Submesoscale Instability and Generation of Mesoscale Anticyclones near a Separation of the California Undercurrent

M. Jeroen Molemaker Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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James C. McWilliams Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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William K. Dewar Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee, Florida

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Abstract

The California Undercurrent (CUC) flows poleward mostly along the continental slope. It develops a narrow strip of large negative vertical vorticity through the turbulent boundary layer and bottom stress. In several downstream locations, the current separates, aided by topographic curvature and flow inertia, in particular near Point Sur Ridge, south of Monterey Bay. When this happens the high-vorticity strip undergoes rapid instability that appears to be mesoscale in “eddy-resolving” simulations but is substantially submesoscale with a finer computational grid. The negative relative vorticity in the CUC is larger than the background rotation f, and Ertel potential vorticity is negative. This instigates ageostrophic centrifugal instability. The submesoscale turbulence is partly unbalanced, has elevated local dissipation and mixing, and leads to dilution of the extreme vorticity values. Farther downstream, the submesoscale activity abates, and the remaining eddy motions exhibit an upscale organization into the mesoscale, resulting in long-lived coherent anticyclones in the depth range of 100–500 m (previously called Cuddies) that move into the gyre interior in a generally southwestward direction. In addition to the energy and mixing effects of the postseparation instability, there is are significant local topographic form stress and bottom torque that retard the CUC and steer the mean current pathway.

Corresponding author address: M. J. Molemaker, IGPP, UCLA, 405 Hilgard Ave., Los Angeles, CA 90095-1567. E-mail: nmolem@atmos.ucla.edu

Abstract

The California Undercurrent (CUC) flows poleward mostly along the continental slope. It develops a narrow strip of large negative vertical vorticity through the turbulent boundary layer and bottom stress. In several downstream locations, the current separates, aided by topographic curvature and flow inertia, in particular near Point Sur Ridge, south of Monterey Bay. When this happens the high-vorticity strip undergoes rapid instability that appears to be mesoscale in “eddy-resolving” simulations but is substantially submesoscale with a finer computational grid. The negative relative vorticity in the CUC is larger than the background rotation f, and Ertel potential vorticity is negative. This instigates ageostrophic centrifugal instability. The submesoscale turbulence is partly unbalanced, has elevated local dissipation and mixing, and leads to dilution of the extreme vorticity values. Farther downstream, the submesoscale activity abates, and the remaining eddy motions exhibit an upscale organization into the mesoscale, resulting in long-lived coherent anticyclones in the depth range of 100–500 m (previously called Cuddies) that move into the gyre interior in a generally southwestward direction. In addition to the energy and mixing effects of the postseparation instability, there is are significant local topographic form stress and bottom torque that retard the CUC and steer the mean current pathway.

Corresponding author address: M. J. Molemaker, IGPP, UCLA, 405 Hilgard Ave., Los Angeles, CA 90095-1567. E-mail: nmolem@atmos.ucla.edu

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 (θS) 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 ζz, 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.

This paper reports on computational simulations of the CCS using grid nesting focused on CUC eddy generation. They indicate a scenario where the CUC develops a narrow strip of strong anticyclonic vertical vorticity, ζz < 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., ζz < −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
e1
where u is the velocity, is the 3D vorticity, and b is the buoyancy (approximately −g/ρ0 times the potential density with g the gravitational acceleration and ρ0 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 ζz + 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 dataset2 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.

Fig. 1.
Fig. 1.

Snapshot of SST on 15 Jul in a climatological simulation of the Pacific basin with a horizontal grid resolution of dx ≤ 12.5 km. Indicated by the blue line is the boundary of the first nested grid (dx = 4 km) near the U.S. West Coast.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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.

Fig. 2.
Fig. 2.

Composite snapshot of SST for 15 Sep of a climatological simulation of the U.S. West Coast region. The compositing is done by displaying the SST field from the finest-scale grid available at each location. Shown are solutions at grid resolutions of dx = 4 km, dx = 1.5 km, and dx = 0.5 km, respectively, with nesting boundaries indicated with solid black lines. The outermost solution is forced at its side boundaries by the monthly averaged solution in the Pacific basin. The finest nested subdomain around Monterey Bay (note the shoreline indentation) has a resolution of dx = 166 m; it is indicated with a purple boundary line, but its SST field is not displayed here.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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.

Fig. 3.
Fig. 3.

