## 1. Introduction

The California Current System (CCS) (Hickey 1998) occurs near the eastern boundary of the subtropical North Pacific wind gyre. It is composed of persistent coastal upwelling in response to prevalently equatorward winds (hence has climatically important stratus clouds and high biological productivity); a broad (800–900 km), shallow (100–300 m), and slow (<0.25 m s^{−1}) southward California Current; an intermittent, inshore, northward, surface Davidson Current; and the northward, subsurface California Undercurrent (CUC). The latter extends about 100 km from the coast and reaches speeds of more than 0.1 m s^{−1} at depths between 100 and 400 m along the upper continental slope (Collins et al. 2000). It is strongest between late spring and early autumn in concert with the wind. Vertical shear in and above the CUC supports a vigorous mesoscale baroclinic instability (Marchesiello et al. 2003). The CCS and its CUC are representative of subtropical eastern boundary currents in all major oceanic basins (Capet et al. 2008a).

The CCS mesoscale eddy field is best known through its surface signatures in drifter trajectories and sea surface height fluctuations (Swenson and Niiler 1996; Stegmann and Schwing 2007; Chelton et al. 2007). The eddies generally drift westward at approximately the first baroclinic Rossby wave speed, and their amplitude decays on the broad scale of the surface California Current, partly because of energy propagating downward along the westward-deepening pycnocline (Haney and Hale 2001; Marchesiello et al. 2003). The mesoscale dynamics are highly nonlinear, as expressed in the name of an earlier CCS field experiment “squirts and jets,” and they give rise to narrow filaments and fronts that arise through cascades of mesoscale energy and tracer variance into the submesoscale range,^{1} clearly evident in satellite images of surface temperature and color (Castelao et al. 2006; Capet et al. 2008b).

Transporting warm, saline equatorial water northward along the coast, the CUC has a well-defined potential temperature-salinity (*θ*−*S*) signature observed from Baja, California, to Vancouver Island (Pierce et al. 2000; Collins et al. 2000). Both *θ* and *S* decrease northward in the CUC apparently through dilution of equatorial water by mixing with cooler and fresher water along its path. This water mass provides a clear marker of the core water of anticyclonic eddies formed from CUC meanders (Huyer et al. 1998). Between 1992 and 1995, Garfield et al. (1999) released 19 subsurface RAFOS floats off the coast of San Francisco and tracked them acoustically. Floats moved generally northward while close to the coast and westward, usually within coherent anticyclones when farther offshore. The eddies seemed to form widely along the coast, developing first as meanders in the CUC before breaking off and moving into the interior (Collins et al. 2013; Pelland et al. 2013).

The dynamical process of CUC eddy generation is an intriguing puzzle. Quasigeostrophic dynamics allows for symmetric behavior between cyclones and anticyclones, and geostrophic turbulence has an eddy recirculation and decorrelation time of about a week. Yet the CUC eddies are often coherent anticyclones with a lifetime of many months. For the preferential selection of anticyclones, we seek explanations in an unstable CUC with a highly nonsymmetric structure in vertical vorticity *ζ*^{z}, or significant violation of quasigeostrophic dynamics during coherent anticyclone generation, or both. For their atypical longevity one hypothesis is that CUC eddies are a form of submesoscale coherent vortex (SCV). Discovered during the POLYMODE Local Dynamics Experiment, SCVs are usually anticyclonic with midwater velocity maxima around cores of relatively homogeneous water presumed to result from localized diapycnal mixing events followed by adjustment to gradient wind momentum balance (McWilliams 1985, 1988). From the perspective of the current paper, this terminology is somewhat confusing as we argue that these structures are generally in geostrophic balance or at least cyclostrophic balance. Nevertheless, since it is widely used for the abundant interior anticyclones with a convex lens shape to the density field, we will not abandon this terminology. Meddies in the Atlantic are well-known SCVs, and they detach from the Iberian slope in conjunction with meandering and instability of the alongslope current (Bower et al. 1995, 1997); this is consistent with the boundary current vorticity generation and separation mechanism invoked by D’Asaro (1988) for a SCV observed off Point Barrow, Alaska. In the context of the CUC and the adjacent slope, the detaching anticyclones might be another form of SCV (suggested by the name Cuddy; Garfield et al. 1999), but if so, the behavior during their generating events has not yet been identified.

*ζ*

^{z}< 0, due to the effect of a bottom turbulent shear layer against the slope. Subsequently the CUC separates, commonly near ridges with strong topographic curvature, and moves into deeper water while still satisfying the criterion for ageostrophic centrifugal instability (i.e.,

*ζ*

^{z}< −

*f*, where

*f*is the local vertical component of the Coriolis frequency vector

**f**). Strictly speaking the instability criterion is related to a spatial sign reversal of Ertel potential vorticity Π (Hoskins 1974), defined by

**u**is the velocity,

*b*is the buoyancy (approximately −

*g*/

*ρ*

_{0}times the potential density with

*g*the gravitational acceleration and

*ρ*

_{0}the mean density). The Ertel vorticity Π is a Lagrangian invariant in the absence of mixing of tracers and/or momentum, while the absolute vertical vorticity

*ζ*

^{z}+

*f*is not; nevertheless, the sign of the latter is a useful proxy for the sign of Π in this context. Centrifugal instability gives rise to strong, partly ageostrophic submesoscale currents and local mixing. Once the mixed vorticity is diluted below in the instability threshold, the flow organizes itself into anticyclonic, balanced, coherent mesoscale vortices. Thus, the generation mechanism combines boundary current separation and instability with submesoscale mixing, balanced adjustment, and upscale flow self-organization.

## 2. Simulation and analysis setup

Our choice of computational code to study meso- and submesoscale currents is the Regional Oceanic Modeling System (ROMS) (Shchepetkin and McWilliams 2005, 2009). It solves the hydrostatic primitive equations for **u**, *θ*, and *S* with the seawater equation of state. To simulate local flows in a realistic large-scale environment, we configure it for the CCS, utilizing open boundary conditions and nested subdomains (Marchesiello et al. 2003; Penven et al. 2006). Because our primary target is submesoscale currents with horizontal scales of *O*(1) km near the eastern topographic slope, we take an aggressive nesting approach with successively finer resolution in a sequence of steps where each “child” grid utilizes “parent” grid data at the open boundaries of the regional domains (Mason et al. 2010). The procedure is offline, one-way nesting from larger to finer scales without feedback from the child grid solution onto the parent grid. Implicit is an assumption that a numerical “zoom” around specific phenomena is valid when it has an essentially local dynamical behavior, albeit with important influences from its environment of basin and regional circulation.

