results from simulations forced by one-halfof the wind stress curl (Fig. 8b) and one and one-half ofthe wind stress curl (Fig. 8c). The wind stress shown inFig. 8b is characterized by a weaker intensification ascompared with the basic case. As a consequence, thewind stress curl is also weaker. In Fig. 8c, on the otherhand, winds are characterized by a stronger intensifica-

tion with stronger curl. Note, however, that althoughthe intensity is different, the spatial structure of thewind stress and wind stress curl fields is identical to thatof the basic case. Time series of Sx (Fig. 9) reveal thatdecreasing the magnitude of the wind stress and windstress curl leads to later jet separation when comparedwith the basic case, while increasing their magnitudesleads to earlier separation. This is consistent with thehypothesis that enhanced upwelling resulting fromstronger winds and stronger curl would favor separa-tion. Note that although the timing of separation is af-fected, the offshore deflection of the jet after about 95days is similar in the three cases.

The previous comparison, although suggestive thatthe structure of the wind fields is important in control-ling details of separation, does not shed light onto thespecific roles of the wind stress and the wind stress curlintensification in the process, because both varied be-tween the cases. In the second group of comparisons,results from the basic case are compared with resultsforced by wind with no curl (Fig. 8d) and by a spatiallyuniform wind (Fig. 8e). In Fig. 8d, the wind is charac-

FIG. 5. Surface velocities (m s�1) and temperature (°C) at days 70, 85, and 110 for simulations forced by basic-case winds with windstress curl (see Fig. 2) and with the cape topography (see Fig. 1). The velocity scale arrow is 1 m s�1. The black contour is a line ofconstant near-surface along-shelf transport.


terized by an intensification south of the cape, but withno curl. The magnitude of the intensification is equal tothe averaged winds within 15 km (�1 internal Rossbyradius of deformation) from the coast in the basic case.Thus, both cases produce roughly the same amount ofEkman transport and upwelling at the coast. The windis spatially uniform in Fig. 8e, with no intensification orcurl. Time series of Sx (Fig. 10) reveal that the windintensification with no curl produces approximately thesame amount of separation as that of spatially uniformwinds. A similar result is obtained if the model is forcedby winds with the same spatial structure as that of thewind with no curl (Fig. 8d), but with a stronger inten-

sification (reaching �0.14 Pa). If left long enough, theinteraction of the flow with the cape causes jet separa-tion, independent of details of the wind structure. Thewind intensification with the curl (basic case; Fig. 8a),on the other hand, causes the jet to separate consider-ably earlier (by about 20–25 days). These results sug-gest the wind stress intensification by itself does not aidin jet separation, and that the cause of the observedvariability in the time of separation in Fig. 9 is thevariability in the wind stress curl between the simula-tions.

To further confirm this conclusion, results from thebasic case are compared with results from simulations

FIG. 6. Vertical sections of alongshore velocities (colors; m s�1, positive northward) andtemperature (white contours; °C) at days (left) 70 and (right) 110 for simulations forced bybasic-case winds with wind stress curl (see Fig. 2) and with the cape topography (see Fig. 1).The 6°, 8°, and 10°C contours are thick. Dashed line shows the bottom of the surface mixedlayer, defined in terms of a 0.1°C temperature step from the surface. The alongshore location(y km) of the section is indicated by the number over land.


Fig 6 live 4/C

forced by winds with the strength decreased by half(Fig. 8f) and increased by one and one-half (Fig. 8g).The offset is spatially constant in the intensification re-gion, leading to the same wind stress curl in all threecases. Therefore, even though the amount of upwellingat the coast changes, the curl-driven upwelling is thesame in all cases. The time series of Sx for the simula-tion forced by winds with half the strength is very simi-lar to the time series for the basic case (Fig. 11). In the

simulation forced by stronger winds (“one-and-one-halfstrength”), there seems to be a slight delay in the timingof the separation. This may be influenced by the way Sx

is computed. Because winds close to the coast are stron-ger when compared with the basic case, locally drivennear-surface currents are also stronger. This means thateven if the jet moves offshore at the same time in bothcases, the near-surface transport in the basic case can bematched in the case forced by stronger winds by inte-grating to a distance closer to the coast. The agreementin the timing of separation in this case is indeed closerif an isotherm is used in the calculation (see section 2).Once the jet starts to move offshore in the simulationforced by stronger winds, Sx quickly becomes very simi-lar to the time series from the basic case. This is con-sistent with the idea that simulations forced by the samewind stress curl field produce roughly similar timingand amounts of separation.

