Modeling vertical transport and submesoscale frontal mixing in dense flows along topography

Dense gravity currents forced by surface buoyancy loss over shallow shelf regions are important contributors to subsurface and abyssal ventilation throughout the World Ocean, yet remain challenging to represent accurately in models. In the first part of this study we present idealized experiments of rotating terrain-following gravity currents employing both the nonhydrostatic MITgcm in z coordinates as well as the hydrostatic GFDL-MOM6 in z* and isopycnal coordinates. In the highest-resolution nonhydrostatic simulations (where the submesoscale range is well-resolved), the dense flow undergoes geostrophic adjustment and forms compensating bottom-intensified and surface-intensified jets. The density front along the topography combined with geostrophic shear initiates submesoscale symmetric instability, which leads to the onset of secondary shear instability, dissipation of geostrophic energy, and water mass modification. We explore the impact of vertical coordinate, horizontal resolution, and parameterizations of shear-driven mixing and mesoscale eddies on the representation of these water mass transformation processes. We find that in isopycnal coordinates limited vertical resolution in certain regions leads to inadequate representation of submesoscale mixing processes. In the second part of this study we propose a parameterization for capturing the effects of submesoscale symmetric instability. The parameterization is based on identifying unstable regions through a balanced Richardson number criterion and subsequently slumping the isopycnals towards a balanced state (similar to the Gent-McWilliams parameterization for baroclinic instability). A fraction of the potential energy released by the slumping is then passed to the shear mixing parameterization, so that potential energy extracted from the large-scale flow by the instabilities is converted to kinetic energy and used for vertical mixing. Parameterizing the effect of submesoscale instabilities by combining isopycnal slumping with irreversible vertical mixing becomes crucial as ocean models move towards (partially) resolving mesoscale eddies and fronts but not the submesoscale mixing processes within them.