We use the Shuttle Radar Topography Mission (SRTM30-plus) bathymetry dataset^{2} based on the 1-min Smith and Sandwell (1997) global dataset, but using higher-resolution data where available. A Gaussian smoothing kernel with a width 4 times that of the topographic grid spacing is used to avoid aliasing whenever the topographic data are available at higher resolution than the computational grid. The maximum depth for all grids is set to 6000 m, which is not a serious distortion for the U.S. West Coast region. Models formulated with a terrain-following coordinate such as ROMS have computational restrictions with regards to the steepness and roughness of the topography (Beckmann and Haidvogel 1993). Where the steepness of the topography on the grid exceeds these criteria, additional local smoothing is applied. Both these procedures lead to topography that is increasingly well resolved in grids with higher resolution, but may differ significantly from the original data in the coarser domains. Following Mason et al. (2010), the topography near the boundaries of the nested domains is matched with the parent topography.

The largest-scale simulation used in this study covers the full Pacific basin (Fig. 1). This grid, as all others in this study, is an orthogonal grid based on an oblique Mercator projection and is designed to have nearly uniform spacing in both horizontal directions. For the Pacific basin, the grid spacing varies between 12.5 km at the central latitude of the grid and 8.5 km at the north and south extremes of the grid around 40°S and 55°N; this is comparable to what is used in eddy-resolving global models, that is, mesoscale resolution. This simulation is forced at the surface by a mean monthly climatology of QuikSCAT scatterometer winds, Scatterometer Climatology of Ocean Winds (SCOW) (Risien and Chelton 2008), and of heat and freshwater fluxes from the Comprehensive Ocean–Atmosphere Dataset (COADS) (Da Silva et al. 1994), using a weak feedback from sea surface temperature (SST) (Barnier et al. 1995). The open boundary information and initial state are taken from the monthly Simple Ocean Data Assimilation (SODA) ocean climatology (Carton and Giese 2008). The SST pattern has both gyre-scale contrasts and mesoscale eddy fluctuations visible in regions of relatively high SST gradient. Lemarié et al. (2012) has full information about a similar Pacific simulation at coarser resolution.

The Pacific model is spun up from interpolated SODA data for 2 yr, after which an approximate statistical equilibrium is reached for kinetic energy. The model is then run for an additional 10 yr for statistical analysis. Its mean monthly climatology is used to force the first nested grid along the U.S. West Coast (Fig. 1) at its open boundaries. While the monthly boundary information does not permit the passing of mesoscale features, it forces the regional domain with a seasonal climatological cycle. The first nested grid is sufficiently large to generate a realistic level of mesoscale eddy activity through regional current instability. This is verified by comparing maps of surface eddy kinetic energy with altimetry-derived eddy kinetic energy. With open boundary conditions in nested grids, it is important to avoid computational artifacts associated with boundary-trapped features (e.g., rim currents) and noisy fields. Our experience is that in the ROMS-to-ROMS nesting interface, these artifacts are largely avoided even for realistic flows with high mesoscale activity (Mason et al. 2010).

Figure 2 shows a snapshot of SST obtained with multiple levels of our nested regional grids. Cold water is found near the coast because of persistent, wind-driven summer upwelling. There is an analogous minimum in sea level, implying a broad, equatorward, geostrophic California Current. The upwelling front is full of filaments, squirts, and jets that expose the mesoscale eddies spawned mainly by baroclinic instability of the CCS (Marchesiello et al. 2003). As with the Pacific grid, these child grids are discretely orthogonal, and they vary even less in their grid spacing over their relatively smaller domains; for example, the first nested subdomain has a grid spacing that varies between *dx* = 4 km and *dx* = 3.97 km. The next three grids have average horizontal spacings of *dx* = 1.5 km, *dx* = 0.5 km, and *dx* = 166 m, respectively. The successive levels of grid refinement spontaneously exhibit an increasing amount of submesoscale activity (cf. Capet et al. 2008a). There are 40 vertical levels in all the grids with the exception of the finest grid where 80 vertical levels are used.

As empirical tests of the realism resulting from this configuration, we have compared the mean sea level and surface geostrophic eddy kinetic energy with altimetric measurements (Rio and Hernandez 2004; Pascual et al. 2006). The result is generally similar to what is reported in Capet et al. (2008a) for a somewhat differently configured U.S. West Coast simulation, with an approximately correct mean CCS circulation and its associated mesoscale eddy variability. We do not show these comparisons here, nor do we present other necessary aspects of an extensive validation of the model. This would require sufficient model integration to allow for accurate estimation of mean and variance fields, which are the primary quantitative basis for assessing a flow with intrinsic variability. The target here is the finer-scale currents near Monterey Bay, where our purpose is to examine the eddy generation process. For this we require phenomenological validity in the simulated behaviors, but for our purposes argue that quantitative statistical precision is not essential. This is a necessary concession because long time integration of the high-resolution subdomains is computationally too expensive to determine its statistical equilibrium structure. The first nested grid along the U.S. West Coast is integrated for 8 yr; the next level grid, covering the California coastal region, is integrated for 3 yr; the central California coast grid is integrated for 15 months, covering a single cycle of seasonal behavior; and the final nested grid around Monterey Bay is run for only 6 months in spring and summer (April through September).

We alternately display results in the model coordinate system of longitude, latitude, and vertical *z* or in a local Cartesian coordinate system (*x*, *y*, and *z*) rotated to align the *y* axis with an average poleward direction (a counterclockwise rotation of 24°) of the coastline in central California, with (*u*, *υ*, and *w*) the associated (cross shore or onshore, alongshore, and vertical) velocity components. We focus on the summer season (July through September) when the wind stress, upwelling, CUC, and mesoscale eddies are strongest (Marchesiello et al. 2003).

## 3. Results

### a. Undercurrent and anticyclonic eddies

We first show that our solutions are in the relevant regime for the mean CUC and mesoscale anticyclonic subsurface vortices. Figure 3 is the summer-mean alongshore velocity *υ* and salinity *S* at 150-m depth. The velocity *υ* is predominantly positive against the eastern boundary over the continental slope all along the U.S. West Coast, most intense in the central California sector; this is the signature of the CUC. The general pattern is consistent with the shipboard measurements in Pierce et al. (2000) that map the CUC all along the U.S. West Coast, as well as with the RAFOS float trajectories in Garfield et al. (1999), many of which systematically move poleward near the boundary. The maximum mean speed here is about 0.15 m s^{−1}, consistent with the observations. The core isopycnal surfaces in the CUC have anomalously warm and salty water of equatorial origin. The right panel in Fig. 3 shows a positive *S* anomaly that is advected poleward by the CUC and spreads offshore beyond the width of the mean current, presumably by mesoscale eddy mixing. The anomaly strength decreases along the current path, again consistent with eddy mixing. An accompanying vertical section of mean *υ*(*x*, *z*) (Fig. 4) indicates that the primary depth range of the CUC is between 100 and 450 m, and its width is several tens of kilometers. The surface coastal current and offshore California Current are both southward (*υ* < 0); both appear rather weak in this particular section, but this feature varies with different averaging periods and, to some degree, is not well determined from these limited duration simulations with grid resolution (cf. Fig. 8). Nevertheless, the width and strength of the CUC in this location are fairly robust across these circumstances. However, this characterization is not valid in particular topographic locations where the mean CUC is interrupted. Examples of the latter are evident in Fig. 3, north of Point Sur, Point Reyes, and Cape Mendocino around 36.5°, 38.5°, and 41°N. Todd et al. (2011) shows measurements of CUC interruption farther south. In the following sections, we focus on the CUC separation around Point Sur.