Last, results from the simulation forced by the basiccase are compared with results from simulations inwhich the offshore extent of the region with positivecurl close to the coast varies. In this comparison, thesame intensity and spatial structure for the wind stressfield are used, except that the center of the intensifica-tion is shifted either inshore (Fig. 8h) or offshore (Figs.8i,j). This leads to a narrower extent of the region ofpositive wind stress curl in Fig. 8h (zero contour at 30km from the coast, when compared with 80 km in thebasic case), and a wider band of positive curl in Figs. 8i,j(zero contour at 130 and 200 km from coast, respec-tively). Note that because the area of positive curl in

FIG. 8. Wind forcing used in the numerical simulations. (top) The along-shelf component of the wind stress and (bottom) therespective wind stress curl are shown. The same color palette and scaling is used throughout. The black contour in the wind stress curlplots is the zero contour. Note that the wind stress curl in (b) (“half curl”) has the same spatial structure (but not the same intensity)as in (a) (basic case), even though the color palette used does not show that.

FIG. 7. Time series of Sx, a measure of separation (see section 2and Fig. 1 for definition), for basic-case simulation (see Figs. 1 and2 for topography and wind forcing, respectively; solid) and for asimulation forced by the same winds, but with a straight coastline(no cape; dashed).


Fig 8 live 4/C

Fig. 8h is considerably smaller, curl-driven upwelling issignificantly reduced in that case (see Table 1).

Decreasing both the offshore extent of the positivewind stress curl to 30 km (Fig. 8h) and its intensity leadsto a separation occurring approximately 15–20 dayslater as compared with that of the basic case (Fig. 12).The amount of separation, that is, how far offshore thejet is deflected, is reduced. Increasing the area of posi-tive curl (zero-curl line at 130 km; Fig. 8i), on the other

hand, leads to more separation. The timing of jet sepa-ration is similar to the basic case. Further increasing theoffshore extent of the area with positive curl to 200 km(Fig. 8j) leads to separation occurring at a later time(similar to the case forced by spatially uniform wind orby intensified wind with no curl; Fig. 10). A longersimulation shows that Sx continues to increase after day110, reaching almost 65 km by day 120.

FIG. 9. Time series of Sx, a measure of separation (see section 2and Fig. 1 for definition), for simulations forced by basic-casewind stress curl (solid), one-half of the wind stress curl (dashed),and one and one-half of the wind stress curl (dot–dashed). SeeFig. 8 for plots of wind stress and wind stress curl.

FIG. 10. Time series of Sx, a measure of separation (see section2 and Fig. 1 for definition), for simulations forced by basic-casewind stress curl (solid), no wind stress curl (dashed), and spatiallyuniform winds (dot–dashed). See Fig. 8 for plots of wind stressand wind stress curl.

FIG. 11. Time series of Sx, a measure of separation (see section2 and Fig. 1 for definition), for simulations forced by basic-casewind stress curl (solid), one-half of the wind stress strength(dashed), and one and one-half of the wind stress strength (dot–dashed). See Fig. 8 for plots of wind stress and wind stress curl.

FIG. 12. Time series of Sx, a measure of separation (see section2 and Fig. 1 for definition), for simulations forced by basic-casewind stress curl (solid), positive wind stress curl restricted to nearthe coast (dashed), and positive wind stress curl reaching far andvery far from the coast (dot–dashed and gray, respectively). SeeFig. 8 for plots of wind stress and wind stress curl.


6. Vorticity balance

To help to clarify the dynamical mechanisms in-volved in jet separation at the cape, the equation for the

vertical component of the relative vorticity of thedepth-averaged flow is analyzed. The vorticity equationis written as

�t � � · �A k̂ � fV � PRE k̂ ��s

�0D k̂ �

�b

�0D k̂� � 0

ten � adv � cor � pre � sur � bot � 0 �5

where �t is the rate of change (tendency) of the verticalcomponent of the vorticity of the depth-averaged flow,A is the sum of the horizontal components of advectionand viscosity, PRE is the pressure gradient term, �b isthe bottom stress vector, �0 is a constant reference den-sity, and the remaining variables/parameters were al-ready defined. Torque terms arise from the nonlinearterms, Coriolis terms, pressure gradient, and surfaceand bottom stresses. Because f is constant, the Coriolisterm represents topographic vortex stretching. The val-ues of torque contributions are calculated using dailyaveraged outputs of the model fields.

