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In computational simulations of an idealized subtropical eastern boundary upwelling current system, similar to the California Current, a submesoscale transition occurs in the eddy variability as the horizontal grid scale is reduced to O(1) km. This first paper (in a series of three) describes the transition in terms of the emergent flow structure and the associated time-averaged eddy fluxes. In addition to the mesoscale eddies that arise from a primary instability of the alongshore, wind-driven currents, significant energy is transferred into submesoscale fronts and vortices in the upper ocean. The submesoscale arises through surface frontogenesis growing off upwelled cold filaments that are pulled offshore and strained in between the mesoscale eddy centers. In turn, some submesoscale fronts become unstable and develop submesoscale meanders and fragment into roll-up vortices. Associated with this phenomenon are a large vertical vorticity and Rossby number, a large vertical velocity, relatively flat horizontal spectra (contrary to the prevailing view of mesoscale dynamics), a large vertical buoyancy flux acting to restratify the upper ocean, a submesoscale energy conversion from potential to kinetic, a significant spatial and temporal intermittency in the upper ocean, and material exchanges between the surface boundary layer and pycnocline. Comparison with available observations indicates that submesoscale fronts and instabilities occur widely in the upper ocean, with characteristics similar to the simulations.

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This paper addresses the structure and dynamical mechanisms of regional and mesoscale physical variability in the subtropical northeast Pacific Ocean using the Regional Oceanic Modeling System (ROMS). The model is configured with a U.S. West Coast domain that spans the California Current System (CCS) with a mesoscale horizontal resolution up to as fine as 3.5 km. Its mean-seasonal forcing is by momentum, heat, and water fluxes at the surface and adaptive nudging to gyre-scale fields at the open water boundaries. Its equilibrium solutions show realistic mean and seasonal states and vigorous mesoscale eddies, fronts, and filaments. The level of eddy kinetic energy (EKE) in the model is comparable to drifter and altimeter estimates in the solutions with sufficiently fine resolution. Because the model lacks nonseasonal transient forcing, the authors conclude that the dominant mesoscale variability in the CCS is intrinsic rather than transiently forced. The primary eddy generation mechanism is the baroclinic instability of upwelling, alongshore currents. There is progressive movement of meanseasonal currents and eddy energy offshore and downward into the oceanic interior in an annually recurrent cycle. The associated offshore eddy heat fluxes provide the principal balance against nearshore cooling by mean Ekman transport and upwelling. The currents are highly nonuniform along the coast, with important influences by capes and ridges in both maintaining mean standing eddies and launching transient filaments and fronts.

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[1] Discretization of the pressure-gradient force is a long-standing problem in terrainfollowing (or s) coordinate oceanic modeling. When the isosurfaces of the vertical coordinate are not aligned with either geopotential surfaces or isopycnals, the horizontal pressure gradient consists of two large terms that tend to cancel; the associated pressuregradient error stems from interference of the discretization errors of these terms. The situation is further complicated by the nonorthogonality of the coordinate system and by the common practice of using highly nonuniform stretching for the vertical grids, which, unless special precautions are taken, causes both a loss of discretization accuracy overall and an increase in interference of the component errors. In the present study, we design a pressure-gradient algorithm that achieves more accurate hydrostatic balance between the two components and does not lose as much accuracy with nonuniform vertical grids at relatively coarse resolution. This algorithm is based on the reconstruction of the density field and the physical z coordinate as continuous functions of transformed coordinates with subsequent analytical integration to compute the pressure-gradient force. This approach allows not only a formally higher order of accuracy, but it also retains and expands several important symmetries of the original second-order scheme to high orders [Mellor et al., 1994;Song, 1998], which is used as a prototype. It also has built-in monotonicity constraining algorithm that prevents appearance of spurious oscillations of polynomial interpolant and, consequently, insures numerical stability and robustness of the model under the conditions of nonsmooth density field and coarse grid resolution. We further incorporate an alternative method of dealing with compressibility of seawater, which escapes pressure-gradient errors associated with interference of the nonlinear nature of equation of state and difficulties to achieve accurate polynomial fits of resultant in situ density profiles. In doing so, we generalized the monotonicity constraint to guarantee nonnegative physical stratification of the reconstructed density profile in the case of compressible equation of state. To verify the new method, we perform traditional idealized (Seamount) and realistic test problems.

This is the second of three papers investigating the regime transition that occurs in numerical simulations for an idealized, equilibrium, subtropical, eastern boundary, upwelling current system similar to the California Current. The emergent upper-ocean submesoscale fronts are analyzed from phenomenological and dynamical perspectives, using a combination of composite averaging and separation of distinctive subregions of the flow. The initiating dynamical process for the transition is near-surface frontogenesis. The frontal behavior is similar to both observed meteorological surface fronts and solutions of the approximate dynamical model called surface dynamics (i.e., uniform interior potential vorticity q and diagnostic force balance) in the intensification of surface density gradients and secondary circulations in response to a mesoscale strain field. However, there are significant behavioral differences compared to the surfacedynamics model. Wind stress acts on fronts through nonlinear Ekman transport and creation and destruction of potential vorticity. The strain-induced frontogenesis is disrupted by vigorous submesoscale frontal instabilities that in turn lead to secondary frontogenesis events, submesoscale vortices, and excitation of even smaller-scale flows. Intermittent, submesoscale breakdown of geostrophic and gradient-wind force balance occurs during the intense frontogenesis and frontal-instability events.