Altimetric measurements show that the surface mesoscale eddy field in the CCS is a nearly equal mixture of cyclones and anticyclones (Chelton et al. 2011). However, this changes within the lower pycnocline, where anticyclones become dominant both in measurements (Garfield et al. 1999) and models similar to the present one at mesoscale resolution (Kurian et al. 2011). Figure 5 shows snapshots of *ζ*^{z}(*x*, *y*) at *z* = 150 m in several nested subdomains. We adopt a convention of normalizing by the Coriolis frequency *f* to define a local Rossby number *ζ*^{z}/*f*. When it is small we expect quasigeostrophic dynamics to be valid. Other behaviors can arise when it is not small and the geostrophic and/or hydrostatic balance approximations are less accurate, which we refer to generally as unbalanced dynamics. Vortices with both parities are evident, but anticyclones with *ζ*^{z} < 0 are more abundant and better shaped as approximately circular monopole vortices. In the simulation with a grid resolution of *dx* = 4 km, there is a relatively modest degree of parity asymmetry. The negative skewness of vorticity at depth becomes more pronounced with increased grid resolution. This skewness at depth is in contrast with the positive skewness of vorticity in the upper ocean (Rudnick 2001).

The peak vorticity amplitude of the mesoscale, offshore anticyclones reaches *ζ*^{z} ≈ −0.4*f*. With increasing grid resolution, the offshore anticyclones get stronger, but there is approximate convergence between the *dx* = 1.5 km and *dx* = 0.5 km simulations to a peak amplitude of *ζ*^{z} ≈ −0.7*f*. As discussed in section 1, a known centrifugal stability threshold for anticyclonic eddies is Π = 0 or *ζ*^{z} = −*f*. The absence of *ζ*^{z} < −*f* indicates centrifugal stability. However, the fact that the peak amplitudes are at least close to this threshold value in the higher-resolution simulations is suggestive of the occurrence of centrifugal instability at some earlier stage in the eddy formation process, nearer the coast. In Fig. 6, probability density functions (PDFs) are shown of the relative vorticity at 150-m depth as shown in Fig. 5. The PDFs confirm the asymmetry between cyclonic and anticyclonic vorticity that is apparent in the maps of *ζ*^{z}(*x*, *y*) at *z* = 150 m. The PDF’s at the two highest resolutions are relatively similar, supporting the approximate convergence of the offshore eddy field. The skewness *γ* of the respective PDFs varies between *γ* = −1.3 for the coarser-resolution results and *γ* = −1.8 for the higher-resolution simulations.

### b. Production of negative vorticity along the slope

*ζ*

^{z}is dominant in the CUC, and if the CUC is unstable in a way that generates vortices after finite-amplitude growth. A possible source of

*ζ*

^{z}< 0 is drag of the boundary against the adjacent poleward flow. If there were a side boundary this would be analogous to the effect of a horizontal boundary layer due to horizontal viscosity and a no-slip boundary condition. For the ocean, however, the physical justifications for a large horizontal eddy viscosity at a side boundary are unclear. The more plausible conception is a bottom boundary with a turbulent shear boundary layer and a significant vertical (or even isotropic) eddy viscosity. If this vertical boundary layer is over a sloping boundary, then the necessary vertical shear also implies a horizontal shear, that is,

*ζ*

^{z}, as illustrated in Fig. 7 for a flow configuration like the CUC. The width of the horizontal shear layer can be estimated as

*s*=

*dz*

_{b}(

*x*)/

*dx*is the slope of the bottom boundary, and Δ

*x*and

*h*are, respectively, the lateral width and vertical height of the shear zones in

*υ*(

*x*,

*z*). For an alongslope flow speed of

*V*, the associated

*ζ*

^{z}magnitude is

*V*/Δ

*x*. The model only has a vertical bottom boundary condition related to viscous boundary stress. It employs a bottom boundary layer parameterization [

*K*-profile parameterization (KPP)] (Large et al. 1994) that exerts a drag on the lowest layers, defined by

*τ*is bottom stress,

*C*

_{d}is a bottom drag coefficient, and

*υ*

_{b}is near-bottom velocity, much as required by classical law of the wall reasoning. Consistent with the effect in Fig. 7, the model vertical boundary layer implies a horizontal shear layer.

The expected structure is seen in a summer-mean *υ*(*x*, *z*) section in the finest-resolution subdomain that intersects the coast about 15 km upstream (south) from Point Sur (Fig. 8, upper panel).^{3} A boundary layer is clearly visible where *υ* approaches zero at the sloping bottom. The lower panel shows the accompanying *ζ*^{z}/*f*. Because the CUC flows north and the boundary is on its east side, the *ζ*^{z} produced by the boundary layer on the slope is negative. Upstream of Point Sur, extreme values of negative vorticity reach down to −10*f*, and the local flow escapes centrifugal instability only because of the suppression by the nearby boundary. In the following sections we show that, once separated from the boundary, the CUC with *ζ*^{z}/*f* ≪ −1 becomes unstable very rapidly, leading to small-scale, unbalanced turbulent currents and vigorous mixing and dissipation. For the California coast, the cross-shelf bottom slope may be as high as 0.25 on this grid, which leads to horizontal boundary layer widths that are only a little larger than the vertical height. From Fig. 8, we can estimate the vertical scale of the boundary layer as 50 m or less and therefore the horizontal scale as 200 m or less with the extreme slope of 0.25. Flows on this scale are not accurately resolved even on our finest grid, and the simulated scale is somewhat wider. For a *υ* magnitude of 0.2 m s^{−1} and a lateral shear zone width of 200 m, the estimated *ζ*^{z} in the boundary layer is −10^{−3} s^{−1}, that is, *O*(−10*f*).