The absolute values of terms in the vorticity equationare spatially averaged around the cape in a region ex-tending 150 km in the offshore direction and 100 km tothe north and south of the cape. Time series of termsfor the simulation with a straight coast forced by thesame winds as in the basic case (discussed in section 4;Fig. 7) are compared with those for the simulation withthe cape forced by winds with curl extending 130 kmfrom the coast (curl far; Figs. 8i and 12), the case inwhich maximum separation occurs (Fig. 13). The labelsbeneath (5) are used in the figure. In the straight-casescenario (Fig. 13 top), when no jet separation occurs,the largest terms after 35 days of simulation are thenonlinear advection and the tendency; after 50 days, theremaining terms (pressure gradient, vortex stretching,and surface and bottom stresses) are smaller by a factorof 3, making a roughly equal contribution to the bal-ance.

In the simulation with a cape (Fig. 13 bottom), thebalance is significantly different from the straight-coastresult. The pressure gradient and the vortex-stretchingterms are as important as the nonlinear advection andtendency terms. After 20 days, the contribution fromthe bottom stress to the vorticity balance is small, as isthe contribution from the surface stress torque, becausethe area in which terms are averaged is substantiallylarger than the area with intensified wind stress curl.These results demonstrate that bottom topography is ofincreased importance to jet separation in the presence

of a cape. There is also a notable increase in both thepressure gradient and the vortex-stretching terms be-tween days 82 and 92, the same period as when the jetrapidly moves offshore (Fig. 12). This is in agreementwith results from section 4, which suggested that bot-tom topography plays an important role in the separa-tion.

7. Discussion and conclusions

By combining information obtained from the two-dimensional simulations (section 3) with results fromcomparisons of the effect of different intensities andspatial structures of the wind stress and wind stress curlfields on separation (section 5), a conceptual model ofhow the wind forcing affects separation can be formed.

The two-dimensional simulations showed that the oc-currence of offshore upwelling driven by the wind stresscurl leads to a significant cross-shelf gradient in thedensity field, which is in geostrophic balance with asouthward offshore jet. The location of the offshoreintensification in the current is closely related to thewidth of the area of positive wind stress curl. The timescale of the spinup of the offshore current intensifica-tion, on the other hand, is related to how strong thecurl-driven upwelling is. In the three-dimensional cases,the maximum in the wind stress and wind stress curlintensifications occurs just south of the cape. Therefore,whenever the wind field is characterized by a regionclose to the coast with positive (negative) curl in theNorthern (Southern) Hemisphere, as is the case offCape Blanco, currents offshore and downstream of thecape are intensified. This leads to alongshore diver-gence in the offshore region, which could be balancedby an offshore flow from the coast converging at theregion of the intensification. The separation of the jet atthe cape, which would occur independently of details inthe wind field (see Fig. 10), is facilitated by this process.A stronger positive wind stress curl (one and one-halfcurl; Fig. 8c) leads to an earlier establishment of theoffshore current intensification (resulting from two-


dimensional, curl-driven upwelling), which leads to jetseparation at the cape at shorter time scales when com-pared with the basic case (Fig. 9). A weaker wind stresscurl (“half curl” and “curl near”; Figs. 8b,h) has anopposite effect, leading to a later establishment of theoffshore current intensification, and later separation(Figs. 9 and 12). If the offshore extent of the region ofpositive wind stress curl is decreased (curl near; Fig.8h), the curl-driven offshore current intensification oc-curs closer to the coast, leading to a smaller offshoredeflection of the jet separated at the cape (Fig. 12). Ifthe area of positive curl is increased (curl far; Fig. 8i),the offshore current intensification occurs farther fromthe coast, leading to more separation (Fig. 12). How-ever, if the width of the region with intensified positivewind stress curl is increased further (“curl very far”;Fig. 8j), the offshore current intensification resultingfrom curl-driven upwelling occurs too far from thecape, no longer being able to interact with currents nearshore and help separation (Fig. 12). Jet separation,then, occurs at the same time scales as when the forcinghas no wind stress curl (Figs. 8d,e and 10), solely byinteractions with the cape. Once the jet separates at thecape and moves several kilometers offshore, it is then

able to interact with the offshore current intensifica-tion, leading to further deflection of the jet.