Horizontal structure of the CUC in (left) alongshore velocity υ(x, y) and (right) salinity S(x, y) at 150-m depth. The fields are a summer mean over 3 yr of simulation in the nested subdomain with a dx = 1.5 km.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

Fig. 4.
Fig. 4.

Cross-shore section of alongshore velocity υ(x, z) off Point Sur (36.15°N). Black lines are mean depths for isopycnals with values starting at σ = 25 kg m−3 and increasing with σ = 0.5 kg m−3. This is a summer mean over 3 yr in the subdomain with dx = 1.5 km. This section is a longer version of the sections in Fig. 8. The exact location of these sections is indicated in Fig. 9.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 ζz(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 ζz/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 ζz < 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).

Fig. 5.
Fig. 5.

Snapshots of ζz(x, y)/f at 150-m depth at the end of summer (26 Sep) in simulations with different grid resolution: (left) dx = 4 km, (middle) dx = 1.5 km, and (right) dx = 0.5 km.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

The peak vorticity amplitude of the mesoscale, offshore anticyclones reaches ζz ≈ −0.4f. 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 ζz ≈ −0.7f. As discussed in section 1, a known centrifugal stability threshold for anticyclonic eddies is Π = 0 or ζz = −f. The absence of ζz < −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 ζz(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.

Fig. 6.
Fig. 6.

PDFs of the fields of ζ/f that are shown in Fig. 5. Blue, red, and green lines shown are PDFs for the field computed at dx = 4 km, dx = 1.5 km, and dx = 0.5 km, respectively.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

b. Production of negative vorticity along the slope

We hypothesize that the offshore-dominant mesoscale anticyclonic vortices originate in the CUC near the boundary. This is plausible if negative ζz 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 ζz < 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, ζz, as illustrated in Fig. 7 for a flow configuration like the CUC. The width of the horizontal shear layer can be estimated as
e2
where s = dzb(x)/dx is the slope of the bottom boundary, and Δx 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 ζz magnitude is Vx. 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 , where τ is bottom stress, Cd is a bottom drag coefficient, and υb 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.
Fig. 7.
Fig. 7.

Sketch of the alongshore velocity structure υ(x, z) in a vertical turbulent boundary layer over a slope with s = dzb/dx, which also projects as a horizontal boundary layer with ζz ≈ ∂xυ.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 ζz/f. Because the CUC flows north and the boundary is on its east side, the ζz produced by the boundary layer on the slope is negative. Upstream of Point Sur, extreme values of negative vorticity reach down to −10f, 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 ζz/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 ζz in the boundary layer is −10−3 s−1, that is, O(−10f).

Fig. 8.
Fig. 8.

Vertical section normal to the coast at about 36°N, south of Point Sur for summer-mean υ (upper) and ζz/f (lower), in the nested subdomain with dx = 166 m. The exact location of this section is indicated in Fig. 9 with a magenta line.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 ζz/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 ζz. Around the point of separation, an area of interspersed negative and positive ζz(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 ∂zυ 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 ζz 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.

Fig. 9.
Fig. 9.

(left) Normalized relative vorticity ζz/f and (right) potential temperature θ (°C) in a horizontal plane at 150-m depth from the nested subdomain with dx = 166 m. These are time averaged over 12 h to remove some of the internal gravity waves. Notice the CUC separation near Point Sur, the submesoscale activity immediately downstream, and the mesoscale anticyclone that is in an early phase of formation to the northwest of Point Sur. The magenta line toward the southeastern side of the figure indicates the location of the vertical sections of Fig. 8.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