### c. Undercurrent separation

Separation of a current behind an obstacle or along a boundary is a common occurrence in fluids. For nonrotating, unstratified flows the separation dynamics are well understood in relation to such influences as boundary shape, viscous vorticity generation, and an imposed, adverse pressure gradient (Acheson 1990). Oceanic currents can also separate behind an island, headland, or submerged bump (e.g., Dong et al. 2007), as well as along a continuous coast because of the changing wind stress curl, boundary curvature away from the downstream flow direction, and an internally generated adverse pressure gradient (e.g., Haidvogel et al. 1992; Kiss 2002). Separation is not necessary along a slowly varying boundary; for example, in conservative quasigeostrophic dynamics, currents tend to follow topographic contour lines to conserve potential vorticity (Pedlosky 1987). However, strong, nonconservative flows often do separate where the boundary curves away, as the Gulf Stream does at Cape Hatteras.

Along the California coast, at the depth of the CUC, there are several headlands with offshore subsurface ridges where separation could be expected, and the mean *υ* pattern in Fig. 3 indicates places where it does so, including the headland of Point Sur, south of Monterey Bay. Accompanying the mean separation of the CUC, the instantaneous local flow is highly variable, yet it recurrently manifests a separation pattern. Figure 9 (left panel) shows *ζ*^{z}/*f* at a depth of 150 m, time averaged over 12 h to remove some of the signal of internal gravity waves. South of the headland, the CUC is firmly attached to the topographic slope with an associated turbulent boundary layer characterized by large, negative values of *ζ*^{z}. Around the point of separation, an area of interspersed negative and positive *ζ*^{z}(*x*, *y*) occurs, dominated by small spatial scales, that is, submesoscale currents. At the same depth of 150 m, the potential temperature *θ* (Fig. 9, right panel) shows positive anomalies in the poleward undercurrent, which accumulate in the resulting anticyclonic eddies. The gradient of *θ* is consistent with strong vertical shear ∂_{z}*υ* in the geostrophic part of the current, but is partially compensated by the opposing salinity gradient (see also Fig. 13). To the northwest of the separation point, an anticyclonic mesoscale eddy, with an approximate vorticity diameter of 30 km, is present by chance. Mesoscale anticyclones are generated at many locations along the CUC as products of the upscaling and dilution of the negative vorticity in the turbulent boundary layer on the slope, and they move around along chaotic trajectories. The Point Sur separation region is an important source of delivery of negative vorticity from the slope boundary into the stratified interior, and sometimes this leads to local formation of mesoscale anticyclones (section 3g), including the one shown here that emerged at an earlier time. Finally, notice in Fig. 9 other locations of submesoscale *ζ*^{z} of both signs, especially around Monterey Canyon and on the north side of the Bay. This indicates local boundary generation by other currents than the separating CUC, which almost never goes inside the bay.

### d. Bottom pressure torque and form stress

*p*

_{b}=

*p*[

*x*,

*y*,

*z*

_{b}(

*x*,

*y*),

*t*], is a force against a sloping boundary. The bottom pressure can be partitioned in a static plus a dynamic part. The static bottom pressure can be thought of as the force that is exerted by the bottom to keep the ocean water in its basin. The vertical component supports the weight of the water above the bottom, and the horizontal component is balanced by an identical force on the opposite side of the ocean basin. One may think of these forces as the pressure forces on, for instance, a glass filled with water. The local interpretation of the dynamic bottom pressure represents a dominant balance with inertial forces. As currents flow around bottom features, inertia has to be overcome by pressure forces against the bottom. The integral of the horizontal component of this force over a designated area

*A*(m

^{2}) is a net force

*F*(N) in a designated horizontal direction

^{2}s

^{−2}), multiplied by

*ρ*

_{0}

*A*, is a force

*F*that contributes to the force in the direction of

*H*. For a terrain-following model like ROMS, the bottom torque can be computed exactly by taking the curl of the vertically integrated horizontal pressure gradient (Song and Wright 1998). From the torque, we can find a pressure anomaly along a contour line of fixed topography depth

*H*

_{0}using

*n*,

*s*) are right-handed horizontal coordinates with

*s*as the distance along a contour. The local slope is ∂

*H*/∂

*n*, oriented to the right of the direction of integration. Using this approach, we can accurately compute the local bottom pressure anomaly up to an integration constant.

This procedure is applied to the Point Sur region in Fig. 10. The left panel shows the bottom pressure torque. The local bottom topographic torque pattern has an anticyclonic barotropic vorticity tendency,

With (5), we compute the corresponding bottom pressure anomalies with the choice of zero integration constants for bottom pressure upstream of the headland at roughly 36.1°N. The right panel of Fig. 10 shows the pressure anomalies.^{4} The positive pressure anomaly forces the undercurrent around the obstacle that is the headland, changing its direction to locally westward. The absence of a negative pressure anomaly on the downstream side of the headland is consistent with the separation of the undercurrent. The undercurrent leaves its contour-following path driven by inertia.

When the pressure anomalies are integrated as described in the preceding paragraph, this pattern yields the total bottom force *F* for this area. The undercurrent interacts with the Point Sur ridge to yield a positive pressure anomaly on the upstream side of the Point Sur headland where the slope faces south. This pattern implies a net southward-facing force, so the form stress is retarding the poleward CUC in this location. Following (3), we obtain the horizontal component of the associated force in the upstream direction, which is about 4 N m^{−2} with a pattern that is not shown, but is similar to *p*_{b} in the right panel of Fig. 10. These values are large compared to typical values of the wind stress *C* between the time-flow and along-flow mean current *υ*_{m} in the direction of *υ*_{m} > 0 and *C* > 0; that is, the equatorward form stress extracts energy out of the mean poleward CUC. This relation is analogous to the rate of wind work at the surface, proportional to the product of the surface current and the surface stress. Thus, where surface and bottom currents are comparable, as here, the relative importance of the topographic energy sink and surface energy source (with equatorward surface current) is roughly the same as the comparison of the respective boundary stresses.

### e. Submesoscale instability and local energy dissipation

The occurrence of centrifugal instability brings with it the potential for diapycnal mixing. Although the fastest growth rates cross isopycnals at a small angle, finite-amplitude overturning is not guaranteed. Diabatic processes may be the result of secondary instabilities.

Figure 11, left panel, shows the unfiltered variance of the horizontal divergence, *δ* = ∂_{x}*u* + ∂_{y}*υ*. Flows that are dominated by a geostrophic force balance are expected to have small values of *δ* relative to the vertical vorticity *ζ*^{z}; hence, large *δ* can be associated with unbalanced dynamics (see also Molemaker et al. 2010; Capet et al. 2008b). Notice how the area of maximum *δ* variance is downstream of the separation point and roughly coincides with the large submesoscale velocity and buoyancy variance. Because the flow is incompressible, with ∂_{z}*w* = −*δ*, the elevated levels of *δ* also are evidence of enhanced *w* variance. We associate strong *w* with flows that are significantly out of geostrophic balance, whose *w* are predicted to be small. Unbalanced instabilities may occur that include vertical or slantwise overturning and diapycnal mixing. During the occurrence of these unbalanced flow events, continuous geostrophic adjustment of the resulting tracer field is active, evidenced in snapshots by the spontaneous emission of inertia–gravity wave patterns radiating from areas with high *δ* (not shown). In our simulations, the radiating component in *δ* is relatively weak compared to the more stationary component downstream from the CUC separation. The emergence of unbalanced motion at small scales is comparable to those that spontaneously appear in Capet et al. (2008b) and Molemaker et al. (2010). We therefore hypothesize a similar active forward cascade to smaller scales and viscous dissipation, as well as to the mixing of tracers.