In all simulations, separation occurs after more than60 days because time is needed for the wind stress curlto affect the density and, as a consequence, velocityfields (see Fig. 3). Before that, the intensification of theoffshore flow is not enough to substantially affect thecurrents near the cape. The response is not linear, how-ever (e.g., doubling the wind stress curl does not de-crease the time of separation by half), and other effectsare also important in the process (e.g., instabilities ofthe flow, inertia around the cape).

To obtain an alternative description of the jet sepa-ration dynamics, we examine the distribution of upper-ocean potential vorticity. For adiabatic, frictionless mo-tion, Ertel’s potential vorticity

Q �1�0��

��

�z

��

�x�

�u

�z

��

�y� �f �

��

�x�

�u

�y� ��

�z� �6

is conserved following a particle. To diagnose the ex-istence of Q contours that separate from the coast nearthe cape, we plot contours of Q, averaged over the top80 m of the water column, from the simulation forced

FIG. 13. Time series of absolute values of the terms of the vorticity equation in (5) averaged over a box extending150 km offshore, and 100 km to the north and to the south of the cape, for simulations (top) with straight coast andbasic wind stress curl forcing and (bottom) with the presence of the cape and wind stress curl reaching far from thecoast (curl far; Fig. 8i).


by winds with the zero-curl line at 130 km from thecoast (curl far; Fig. 8i) at day 110 (Fig. 14). We choose80 m because this is a typical depth for the midshelflocation of the coastal upwelling jet upstream of thecape. The diagnostic calculation of Q shows that a par-ticle following lines of constant potential vorticity willbe deflected offshore, agreeing with the position of thecore of the jet (thick blue line). Note also the isolatedpool of Q inshore of the separated jet, indicating thepotential for water and the material it contains to beisolated there.

An estimation of the potential vorticity modificationby currents generated by the wind stress curl field can

be obtained by a series of two-dimensional model simu-lations. The alongshore spacing between the two-di-mensional sections is 30 km, and the wind forcing cross-sectional profile is the same as the wind forcing cross-sectional profile in the three-dimensional case at thatlocation. Results at day 110 from the simulations aregrouped and used to compute Q2D (Q that is computedbased on the two-dimensional simulations will be re-ferred to as Q2D), which is then averaged over the top80 m. The wind stress curl–driven currents change thebackground relative vorticity south of the cape, creat-ing Q2D contours that favor separation (black contoursin Fig. 14). If it were not for the currents generated bythe wind intensification south of the cape, contours ofQ2D would follow contours of f /D (because the cross-shore bottom topography profile does not vary amongthe sections). Results are similar if Q2D is computed foreach two-dimensional simulation first [note that in thatcase y derivatives in (6) are zero], and then is interpo-lated between the cross sections.

It is important to realize that the previous simula-tions were highly idealized and do not reproduce someimportant characteristics of jet separation at CapeBlanco. Satellite and in situ observations show thatonce the jet separates at the cape it stays offshore of theshelf break, becoming an oceanic jet. In the numericalsimulations presented here, the separated jet reattachesto the shelf about 100 km downstream of the cape.Although differences in the details of the bottombathymetry between the real ocean and the used ideal-ized domain may be partially responsible for the differ-ent response, we believe the boundary conditions thatare used also play an important role. As described insection 2, we used a Flather condition (Flather 1976) forthe depth-averaged normal velocity at the southernboundary. In the Flather condition, one needs tospecify the velocity at the boundary, and we chose touse results from two-dimensional simulations (forcedby the same wind profile imposed at the southernboundary in the three-dimensional run) as the source ofthe boundary velocity data. Of course, the two-dimensional run is consistent with the classical pictureof coastal upwelling forced by constant winds (remem-ber, there is only a thin band of weak, positive windstress curl close to the coast in that case), and the up-welling jet is located over the shelf. The differencesbetween the velocity calculated by the model and thespecified two-dimensional velocity are allowed to radi-ate out of the domain at the speed of the external grav-ity waves (Palma and Matano 1998). Nonetheless, thetwo-dimensional velocity “imposed” at the boundaryrepresents a constraint on the circulation via the conti-nuity equation acting to preclude jet separation.

FIG. 14. Ertel’s potential vorticity Q [ l0�9 m�1 s�1; see (6)]averaged over the top 80 m of the water column at day 110 for asimulation forced by winds with zero-curl line at 130 km from thecoast (curl far; Fig. 8i). The thick blue line shows the location ofthe core of the jet. Black contours are an estimation of the Ertel’spotential vorticity based of a series of two-dimensional simula-tions.