d. Bottom pressure torque and form stress

Bottom pressure, pb = p[x, y, zb(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 (m2) is a net force F (N) in a designated horizontal direction , defined by
e3
The form stress (m2 s−2), multiplied by ρ0A, is a force F that contributes to the force in the direction of acting on the volume integral of (McCabe et al. 2006). The role of form stress in, for example, airplane flight is well known, but its role in particular oceanic currents is more subtle. As the dynamic part of the bottom pressure balances inertia to force flow around an obstacle, a positive pressure anomaly will be present on the upstream side of the obstacle, together with a negative bottom pressure anomaly on the downstream side when the current continues to follow bottom contour lines. The positive and negative pressure anomalies are on opposite-facing slopes, both will contribute to the net force exerted by the obstacle, following (3). For isolated obstacles, this characterization works well (see also MacCready et al. 2003). For flow along a continental margin in a domain with open boundaries, as in the current study, it is not trivial to separate the different contributions of the bottom pressure and to interpret the associated net force. These issues are further explained in the appendix within an idealized framework of quasigeostrophic dynamics, where relations are derived among the local bottom pressure and bottom torque and integrated bottom stress and energy conversion with the large-scale flow.
To investigate the role of bottom pressure in the integral balance of the CCS, and more specifically around the Point Sur headland where it separates, we devise a diagnostic procedure for evaluating (3). Since the dynamic pressure anomaly is small, relative to the static pressure, special care must be taken to isolate it. We make use of the relation between bottom pressure anomalies and bottom pressure torque :
e4
the Jacobian of the bottom pressure and the resting depth 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 H0 using
e5
The quantities (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, south of the offshore nose of Sur Ridge, at the depth of the undercurrent. This acts to turn the CUC around the ridge as it flows poleward. Downstream of this pattern is a smaller-amplitude pattern of positive , acting against the inertial separation tendency of centrifugal force along the curved flow pathway. There are small-scale dipole patterns of both parities in straddling the submarine canyons north and west of the ridge; these act to assist the mean flow to follow levels of constant depth without flow separation, consistent with the discussion above.

Fig. 10.
Fig. 10.

Interaction of the California Undercurrent with the topography at the Point Sur headland in the nested subdomain with dx = 166 m. (left) The bottom pressure torque (N m−3). A large negative torque is shown upstream (south) of the undersea headland where the undercurrent is forced westward around the ridge obstacle. (right) The local bottom pressure anomaly (N m−2 = Pa) computed from . The force needed for the undercurrent to flow around the ridge is visible in a positive pressure anomaly on the upstream side of the headland. The absence of a corresponding negative pressure anomaly on the downstream side is consistent with the undercurrent separating from the coast at the headland.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 pb in the right panel of Fig. 10. These values are large compared to typical values of the wind stress over the CCS. More important than the total retarding force acting on the undercurrent is the result of separating the undercurrent from the shelf break. Because the bottom does not move, no work can be done by the bottom pressure force or the related bottom torque; that is, it provides no energy tendency when integrated over the domain. However, it does induce an energy conversion C between the time-flow and along-flow mean current υm in the direction of and the time-mean standing eddies, which is proportional to (see the appendix). With υm > 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 = ∂xu + ∂yυ. Flows that are dominated by a geostrophic force balance are expected to have small values of δ relative to the vertical vorticity ζz; 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 ∂zw = −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.

Fig. 11.
Fig. 11.

Ageostrophic variance and energy dissipation downstream of the separation of the California Undercurrent at the Point Sur headland at a depth of z = 50 m. (left) Normalized variance of horizontal divergence δ/f, showing areas with pronounced unbalance and sustained mixing. (right) Time-mean energy dissipation (m2 s−3), showing areas downstream of the separation point with enhanced levels of local energy dissipation.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 m2 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 ζz/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.

Fig. 12.
Fig. 12.

Instantaneous distribution of Π in a horizontal plane at 150-m depth in the subdomain with dx = 166 m. Negative values are shown in blue colors.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 ζz 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).

Fig. 13.
Fig. 13.

Cross-shore vertical section at 36.2°N of ζz/f. The right side of the section is close to the separation point, and the left side intersects the same mesoscale anticyclone as in Fig. 9. The field is from the subdomain with dx = 166 m, and it is averaged over 12 h to remove some of the internal gravity waves.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 ζz < 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 ζz < 0 near the topography. Initially, the flow is dominated by small-scale structures that have large negative ζz. 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.

Fig. 14.
Fig. 14.

Sequence of snapshots of ζz/f at 150-m depth showing merging of small-scale negative vorticity elements into a mesoscale subsurface anticyclone. Frames are 7 days apart starting at the upper-left panel and proceed according to the labels. The color bar is the same as in Fig. 9, and the plotting area is as in Fig. 11. The field is obtained from the subdomain with dx = 166 m.

Citation: Journal of Physical Oceanography 45, 3; 10.1175/JPO-D-13-0225.1

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 ζz < −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 ζz/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 ζz/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).