Using the discrete formulation of the model, we can explicitly compute the kinetic energy dissipation rates. This is achieved by taking the inner product of the horizontal velocities with the dissipative terms in the momentum equations, similar to the approach used in Molemaker and McWilliams (2010) and Molemaker et al. (2010). The local total energy dissipation rate, at the depth of the undercurrent, is shown in Fig. 11 (right panel), downstream of the separation of the undercurrent at the Point Sur headland. The local energy dissipation is the sum of the effects of horizontal and vertical mixing processes as they are parameterized by the model. Generally, the energy dissipation is dominated by the vertical mixing terms that represent the parameterization of small Richardson number processes and static instabilities (Large et al. 1994). This yields dissipation rates between 3 and 6 × 10^{−8} m^{2} s^{−3} (or W kg^{−1}), which is significantly larger than background values of dissipation observed in the interior and of the same order of routine dissipation rates that occur in the surface boundary layer (Dillon and Caldwell 1980; Greenan et al. 2001). It is, however, roughly two orders of magnitude weaker than the dissipation observed by D’Asaro et al. (2011) in an intense Kuroshio front. This is perhaps not surprising given that the shears in the Kuroshio are an order of magnitude larger than those of the CUC. Over a distance of *O*(10) km, the submesoscale variance decays (see Fig. 11, left panel) and the dissipation abates. Assuming a mean velocity of the undercurrent of *V* ≈ 0.1 m s^{−1}, this corresponds to a decay time of about 2 days.

While one can question the details of how the model reacts to centrifugal instability, it provides strong support for the conjecture that separation at Point Sur results in enhanced local dissipation of energy. Accompanying increased levels of diapycnal mixing are likely to occur in this area, but are not explicitly diagnosed. In contrast to most oceanic explanations for mixing, this occurs for reasons other than internal wave–driven Kelvin–Helmholtz shear instability or double diffusion. In a companion paper (Dewar et al. 2015), a more explicit diagnosis of the diapycnal mixing during centrifugal instability is made using an even finer-scale, nonhydrostatic nested model.

### f. Dilution to the centrifugal instability threshold

Presumably as a result of the centrifugal instability, the potential vorticity Π evolves toward stable profiles, that is, it becomes one signed, consistent with the premise that centrifugal instability drives the current toward a state of marginal stability. This can be observed in Fig. 12 where the distribution of potential vorticity is shown as *z* = 150 m. Negative values are observed upstream of the separation point. Downstream of separation, small scales are visible, and values of potential vorticity rapidly return to zero or positive values. Such dilution is a result of both the diapycnal and isopycnal mixing instigated during the instability, given the presence of subcritical, positive, potential vorticity elsewhere near the separation, and it continues until all negative Π has been eliminated (Fig. 12). Typical values for the extrema in the resulting upscaled anticyclones are *ζ*^{z}/*f* ≈ −0.7 (Fig. 5), indicating some residual mixing exists beyond the threshold of centrifugal instability. Two candidates to explain these potential vorticity values are the ageostrophic anticyclonic instability (Yavneh et al. 2001; McWilliams et al. 2004; Molemaker et al. 2005), which can occur for smaller |Ro| values than the centrifugally critical value of Ro = −1, and vertical shear, which can reduce the vertical component of relative vorticity to subcritical values, while arresting the potential vorticity at the critical value of zero on an isopycnal.

### g. Upscaling to mesoscale anticyclones

In animations of these simulations in all of the nested subdomains, ranging from *dx* = 4 km down to *dx* = 166 m, the offshore anticyclones behave with striking similarities to coherent vortices in two-dimensional and geostrophic turbulence (McWilliams 1984; McWilliams et al. 1994): they emerge as well-shaped, long-lived vortices from finer-scale fragments of *ζ*^{z} and Π through the processes of horizontal axisymmetrization and vertical alignment. They move chaotically by mutual advection, as in a point vortex model, and they undergo mergers during close encounters that lead to a growth in size both horizontally and vertically (Fig. 13). The mesoscale vortex has vertical coherence over several hundred meters, while the submesoscale currents have scales of 100 m or less. In a later stage, the mesoscale vortices are usually widely enough separated that further size growth through mergers ceases to be common, and in addition to mutual advection, the dominant propagation influence is the Coriolis gradient, *β* = *df*/*dy*, with movement generally toward the southwest (Kurian et al. 2011). In this state, their spatial structure, water mass anomaly, and longevity are qualitatively consistent with the SCVs observed in many places, and they are appropriately called Cuddies (section 1).

The connection with the CUC is through its instability as a source of vorticity in the interior, especially around places where it separates. In our coarser grid, mesoscale simulations, the shear instability occurs mainly through balanced dynamics. The vorticity fragmentation during instability is not severe, and so little scale growth occurs during initial vortex emergence, which thus resembles a “roll-up” characteristic of two-dimensional wake flows. The favored selection of anticyclones is due to the asymmetry of the upstream current profile with stronger inshore anticyclonic vorticity arising from bottom drag on a slope (section 3b). Once the coherent vortices emerge, they evolve as described in the preceding paragraph. In submesoscale simulations, however, the postseparation centrifugal instability of the CUC is more violent, and the instability products are the finescale flows evident in Figs. 9, 11, 12, and 13 (right). The self-organization and upscaling pathway typically involves multiple steps of submesoscale filament and vortex amalgamation of *ζ*^{z} < 0 fragments, whose tendency for coalescence is essentially the same as in vortex pair merger and alignment. Only a modest fraction of the fluid parcels in the CUC end up in coherent mesoscale vortices after, and the evolutionary pathway to any particular Cuddy seems inherently unpredictable.

An example of a formation of a particular mesoscale anticyclone in Monterey Bay is shown in Fig. 14. Clearly visible is the separation of the CUC with its associated *ζ*^{z} < 0 near the topography. Initially, the flow is dominated by small-scale structures that have large negative *ζ*^{z}. During the merger, the magnitude of vorticity is diluted to smaller values and larger surface areas, leading to the formation of the mesoscale anticyclone in the northern part of Monterey Bay. The upscaling evolution continues beyond the sequence shown here, with an outcome illustrated by the large horizontal and vertical vortex size in Figs. 9 and 13.