Fig 14 live 4/C

Instead of using a two-dimensional simulation as thesource of the boundary data, one could use in situ ob-servations, or even climatological data. That option wasnot pursued here because other issues would be raised.In the observations (or climatology), for example, theupwelling jet during summer is separated from thecoast, being found around 120 km from the coast(Huyer et al. 2005). If that is used as boundary condi-tion for the model, a strong southward jet would beimposed in the offshore region at the southern bound-ary of the domain. That information would propagateinto the domain by coastally trapped waves, affectingthe circulation around the cape. In other words, jetseparation in the model could occur at the cape not byadjustment to internal dynamics, but via volume con-servation to satisfy the boundary condition in the south.Although the two-dimensional results used here asboundary conditions may also affect separation, at leasttheir effect is to preclude (and not enhance) separation.Therefore, any simulated jet separation is due to ad-justment to the topography/forcing fields, and not aresponse to the boundary condition.

Although the boundary conditions probably play animportant role in jet reattachment in the simulations,other factors not considered in the simulations are alsolikely to be important. The north–south variation in theCoriolis parameter (the � effect), the poleward under-current, and the time variability in the forcing are pos-sibly the most important.

Several studies have shown that �-plane dynamicsare important to allow coastally generated jets and fila-ments to propagate offshore. The offshore scale of theresponse of the coastal zone to fluctuations in the windwith period P1, at low frequencies, is the distanceRossby waves travel in time P1 (Philander and Yoon1982). This is consistent with satellite observations,which show a westward movement of the upwelling jetat speeds consistent with Rossby wave dynamics (Struband James 2000). The upwelling front off central Cali-fornia (Point Sur) also seems to move offshore atspeeds consistent with Rossby wave propagation overlong periods (Breaker and Mooers 1986). In the CapeBlanco region, once the jet is off the continental slopeand free of the strong topographic constrain, variationsin the planetary vorticity could aid to its offshorepropagation. The implicit “separation formula” derivedby Marshall and Tansley (2001) shows that, for an east-ern boundary current, the planetary vorticity gradientacts to decelerate the current and, therefore, alwaysencourages separation. Sensitivity studies pursued inprevious numerical studies (e.g., Batteen 1997; Marche-siello et al. 2003) show that the inclusion of the � effectincreases the horizontal and vertical shear in the up-

per layers. Currents can become baroclinically andbarotropically unstable, leading to the development ofmeanders and upwelling filaments. Unfortunately, theboundary conditions used do not allow for the � effectto be included in the simulations.

It is not clear how important the �-plane mechanismis in the region around Cape Blanco. At this latitude(�43°N), Rossby waves propagate at fairly low speeds.However, the � effect could also favor separation byenhancing convergence at the cape. The area south ofthe cape is characterized by strong, persistent positivewind stress curl. A positive surface stress curl woulddrive a depth-averaged northward flow via Sverdrupbalance. This would lead to convergence at the cape. Aconvergence in the along-shelf direction ( � / y � 0) atthe cape would drive a westward flow by continuity( u/ y � 0, with u � 0 at the coast), which could helpadvect momentum offshore.

Another important factor leading to convergence atthe cape is wind relaxation events. Gan and Allen(2002) showed that as the upwelling jet passes aroundPoint Reyes in central California, nonlinear terms be-came important, changing the cross-shelf momentumbalance from geostrophic to gradient wind (Holton1992). This leads to an additional ageostrophic decreasein pressure at the coast. A negative pressure gradient isestablished south of the cape, and this scenario is bal-anced under constant wind forcing. As the wind relaxes,a northward flow is established. Barth et al. (2005a)suggested that a similar balance holds at Heceta Bank,Oregon, and acts to drive northward flow followingwind relaxation. Because of similarities between theregions, we expect a similar situation to occur at CapeBlanco. Wind relaxation could lead to northward flow,causing convergence at the cape. As discussed above,that could aid in jet separation. There seems to be someevidence of a link between convergence at Cape Blancoand jet separation. Mooring data suggest that the tim-ing of jet separation, as seen from satellite images, isroughly coincident with times of strong convergence atthe cape (S. Ramp 2006, personal communication).However, nearshore convergence south of the cape isexpected to occur as a result of separation (Fig. 5),making it difficult to isolate the cause and effect.

