Zonostrophic instability leads to the spontaneous emergence of zonal jets on a b plane from a jetless basicstate flow that is damped by bottom drag and driven by a random body force. Decomposing the barotropic vorticity equation into the zonal mean and eddy equations, and neglecting the eddy-eddy interactions, defines the quasilinear (QL) system. Numerical solution of the QL system shows zonal jets with length scales comparable to jets obtained by solving the nonlinear (NL) system.Starting with the QL system, one can construct a deterministic equation for the evolution of the two-point single-time correlation function of the vorticity, from which one can obtain the Reynolds stress that drives the zonal mean flow. This deterministic system has an exact nonlinear solution, which is an isotropic and homogenous eddy field with no jets. The authors characterize the linear stability of this jetless solution by calculating the critical stability curve in the parameter space and successfully comparing this analytic result with numerical solutions of the QL system. But the critical drag required for the onset of NL zonostrophic instability is sometimes a factor of 6 smaller than that for QL zonostrophic instability.Near the critical stability curve, the jet scale predicted by linear stability theory agrees with that obtained via QL numerics. But on reducing the drag, the emerging QL jets agree with the linear stability prediction at only short times. Subsequently jets merge with their neighbors until the flow matures into a state with jets that are significantly broader than the linear prediction but have spacing similar to NL jets.
Oceanic surface submesoscale currents are characterized by anisotropic fronts and filaments with widths from 100 m to a few kilometers; an O(1) Rossby number; and large magnitudes of lateral buoyancy and velocity gradients, cyclonic vorticity, and convergence. We derive an asymptotic model of submeoscale frontogenesis—the rate of sharpening of submesoscale gradients—and show that in contrast with “classical” deformation frontogenesis, the near-surface convergent motions, which are associated with the ageostrophic secondary circulation, determine the gradient sharpening rates. Analytical solutions for the inviscid Lagrangian evolution of the gradient fields in the proposed asymptotic regime are provided, and emphasize the importance of ageostrophic motions in governing frontal evolution. These analytical solutions are further used to derive a scaling relation for the vertical buoyancy fluxes that accompany the gradient sharpening process. Realistic numerical simulations and drifter observations in the northern Gulf of Mexico during winter confirm the applicability of the asymptotic model to strong frontogenesis. Careful analysis of the numerical simulations and field measurements demonstrates that a subtle balance between boundary layer turbulence, pressure, and Coriolis effects (e.g., turbulent thermal wind; Gula et al. 2014) leads to the generation of the surface convergent motions that drive frontogenesis in this region. Because the asymptotic model makes no assumptions about the physical mechanisms that initiate the convergent frontogenetic motions, it is generic for submesoscale frontogenesis of O(1) Rossby number flows.
Current-topography interactions in the ocean give rise to eddies spanning a wide range of spatial and temporal scales. Latest modeling efforts indicate that coastal and underwater topography are important generation sites for submesoscale coherent vortices (SCVs), characterized by horizontal scales of (0.1 – 10) km. Using idealized, submesoscale and BBL-resolving simulations and adopting an integrated vorticity balance formulation, we quantify precisely the role of bottom boundary layers (BBLs) in the vorticity generation process. In particular, we show that vorticity generation on topographic slopes is attributable primarily to the torque exerted by the vertical divergence of stress at the bottom. We refer to this as the Bottom Stress Divergence Torque (BSDT). BSDT is a fundamentally nonconservative torque that appears as a source term in the integrated vorticity budget and is to be distinguished from the more familiar Bottom Stress Curl (BSC). It is closely connected to the bottom pressure torque (BPT) via the horizontal momentum balance at the bottom and is in fact shown to be the dominant component of BPT in solutions with a well-resolved BBL. This suggests an interpretation of BPT as the sum of a viscous, vorticity generating component (BSDT) and an inviscid, ‘flow-turning ’ component. Companion simulations without bottom drag illustrate that although vorticity generation can still occur through the inviscid mechanisms of vortex stretching and tilting, the wake eddies tend to have weaker circulation, be substantially less energetic, and have smaller spatial scales.
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