## 4. Summary and discussion

We have examined the formation of long-lived subsurface mesoscale anticyclones (Cuddies) in the California Current System at a depth range of 100 to 500 m. These eddies are often generated through episodes of intense submesoscale instability in the California Undercurrent (CUC) adjacent to the continental slope. The anticyclonic dominance of these subsurface eddies is related to the predominantly northward direction of the CUC when the bottom boundary layer generates a narrow strip of highly negative vertical vorticity against the slope. The CUC follows depth contours in many places, but it also intermittently separates at particular topographic features. This separation leads to regions away from the coast with *ζ*^{z} < −*f* and Π < 0. This instigates unbalanced centrifugal instability, and the ensuing submesoscale currents exhibit an advective dynamics with turbulent cascades in kinetic energy and buoyancy apparently leading to enhanced mixing and dissipation. As a result, the extreme vorticity values are mixed and diluted with the surrounding water until they become subcritical for centrifugal instability. Afterward, a chaotic, self-organizing, axisymmetrization process leads to coherent, balanced, anticyclonic mesoscale vortices (Cuddies) that move into the ocean interior. In association with its separation, the CUC has a large lateral form drag over the topography; we argue this is the true physical basis for the horizontal viscous stress often appearing at the side boundaries that are commonly included in oceanic circulation models. We stress that the mechanics of the drag formation are quite different between these two cases and that side boundaries in the real ocean are rare or small.

A potentially delicate issue is that the details of small-scale flow and mixing are only marginally resolved in our model in spite of the multilevel grid nesting. This warrants further technical improvements (see Dewar et al. 2015). However, the simulations here with increasingly fine resolution show that the characteristics of resulting subsurface eddies are converging in both scale and rotational intensity. They suggest that the boundary current separation, instability, and subsequent formation of these anticyclones are robust phenomena.

This process can be viewed as generic for boundary slope currents moving cyclonically around a basin, generating strong *ζ*^{z}/*f* < 0 within the bottom boundary layer, subsequently separating over complex topography and giving birth to coherent anticyclonic vortices. In addition to the CUC generation of Cuddies, the process is relevant to the detected Meddies and Point Barrow anticyclones and perhaps other SCV types as well. Without direct float tracking and/or an identifying water mass anomaly in the parent boundary current, observational detection may be elusive.

By the same process as sketched in Fig. 7, boundary slope currents in the opposite direction will generate large *ζ*^{z}/*f* > 0 in the bottom boundary layer before separating. The evolutionary sequence would not include centrifugal instability as centrally as here, but it might include a different submesoscale route to loss of balance, mixing, and dissipation, namely*,* an arrested topographic (or Kelvin) wave propagating against the mean current (Molemaker et al. 2001; Dewar and Hogg 2010; Dewar et al. 2011). Other unbalanced instabilities may also be possible, and coherent cyclonic vortices may develop. These are topics for future investigation.

## Acknowledgments

This research is supported by the Office of Naval Research (N00014-08-1-0597) and the National Science Foundation (OCE-0550227 and OCE-1049134).

## APPENDIX

### Bottom Pressure Torque, Stress, and Energy Conversion

To support the discussion in section 3d, we use quasigeostrophic theory (QG) to establish several relations involving the pressure force at the bottom. QG is a subject of standard texts (Pedlosky 1987).

*υ*

_{m}> 0 in the

*z*=

*z*

_{b}(

*x*,

*y*) = −

*H*= −

*H*

_{0}+

*h*

_{b}(

*x*,

*y*), where

*H*

_{0}is the mean depth in the region (note that the elevation

*h*has the opposite sign to resting depth

*H*). In QG, pressure, horizontal velocity, buoyancy, vertical vorticity, and potential vorticity anomaly can all be expressed in terms of the streamfunction

*ψ*by

*f*and

*N*(

*z*) are Coriolis and stratification frequencies, and the subscript

*h*denotes the horizontal vector component. We decompose

*ψ*into along-flow mean, standing eddy, and transient components by

*υ*

_{m}= ∂

_{x}

*ψ*

_{m}.

*w*at the bottom and top surface are

*J*

_{h}is the horizontal Jacobian operator representing geostrophic advection.

*,*

*x*,

*y*,

*t*).

*y*-averaged,

*y*-momentum balance as

*x*,

*t*), and through averaging it loses some local effects in

*p*

_{b}=

*fρ*

_{0}

*ψ*

_{b}. We can relate

*y*-averaged bottom torque by

*y*periodicity or decay of fluctuations in the flow and/or topography. The term

*C*is a global- and time-averaged quantity.

*υ*

_{m}> 0; i.e., there is net high bottom pressure on the upstream side of the topography and vice versa. This implies

*n*,

*s*) around the topographic structure, with

*n*directed uphill and

*s*following an isobath, then

_{s}

*h*

_{b}= 0 by construction. Also, ∂

_{n}

*h*

_{b}> 0. On the left side of a topographic feature with a locally retarding form stress pattern, ∂

_{s}

*p*

_{b}< 0 and

Guided by the terms in (A3), we can compare various integral measures of *C* can be compared with the local wind and bottom-drag work and eddy-mean energy conversions. For any particular topographic structure, a dynamical solution is required to diagnose these quantities.

## REFERENCES

Acheson, D. J., 1990:

*Elementary Fluid Dynamics.*Oxford University Press, 397 pp.Barnier, B., L. Siefried, and P. Marchesiello, 1995: Thermal forcing for a global ocean circulation model using a three-year climatology of ECMWF analyses.

,*J. Mar. Syst.***6**, 363–380, doi:10.1016/0924-7963(94)00034-9.Beckmann, A., and D. Haidvogel, 1993: Numerical simulation of flow around a tall isolated seamount. Part I: Problem formulation and model accuracy.

,*J. Phys. Oceanogr.***23**, 1736–1753, doi:10.1175/1520-0485(1993)023<1736:NSOFAA>2.0.CO;2.Bower, A., L. Armi, and I. Ambar, 1995: Direct evidence of Meddy formation off the southwestern coast of Portugal.

,*Deep-Sea Res. I***42**, 1621–1630, doi:10.1016/0967-0637(95)00045-8.Bower, A., L. Armi, and I. Ambar, 1997: Lagrangian observations of Meddy formation during a Mediterranean Undercurrent seeding experiment.

,*J. Phys. Oceanogr.***27**, 2545–2575, doi:10.1175/1520-0485(1997)027<2545:LOOMFD>2.0.CO;2.Capet, X., J. McWilliams, M. Molemaker, and A. Shepetkin, 2008a: Mesoscale to submesoscale transition in the California Current System: Flow structure and eddy flux.

,*J. Phys. Oceanogr.***38**, 29–43, doi:10.1175/2007JPO3671.1.Capet, X., J. McWilliams, M. Molemaker, and A. Shepetkin, 2008b: Mesoscale to submesoscale transition in the California Current System: Frontal processes.