Observations also suggest that the poleward under-current, absent in the present simulations, may contrib-ute to separation. Barth et al. (2000) used in situ datafrom 1995 to show that once the upwelling jet is alreadyoff the shelf, it is deep enough to interact with the upperpart of the poleward undercurrent, causing a portion ofthe undercurrent to turn offshore and then southward,augmenting the now-separated equatorward jet. Theyconcluded that the offshore branch of the poleward un-


dercurrent contributed about 20% of the jet transportat the time of the survey.

Despite the limitations discussed above, the presentstudy sheds light on the effects of the wind stress andwind stress curl on the separation of an upwelling jet ata cape. In summary, the results are in agreement withprevious studies, in the sense that the presence of thecape is crucial for separation. The pressure gradientand vortex-stretching terms are very important in thearea-averaged vorticity balance around the cape, andjet separation occurs regardless of the structure of thewind field. Wind intensification by itself, without windstress curl, does not aid in jet separation. The windstress curl, on the other hand, does affect details of theseparation process. The intensity of the wind curl af-fects the timing of the separation, while the spatialstructure of the wind stress curl field affects the amountof separation. Cases in which the jet separates earlierare in closer agreement with observations of jet dis-placements in the Cape Blanco region. These resultspoint out that numerical modeling efforts to simulatethe circulation in the Cape Blanco region and to under-stand its dynamics should include spatially variablewind forcing to represent the wind stress curl.

Last, recently revealed air–sea interactions in theCCS during summer suggest that the use of a coupledocean–atmospheric model might be advisable. Cheltonet al. (2007) showed that surface winds are weaker overcold water, and stronger over warm water. If the windblows along a SST front with cold water to the leftlooking downstream, as is the case most of the time inthe Cape Blanco region, positive wind stress curl is gen-erated. Jet separation can then be enhanced by thistime-evolving interaction. The offshore movement ofthe jet causes cold water to reach greater distances fromthe coast. That increases the width of the region withpositive wind stress curl via the air–sea interaction de-scribed above. Positive wind curl would then cause off-shore upwelling, leading to current intensification evenfarther from the coast, aiding further separation. Thisfeedback mechanism would be most efficiently investi-gated with a coupled model.

Acknowledgments. The authors are grateful to JohnAllen, Roger Samelson, and Murray Levine for helpfulcomments and suggestions. Alexander Kurapov helpedwith the implementation of the open boundary condi-tions. This research was supported by the National Sci-ence Foundation under Grant OCE-9907854. AuthorRC acknowledges support by the Brazilian NationalResearch Council (CNPq Grant 200147/01-3). Addi-tional support was provided by the National Oceanicand Atmospheric Administration (NOAA), U.S. De-

partment of Commerce Award NA03NES4400001 toOregon State University. The statements, findings, con-clusions, and recommendations are those of the authorsand do not necessarily reflect the views of NOAA orthe Department of Commerce.

APPENDIX

Thermal Balance Computation

To evaluate terms in the potential temperature equa-tion, we follow Gan and Allen (2005b). Their approachis repeated here for completeness.

The potential temperature equation is given by (inCartesian coordinates, for simplicity)

�T

�t�

�

�x�uT �

�

�y��T �

�

�z�wT

� HDIFF � VDIFF � 0, �A1

where w is the vertical velocity, and HDIFF and VDIFFare the horizontal and vertical diffusion terms, respec-tively. No external forcing (e.g., heat flux) is consid-ered. The first term in (Al) is the time rate of change oftemperature, while the second through fourth are theadvection terms. Note that the upstream bias advectionscheme used in ROMS carries with it some intrinsicsmoothing. Therefore, the advection terms includesome implicit diffusion, but this is much smaller thanthe magnitude of the advection terms.

In ROMS, the nonlinear advection terms in the tem-perature equation are written in conservation (or diver-gence) form. To evaluate the relative contribution ofhorizontal versus vertical temperature advection, it isnecessary to remove terms in the continuity equationfrom the potential temperature equation (Al). Termsare then time averaged over the time interval of inter-est. To help identify the net contributions of horizontal(ADVH) and vertical (ADVV) advection to the timerate of change of temperature, we further remove anycommon part of opposite sign that cancels in their sum,

ADV � ADVH � ADVV, �A2

following Gan and Allen (2005b). For example, forADV � 0, we define

HOR �12

�ADVH � |ADVH|

�12

�ADVV � |ADVV| and �A3

VER �12

�ADVV � |ADVV|

�12

�ADVH � |ADVH|. �A4


As pointed out by Gan and Allen (2005b), the sum ispreserved (ADV � HOR � VER), and the commonpart of opposite sign that would cancel in the sum isremoved. For ADV � 0, the signs of the terms withabsolute values in (A3) and (A4) are reversed.