Consider a broad mean flow υm > 0 in the direction above a bottom located at z = zb(x, y) = −H = −H0 + hb(x, y), where H0 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
ea1
where 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
ea2
where the brackets denote a spatial average over the coordinate indicated by the superscript, and the overbar denotes a time average. From (A1), υm = ∂xψm.
Topographic effects arise through the vertical kinematic and stress boundary conditions conveyed to the interior vorticity and potential vorticity balances through unresolved Ekman boundary layers. In QG, the near-boundary “pumping” relations on w at the bottom and top surface are
ea3
The term is the viscous turbulent bottom stress, the surface wind stress, and Jh is the horizontal Jacobian operator representing geostrophic advection.
In a depth-averaged vertical vorticity balance, the topographic term enters as a bottom torque ; that is,
ea4
The ellipses here and below indicate other contributions beside the topographic one (including the terms). The value is a local quantity in (x, y, t).
The form stress in (3) is only meaningfully defined in an along-flow average. With , it enters the depth-integrated, y-averaged, y-momentum balance as
ea5
It is a semilocal quantity in (x, t), and through averaging it loses some local effects in . It is recognizable as a bottom form stress by the QG relation with dynamic pressure at the bottom, pb = 0ψb. We can relate to the y-averaged bottom torque by
ea6
if we assume benign (i.e., noncontributing) boundary conditions in the along-flow direction, for example, y periodicity or decay of fluctuations in the flow and/or topography. The term is of greater interest when lateral boundary effects are not important to the momentum balance. In time-averaged balances, the relevant form stress involves only the standing eddy components of the flow and topography:
ea7
The depth-integrated, area-averaged QG energy is defined by
ea8
The QG energy budget and its balance relation have no contribution from the bottom topography. However, topography does provide a conversion between the energies of the mean and standing eddy components. In particular, in a time average,
ea9
where we continue to ignore lateral boundary terms. The right-side conversion term C is a global- and time-averaged quantity.
If the form stress acts to retard the mean flow in (A5), then when υm > 0; i.e., there is net high bottom pressure on the upstream side of the topography and vice versa. This implies ; that is, there is energy conversion from the mean flow to the mean standing eddies. From (A3) and (A4), the vertical velocity tends to be locally opposite in sign to the bottom torque. Taking a downstream average and using (A5)(A6),
ea10
Thus, there is an average secondary circulation associated with the form stress. If is negative and peaks somewhere over an isolated topographic structure, then there is upward flow on the left side of the topography facing downstream and downward flow on the right side. If we define local curvilinear coordinates (n, s) around the topographic structure, with n directed uphill and s following an isobath, then
ea11
because ∂shb = 0 by construction. Also, ∂nhb > 0. On the left side of a topographic feature with a locally retarding form stress pattern, ∂spb < 0 and . Thus, there is an anticyclonic barotropic vorticity tendency that acts to curve the flow around the feature against any centrifugal tendency for separation. On the right side, the tendency is cyclonic, hence again acting to curve the flow around the topography. For a submarine ridge, as offshore of Point Sur, only the left-side pathway is available.

Guided by the terms in (A3), we can compare various integral measures of and with analogous measures of the surface wind and bottom viscous stress and curl, and 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.

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  • 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, 119130.

  • Marchesiello, P., J. McWilliams, and A. Shchepetkin, 2003: Equilibrium structure and dynamics of the California Current System. J. Phys. Oceanogr., 33, 753783, doi:10.1175/1520-0485(2003)33<753:ESADOT>2.0.CO;2.

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  • 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, 115, doi:10.1016/j.ocemod.2010.05.007.

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  • McCabe, R., P. MacCready, and G. Pawlak, 2006: Form drag due to flow separation at a headland. J. Phys. Oceanogr., 36, 21362152, doi:10.1175/JPO2966.1.

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    • Export Citation
  • McWilliams, J. C., 1984: The emergence of isolated, coherent vortices in turbulent flow. J. Fluid Mech., 146, 2143, doi:10.1017/S0022112084001750.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 1985: Submesoscale, coherent vortices in the ocean. Rev. Geophys., 23, 165182, doi:10.1029/RG023i002p00165.

  • McWilliams, J. C., 1988: Vortex generation through balanced adjustment. J. Phys. Oceanogr., 18, 11781192, doi:10.1175/1520-0485(1988)018<1178:VGTBA>2.0.CO;2.

    • Search Google Scholar
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  • McWilliams, J. C., J. Weiss, and I. Yavneh, 1994: Anisotropy and coherent structures in planetary turbulence. Science, 264, 410413, doi:10.1126/science.264.5157.410.