,*J. Phys. Oceanogr.***38**, 44–64, doi:10.1175/2007JPO3672.1.Carton, J., and B. Giese, 2008: A reanalysis of ocean climate using Simple Ocean Data Assimilation (SODA).

,*Mon. Wea. Rev.***136**, 2999–3017, doi:10.1175/2007MWR1978.1.Castelao, R. M., T. P. Mavor, J. A. Barth, and L. C. Breaker, 2006: Sea surface temperature fronts in the California Current System from geostationary satellite observations.

,*J. Geophys. Res.***111**, C09026, doi:10.1029/2006JC003541.Chelton, D., M. Schlax, and R. Samelson, 2007: Global observations of large ocean eddies.

,*Geophys. Res. Lett.***34**, L15606, doi:10.1029/2007GL030812.Chelton, D., M. Schlax, and R. Samelson, 2011: Global observations of nonlinear mesoscale eddies.

*Prog. Oceanogr.,***91,**167–216, doi:10.1016/j.pocean.2011.01.002.Collins, C., N. Gareld, T. Rago, F. Rishmiller, and E. Carter, 2000: Mean structure of the inshore countercurrent and California Undercurrent off Pt. Sur, California.

,*Deep-Sea Res. II***47**, 765–782, doi:10.1016/S0967-0645(99)00126-5.Collins, C., T. Marglina, T. Rago, and L. Ivanov, 2013: Looping RAFOS floats in the California Current System.

,*Deep-Sea Res. II***85**, 42–61, doi:10.1016/j.dsr2.2012.07.027.D’Asaro, E., 1988: Generation of submesoscale vortices: A new mechanism.

,*J. Geophys. Res.***93**, 6685–6693, doi:10.1029/JC093iC06p06685.D’Asaro, E., C. Lee, L. Rainville, R. Harcourt, and L. Thomas, 2011: Enhanced turbulence and energy dissipation at ocean fronts.

,*Science***332**, 318–322, doi:10.1126/science.1201515.Da Silva, A. M., C. Young, and S. Levitus, 1994:

*Algorithms and Procedures.*Vol. 1,*Atlas of Surface Marine Data 1994,*NOAA Atlas NESDIS 6, 74 pp.Dewar, W. K., and A. M. Hogg, 2010: Topographic inviscid dissipation of balanced flow.

,*Ocean Modell.***32**, 1–13, doi:10.1016/j.ocemod.2009.03.007.Dewar, W. K., P. Berloff, and A. Hogg, 2011: Submesoscale generation by boundaries.

,*J. Mar. Res.***69**, 501–522, doi:10.1357/002224011799849345.Dewar, W. K., M. Molemaker, and J. McWilliams, 2015: Centrifugal instability and mixing in the California Undercurrent.

, doi:10.1175/JPO-D-13-0269.1, in press.*J. Phys. Oceanogr.*Dillon, T., and D. Caldwell, 1980: The Batchelor spectrum and dissipation in the upper ocean.

,*J. Geophys. Res.***85**, 1910–1916, doi:10.1029/JC085iC04p01910.Dong, C., J. McWilliams, and A. Shchepetkin, 2007: Island wakes in deep water.

,*J. Phys. Oceanogr.***37**, 962–981, doi:10.1175/JPO3047.1.Garfield, N., C. Collins, R. Paquette, and E. Carter, 1999: Lagrangian exploration of the California Undercurrent.

,*J. Phys. Oceanogr.***29**, 560–583, doi:10.1175/1520-0485(1999)029<0560:LEOTCU>2.0.CO;2.Greenan, B., N. Oakey, and F. Dobson, 2001: Estimates of dissipation in the ocean mixed layer using a quasi-horizontal microstructure profiler.

,*J. Phys. Oceanogr.***31**, 992–1004, doi:10.1175/1520-0485(2001)031<0992:EODITO>2.0.CO;2.Haidvogel, D., J. McWilliams, and P. Gent, 1992: Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model.

,*J. Phys. Oceanogr.***22**, 882–902, doi:10.1175/1520-0485(1992)022<0882:BCSIAQ>2.0.CO;2.Haney, R., and R. Hale, 2001: Oshore propagation of eddy kinetic energy in the California Current.

,*J. Geophys. Res.***106**, 11 709–11 717, doi:10.1029/2000JC000433.Hickey, B., 1998: Coastal oceanography of western North America from the tip of Baja, California to Vancouver Island.

*The Global Coastal Ocean: Regional Studies and Syntheses,*A. R. Robinson and K. H. Brink, Ed., The Sea—Ideas and Observations on Progress in the Study of the Seas, Vol. 11, John Wiley and Sons, 345–393.Hoskins, B., 1974: The role of potential vorticity in symmetric stability and instability.

,*Quart. J. Roy. Meteor. Soc.***100**, 480–482, doi:10.1002/qj.49710042520.Huyer, A., J. Barth, P. Kosro, R. Shearman, and R. Smith, 1998: Upper-ocean water mass characteristics of the California Current, summer 1993.

,*Deep-Sea Res. II***45**, 1411–1442, doi:10.1016/S0967-0645(98)80002-7.Kiss, A., 2002: Potential vorticity “crises”, adverse pressure gradients, and western boundary current separation.

,*J. Mar. Res.***60**, 779–803, doi:10.1357/002224002321505138.Kurian, J., F. Colas, X. Capet, J. McWilliams, and D. Chelton, 2011: Eddy properties in the California Current System.

*J. Geophys. Res.,***116,**C08027, doi:10.1029/2010JC006895.Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization.

,*Rev. Geophys.***32**, 363–403, doi:10.1029/94RG01872.Lemarié, F., J. Kurian, A. Shchepetkin, M. Molemaker, F. Colas, and J. McWilliams, 2012: Are there inescapable issues prohibiting the use of terrain-following coordinates in climate models?

*Ocean Modell.,***42,**57–79, doi:10.1016/j.ocemod.2011.11.007.MacCready, P., G. Pawlak, K. A. Edwards, and R. McCabe, 2003: Form drag on ocean flows.

*Proc. 13th ‘Aha Huliko‘a Hawaiian Winter Workshop on Near Boundary Processes and their Parameterization,*Honolulu, HI, University of Hawai‘i at Mānoa, 119–130.Marchesiello, P., J. McWilliams, and A. Shchepetkin, 2003: Equilibrium structure and dynamics of the California Current System.

,*J. Phys. Oceanogr.***33**, 753–783, doi:10.1175/1520-0485(2003)33<753:ESADOT>2.0.CO;2.Mason, E., J. Molemaker, A. Shchepetkin, F. Colas, J. C. McWilliams, and P. Sangrà, 2010: Procedures for offline grid nesting in regional ocean models.