REFERENCES

Allen, J. S., 1980: Models of wind-driven currents on the conti-nental shelf. Annu. Rev. Fluid Mech., 12, 389–433.

Arthur, R. S., 1965: On the calculation of vertical motion in east-ern boundary currents from determinations of horizontal mo-tion. J. Geophys. Res., 70, 2799–2803.

Barth, J. A., and R. L. Smith, 1998: Separation of a coastal up-welling jet at Cape Blanco, Oregon, USA. S. Afr. J. Mar. Sci.,19, 5–14.

——, S. D. Pierce, and R. L. Smith, 2000: A separating coastalupwelling jet at Cape Blanco, Oregon and its connection tothe California Current System. Deep-Sea Res. II, 47, 783–810.

——, T. J. Cowles, P. M. Kosro, R. K. Shearman, A. Huyer, andR. L. Smith, 2002: Injection of carbon from the shelf to off-shore beneath the euphotic zone in the California Current. J.Geophys. Res., 107, 3057, doi:10.1029/2001JC000956.

——, S. D. Pierce, and R. M. Castelao, 2005a: Time-dependent,wind-driven flow over a shallow midshelf submarine bank. J.Geophys. Res., 110, C10S05, doi:10.1029/2004JC002761.

——, ——, and T. J. Cowles, 2005b: Mesoscale structure and itsseasonal evolution in the northern California Current Sys-tem. Deep-Sea Res. II, 52, 5–28.

Batteen, M. L., 1997: Wind-forced modeling studies of currents,meanders, and eddies in the California Current System. J.Geophys. Res., 102, 985–1010.

Breaker, L. C., and C. N. K. Mooers, 1986: Oceanic variability offthe central California coast. Prog. Oceanogr., 17, 61–135.

Capet, X. J., P. Marchesiello, and J. C. McWilliams, 2004: Up-welling response to coastal wind profiles. Geophys. Res. Lett.,31, L13311, doi:10.1029/2004GL020123.

Castelao, R. M., and J. A. Barth, 2006: The relative importance ofwind strength and alongshelf bathymetric variations on theseparation of a coastal upwelling jet. J. Phys. Oceanogr., 36,412–425.

——, T. P. Mavor, J. A. Barth, and L. C. Breaker, 2006: Sea sur-face temperature fronts in the California Current Systemfrom geostationary satellite observations. J. Geophys. Res.,111, C09026, doi:10.1029/2006JC003541.

Chapman, D. C., 1985: Numerical treatment of across-shore openboundaries in a barotropic ocean model. J. Phys. Oceanogr.,15, 1060–1075.

Chelton, D. B., M. G. Schlax, M. H. Freilich, and R. F. Milliff,2004: Satellite measurements reveal persistent small-scalefeatures in ocean winds. Science, 303, 978–983.

——, ——, and R. M. Samelson, 2007: Summertime coupling be-tween sea surface temperature and wind stress in the Cali-fornia Current System. J. Phys. Oceanogr., 37, 495–517.

Dale, A. C., and J. A. Barth, 2001: The hydraulics of an evolvingupwelling jet flowing around a cape. J. Phys. Oceanogr., 31,226–243.

Dorman, C. E., T. Holt, D. P. Rogers, and K. Edwards, 2000:Large-scale structure of the June–July 1996 marine boundarylayer along California and Oregon. Mon. Wea. Rev., 128,1632–1652.

Flather, R. A., 1976: A tidal model of the northwest Europeancontinental shelf. Mem. Soc. Roy. Sci. Liege, 6, 141–164.

Galperin, B., L. H. Kantha, S. Hassid, and A. Rosati, 1988: Aquasi-equilibrium turbulent energy model for geophysicalflows. J. Atmos. Sci., 45, 55–62.

Gan, J., and J. S. Allen, 2002: A modeling study of shelf circula-tion off northern California in the region of the CoastalOcean Dynamics Experiment: Response to relaxation of up-welling winds. J. Geophys. Res., 107, 3123, doi:10.1029/2000JC000768.

——, and ——, 2005a: On open boundary conditions for a limited-area coastal model off Oregon. Part 1: Response to idealizedwind forcing. Ocean Modell., 8, 115–133.

——, and ——, 2005b: Modeling upwelling circulation off theOregon coast. J. Geophys. Res., 110, C10S07, doi:10.1029/2004JC002692.