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    • Export Citation
  • McWilliams, J. C., M. J. Molemaker, and I. Yavneh, 2004: Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current. Phys. Fluids, 16, 37203725, doi:10.1063/1.1785132.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., and J. C. McWilliams, 2010: Local balance and cross-scale flux of available potential energy. J. Fluid Mech., 645, 295314, doi:10.1017/S0022112009992643.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2001: Instability and equilibration of centrifugally-stable stratified Taylor-Couette flow. Phys. Rev. Lett., 86, 52705273, doi:10.1103/PhysRevLett.86.5270.

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  • Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2005: Baroclinic instability and loss of balance. J. Phys. Oceanogr., 35, 15051517, doi:10.1175/JPO2770.1.

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    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and X. Capet, 2010: Balanced and unbalanced routes to dissipation in equilibrated Eady flow. J. Fluid Mech., 654, 3563, doi:10.1017/S0022112009993272.

    • Search Google Scholar
    • Export Citation
  • 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.

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  • 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, 20252053, doi:10.1175/JPO-D-12-086.1.

    • Search Google Scholar
    • Export Citation
  • 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, 157187, doi:10.1016/j.ocemod.2005.05.002.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • 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.

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  • 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, 23792413, doi:10.1175/2008JPO3881.1.

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  • Rudnick, D., 2001: On the skewness of vorticity in the upper ocean. Geophys. Res. Lett., 28, 20452048, 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, 347404, doi:10.1016/j.ocemod.2004.08.002.

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  • 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.

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  • Smith, W., and D. Sandwell, 1997: Global seafloor topography from satellite altimetry and ship depth soundings. Science, 277, 19571962, doi:10.1126/science.277.5334.1956.

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    • Export Citation
  • 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.

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  • Yavneh, I., J. C. McWilliams, and M. J. Molemaker, 2001: Non-axisymmetric instability of centrifugally-stable stratified Taylor–Couette flow. J. Fluid Mech., 448, 121, doi:10.1017/S0022112001005109.

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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.

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  • 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, 115, doi:10.1016/j.ocemod.2010.05.007.

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    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 1985: Submesoscale, coherent vortices in the ocean. Rev. Geophys., 23, 165182, doi:10.1029/RG023i002p00165.

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    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., J. Weiss, and I. Yavneh, 1994: Anisotropy and coherent structures in planetary turbulence. Science, 264, 410413, doi:10.1126/science.264.5157.410.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., M. J. Molemaker, and I. Yavneh, 2004: Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current. Phys. Fluids, 16, 37203725, doi:10.1063/1.1785132.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., and J. C. McWilliams, 2010: Local balance and cross-scale flux of available potential energy. J. Fluid Mech., 645, 295314, doi:10.1017/S0022112009992643.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2001: Instability and equilibration of centrifugally-stable stratified Taylor-Couette flow. Phys. Rev. Lett., 86, 52705273, doi:10.1103/PhysRevLett.86.5270.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2005: Baroclinic instability and loss of balance. J. Phys. Oceanogr., 35, 15051517, doi:10.1175/JPO2770.1.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and X. Capet, 2010: Balanced and unbalanced routes to dissipation in equilibrated Eady flow. J. Fluid Mech., 654, 3563, doi:10.1017/S0022112009993272.

    • Search Google Scholar
    • Export Citation
  • 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.

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    • Export Citation
  • 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, 20252053, doi:10.1175/JPO-D-12-086.1.

    • Search Google Scholar
    • Export Citation
  • 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, 157187, doi:10.1016/j.ocemod.2005.05.002.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • 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, 23792413, doi:10.1175/2008JPO3881.1.

    • Search Google Scholar
    • Export Citation
  • Rudnick, D., 2001: On the skewness of vorticity in the upper ocean. Geophys. Res. Lett., 28, 20452048, 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, 347404, doi:10.1016/j.ocemod.2004.08.002.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • Smith, W., and D. Sandwell, 1997: Global seafloor topography from satellite altimetry and ship depth soundings. Science, 277, 19571962, doi:10.1126/science.277.5334.1956.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • Stegmann, P., and F. Schwing, 2007: Demographics of mesoscale eddies in the California Current. Geophys. Res. Lett., 34, L14602, doi:10.1029/2007GL029504.

    • Search Google Scholar
    • Export Citation
  • Swenson, M., and P. Niiler, 1996: Statistical analysis of the surface circulation of the California Current. J. Geophys. Res., 101, 22 63122 645, doi:10.1029/9