,*Ocean Modell.***35**, 1–15, doi:10.1016/j.ocemod.2010.05.007.McCabe, R., P. MacCready, and G. Pawlak, 2006: Form drag due to flow separation at a headland.

,*J. Phys. Oceanogr.***36**, 2136–2152, doi:10.1175/JPO2966.1.McWilliams, J. C., 1984: The emergence of isolated, coherent vortices in turbulent flow.

,*J. Fluid Mech.***146**, 21–43, doi:10.1017/S0022112084001750.McWilliams, J. C., 1985: Submesoscale, coherent vortices in the ocean.

,*Rev. Geophys.***23**, 165–182, doi:10.1029/RG023i002p00165.McWilliams, J. C., 1988: Vortex generation through balanced adjustment.

,*J. Phys. Oceanogr.***18**, 1178–1192, doi:10.1175/1520-0485(1988)018<1178:VGTBA>2.0.CO;2.McWilliams, J. C., J. Weiss, and I. Yavneh, 1994: Anisotropy and coherent structures in planetary turbulence.

,*Science***264**, 410–413, doi:10.1126/science.264.5157.410.McWilliams, J. C., M. J. Molemaker, and I. Yavneh, 2004: Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current.

,*Phys. Fluids***16**, 3720–3725, doi:10.1063/1.1785132.Molemaker, M. J., and J. C. McWilliams, 2010: Local balance and cross-scale flux of available potential energy.

,*J. Fluid Mech.***645**, 295–314, doi:10.1017/S0022112009992643.Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2001: Instability and equilibration of centrifugally-stable stratified Taylor-Couette flow.

,*Phys. Rev. Lett.***86**, 5270–5273, doi:10.1103/PhysRevLett.86.5270.Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2005: Baroclinic instability and loss of balance.

,*J. Phys. Oceanogr.***35**, 1505–1517, doi:10.1175/JPO2770.1.Molemaker, M. J., J. C. McWilliams, and X. Capet, 2010: Balanced and unbalanced routes to dissipation in equilibrated Eady flow.

,*J. Fluid Mech.***654**, 35–63, doi:10.1017/S0022112009993272.Pascual, A., F. Faugre, G. Larnicol, and P. L. Traon, 2006: Improved description of the ocean mesoscale variability by combining four satellite altimeters.

,*Geophys. Res. Lett.***33**, L02611, doi:10.1029/2005GL024633.Pedlosky, J., 1987:

*Geophysical Fluid Dynamics.*2nd ed. Springer-Verlag, 710 pp.Pelland, N., C. Eriksen, and C. Lee, 2013: Subthermocline eddies over the Washington continental slope as observed by seagliders, 2003–09.

,*J. Phys. Oceanogr.***43**, 2025–2053, doi:10.1175/JPO-D-12-086.1.Penven, P., L. Debreu, P. Marchesiello, and J. McWilliams, 2006: Application of the ROMS embedding procedure for the central California upwelling system.

,*Ocean Modell.***12**, 157–187, doi:10.1016/j.ocemod.2005.05.002.Pierce, S. D., R. L. Smith, P. M. Kosro, J. A. Barth, and C. D. Wilson, 2000: Continuity of the poleward undercurrent along the eastern boundary of the mid-latitude North Pacific.

,*Deep-Sea Res. II***47**, 811–829, doi:10.1016/S0967-0645(99)00128-9.Rio, M.-H., and F. Hernandez, 2004: A mean dynamic topography computed over the world ocean from altimetry, in situ measurements, and a geoid model.

,*J. Geophys. Res.***109**, C12032, doi:10.1029/2003JC002226.Risien, C., and D. Chelton, 2008: A global climatology of surface wind and wind stress fields from eight years of QuikSCAT scatterometer data.

,*J. Phys. Oceanogr.***38**, 2379–2413, doi:10.1175/2008JPO3881.1.Rudnick, D., 2001: On the skewness of vorticity in the upper ocean.

,*Geophys. Res. Lett.***28**, 2045–2048, doi:10.1029/2000GL012265.Shchepetkin, A. F., and J. C. McWilliams, 2005: The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model.

,*Ocean Modell.***9**, 347–404, doi:10.1016/j.ocemod.2004.08.002.Shchepetkin, A. F., and J. C. McWilliams, 2009: Correction and commentary for “Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system” by Haidvogel et al., J. Comput. Phys. 227, pp. 3595–3624.

*J. Comput. Phys.,***228,**8985–9000, doi:10.1016/j.jcp.2009.09.002.Smith, W., and D. Sandwell, 1997: Global seafloor topography from satellite altimetry and ship depth soundings.

,*Science***277**, 1957–1962, doi:10.1126/science.277.5334.1956.Song, Y., and D. Wright, 1998: A general pressure gradient formulation for ocean models. Part II: Energy, momentum, and bottom torque consistency.

,*Mon. Wea. Rev.***126**, 3231–3247, doi:10.1175/1520-0493(1998)126<3231:AGPGFF>2.0.CO;2.Stegmann, P., and F. Schwing, 2007: Demographics of mesoscale eddies in the California Current.

,*Geophys. Res. Lett.***34**, L14602, doi:10.1029/2007GL029504.Swenson, M., and P. Niiler, 1996: Statistical analysis of the surface circulation of the California Current.

,*J. Geophys. Res.***101**, 22 631–22 645, doi:10.1029/96JC02008.Todd, R., D. Rudnick, M. Mazloff, R. Davis, and B. Cornuelle, 2011: Poleward flows in the southern California Current System: Glider observations and numerical simulation.

,*J. Geophys. Res.***116**, C02026, doi:10.1029/2010JC006536.Yavneh, I., J. C. McWilliams, and M. J. Molemaker, 2001: Non-axisymmetric instability of centrifugally-stable stratified Taylor–Couette flow.

,*J. Fluid Mech.***448**, 1–21, doi:10.1017/S0022112001005109.

^{1}

Submesoscale is defined as smaller than mesoscale (i.e., smaller in the horizontal than the first baroclinic deformation radius and in the vertical than the first baroclinic mode), yet large enough to be significantly influenced by Earth’s rotation and stable density stratification. In rough terms, this means scales of 10 km or less horizontally and about 100 m vertically. This scale range overlaps with inertia–gravity waves, whose propagation dynamics are different from the more advective dynamics of submesoscale currents.

^{3}

This cross-shore *υ* profile has obvious differences relative to the longer time-mean profile in the coarser-resolution simulation in Fig. 4, in particular the stronger surface southward currents. This difference is modestly influenced by the location of the section and the grid resolution, but it is mostly a result of intrinsic flow variability.

^{4}

Notice that typical values are about 25 Pa. This is the equivalent of 0.25 mb of surface atmospheric pressure variation or 0.25 cm in hydrostatic sea surface height.