Haidvogel, D. B., A. Beckman, and K. Hedstrom, 1991: Dynami-cal simulations of filament formation and evolution in thecoastal transition zone. J. Geophys. Res., 96, 15 017–15 040.

Haynes, R., E. D. Barton, and I. Pilling, 1993: Development, per-sistence and variability of upwelling filaments off the Atlanticcoast of the Iberian Peninsula. J. Geophys. Res., 98, 22 681–22 692.

Holton, J. R., 1992: An Introduction to Dynamic Meteorology.Academic Press, 511 pp.

Huyer, A., J. H. Fleischbein, J. Keister, P. M. Kosro, N. Perlin,R. L. Smith, and P. A. Wheeler, 2005: Two coastal upwellingdomains in the northern California Current System. J. Mar.Res., 63, 901–929.

Marchesiello, P., J. C. McWilliams, and A. Shchepetkin, 2001:Open boundary conditions for long-term integration of re-gional oceanic models. Ocean Modell., 3, 1–20.

——, ——, and ——, 2003: Equilibrium structure and dynamics ofthe California Current System. J. Phys. Oceanogr., 33, 753–783.

Marshall, D. P., and C. E. Tansley, 2001: An implicit formula forboundary current separation. J. Phys. Oceanogr., 31, 1633–1638.

Mellor, G. L., and T. Yamada, 1982: Development of a turbulenceclosure model for geophysical fluid problems. Rev. Geophys.,20, 851–875.

Mesias, J. M., R. P. Matano, and P. T. Strub, 2001: A numericalstudy of the upwelling circulation off central Chile. J. Geo-phys. Res., 106, 19 611–19 623.

——, ——, and ——, 2003: Dynamical analysis of the upwellingcirculation off central Chile. J. Geophys. Res., 108, 3085,doi:10.1029/2001JC001135.

Narimousa, S., and T. Maxworthy, 1987: On the effects of coast-line perturbations on coastal currents and fronts. J. Phys.Oceanogr., 17, 1296–1303.

Palma, E. D., and R. P. Matano, 1998: On the implementation ofpassive open boundary conditions for a general circulationmodel: The barotropic mode. J. Geophys. Res., 103, 1319–1341.

Peffley, M. B., and J. J. O’Brien, 1976: A three-dimensional simu-lation of coastal upwelling off Oregon. J. Phys. Oceanogr., 6,164–180.

Penven, P., C. Roy, A. Colin de Verdière, and J. Largier, 2000:Simulation of a coastal jet retention process using a barotro-pic model. Oceanol. Acta, 23, 615–634.

Perlin, N., R. M. Samelson, and D. B. Chelton, 2004: Scatterom-eter and model wind and wind stress in the Oregon–northernCalifornia coastal zone. Mon. Wea. Rev., 132, 2110–2129.


Philander, S. G. H., and J.-H. Yoon, 1982: Eastern boundary cur-rents and coastal upwelling. J. Phys. Oceanogr., 12, 862–879.

Pickett, M. H., and J. D. Paduan, 2003: Ekman transport andpumping in the California Current based on the U.S. Navy’shigh-resolution atmospheric model (COAMPS). J. Geophys.Res., 108, 3327, doi:10.1029/2003JC001902.

Samelson, R., and Coauthors, 2002: Wind stress forcing of theOregon coastal ocean during the 1999 upwelling season. J.Geophys. Res., 107, 3034, doi:10.1029/2001JC000900.

Shchepetkin, A. F., and J. C. McWilliams, 2003: A method forcomputing horizontal pressure-gradient force in an oceanicmodel with a nonaligned vertical coordinate. J. Geophys.Res., 108, 3090, doi:10.1029/2001JC001047.

——, and ——, 2005: The Regional Oceanic Modeling System(ROMS): A split-explicit, free-surface, topography-follow-ing-coordinate oceanic model. Ocean Modell., 9, 347–404.

Song, Y. T., and D. B. Haidvogel, 1994: A semi-implicit oceancirculation model using a generalized topography-followingcoordinate system. J. Comput. Phys., 115, 228–244.

Strub, P. T., and C. James, 1995: The large-scale summer circula-tion of the California current. Geophys. Res. Lett., 22, 207–210.

——, and ——, 2000: Altimeter-derived variability of surface ve-locities in the California Current System. 2: Seasonal circu-lation and eddy statistics. Deep-Sea Res. II, 47, 831–870.


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