We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.
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.
In this study we revisit the problem of rotating dense overflow dynamics by performing nonhydrostatic numerical simulations, resolving submesoscale variability. Thermohaline stratification and buoyancy forcing are based on data from the Eurasian Basin of the Arctic Ocean, where overflows are particularly crucial to exchange of dense water between shelves and deep basins, yet relatively little studied. A nonlinear equation of state is used, allowing proper representation of thermohaline structure and mixing. We examine three increasingly complex scenarios: nonrotating 2D, rotating 2D, and rotating 3D. The nonrotating 2D case behaves according to known theory – the gravity current descends alongslope until reaching a relatively shallow neutral buoyancy level. However, in the rotating cases we have identified novel dynamics: in both 2D and 3D the submesoscale range is dominated by symmetric instability (SI). Rotation leads to geostrophic adjustment, causing dense water to be confined within the forcing region longer and attain a greater density anomaly. In the 2D case, Ekman drainage leads to descent of the geostrophic jet, forming a highly dense alongslope front. Beams of negative Ertel potential vorticity develop parallel to the slope, initiating SI and vigorous mixing in the overflow. In 3D, baroclinic eddies are responsible for cross-isobath dense water transport but SI again develops along the slope and at eddy edges. Remarkably, through two different dynamics the 2D SI-dominated case and 3D eddy-dominated case attain roughly the same final water mass distribution, highlighting the potential role of SI in driving mixing within certain regimes of dense overflows.
