Effect of subgrid-scale mixing on the evolution of forced submesoscale instabilities

Abstract

We study the effect of subgrid-scale (SGS) mixing on the evolution of a density front initially in thermal-wind balance with a meridional density gradient and forced by downfront surface winds. The horizontal size of the model domain (O(100km)) is large enough to contain mesoscale eddies while the horizontal grid resolution (500m) is fine enough to resolve submesoscale eddies. The twin goals of this study are: (i) to determine what is a realistic level of SGS dissipation; and (ii) to explore the sensitivity of the resolved-scale dynamics to the SGS dissipation. To this end, we effect different levels of SGS dissipation using two SGS models: (i) constant lateral SGS viscosities (1m2s−1 and 5m2s−1) and an analytically prescribed vertical SGS viscosity; and (ii) an existing anisotropic Smagorinsky model (ASM) developed for anisotropic grids with large aspect ratios between the horizontal and the vertical directions. An analysis of the eddy kinetic energy (EKE) budgets shows the surface stress boundary condition constrains all simulations to yield realistic values of SGS dissipation in a near-surface layer that is shear-driven and similar to the traditional Monin–Obukhov layer. Deeper down within the mixed layer, the EKE budget is buoyancy-driven with a more complicated balance that varies considerably among the different simulations. The simulations with constant Kx predict the buoyant generation of EKE is balanced almost solely by pressure transport with negligible local destruction, which gives rise to waves near the front. Recent observations near fronts show enhanced levels of irreversible destruction. The simulations with the ASM predict EKE budgets where both local destruction—through SGS dissipation—and pressure transport are part of the EKE balance.The results obtained using the constant-Kx simulations suggest both horizontal and vertical SGS parameterizations have important effects on the resolved-scale dynamics. The simulations with Kx=5m2s−1 yield the most unrealistic results partly because the lateral viscosity is high enough to directly influence the instability scale. Yet the observed differences among the constant-Kx simulations are sometimes subtle and cannot be explained trivially by comparing Kx alone. For fixed Kx, we find simulations can exhibit higher spectral levels and stronger cascades (forward and inverse) upon increasing the vertical SGS viscosity. This suggests the sensitivity of submesoscale-resolving simulations to the vertical SGS parameterization needs to be better explored.