Parameterization of Submesoscale Symmetric Instability in Dense Flows Along Topography

We develop a parameterization for representing the effects of submesoscale symmetric instability (SI) in the ocean interior. SI may contribute to water mass modification and mesoscale energy dissipation in flow systems throughout the World Ocean. Dense gravity currents forced by surface buoyancy loss over shallow shelves are a particularly compelling test case, as they are characterized by density fronts and shears susceptible to a wide range of submesoscale instabilities. We present idealized experiments of Arctic shelf overflows employing the GFDL-MOM6 in z* and isopycnal coordinates. At the highest resolutions, the dense flow undergoes geostrophic adjustment and forms bottom- and surface-intensified jets. The density front along the topography combined with geostrophic shear initiates SI, leading to onset of secondary shear instability, dissipation of geostrophic energy, and turbulent mixing. We explore the impact of vertical coordinate, resolution, and parameterization of shear-driven mixing on the representation of water mass transformation. We find that in isopycnal and low-resolution z* simulations, limited vertical resolution leads to inadequate representation of diapycnal mixing. This motivates our development of a parameterization for SI-driven turbulence. The parameterization is based on identifying unstable regions through a balanced Richardson number criterion and slumping isopycnals toward a balanced state. The potential energy extracted from the large-scale flow is assumed to correspond to the kinetic energy of SI which is dissipated through shear mixing. Parameterizing submesoscale instabilities by combining isopycnal slumping with diapycnal mixing becomes crucial as ocean models move toward resolving mesoscale eddies and fronts but not the submesoscale phenomena they host.