A Breakdown in Potential Vorticity Estimation Delineates the Submesoscale-to-Turbulence Boundary in Large Eddy Simulations

Most submesoscale motions-fronts, eddies, filaments, and even large internal waves-are sufficiently rapidly rotating and stratified as to be strongly influenced by potential vorticity dynamics. Below the Ozmidov scale where turbulence overturns and isotropizes, potential vorticity is not commonly considered. Here, it is shown that in Large Eddy Simulations, the velocity gradients, buoyancy gradients, and potential vorticity are strongly influenced by grid-scale processes. Grid-scale processes in Large Eddy Simulations, as opposed to those in Direct Numerical Simulations, imply that spuriously noisy potential vorticity variance will become increasingly dominant as resolution increases-analogous to ultraviolet catastrophe. A solution, the prefiltered potential vorticity, is shown to be effective in linking the potential vorticity dynamics of the submesoscale to the nearly-isotropic turbulent fluxes beyond the Ozmidov scale, and a derivation is provided for a set of closed conservation equations for use in interpreting potential vorticity dynamics in Large Eddy Simulations. This diagnostic approach is exceptional in that Large Eddy Simulation analysis and hydrostatic ocean modeling with parameterized turbulence analysis are harmonized. Plain Language Summary In the study of geophysical fluid dynamics, such as oceans and atmosphere, it is common to use models such as Large Eddy Simulations (LES) that favor large-scale dynamics over dynamics near the grid scale, which are approximated using turbulence closures. So, if parameterizations of small-scale processes hidden below or near the model grid scale dominate, caution must be taken in interpretation of results. Potential vorticity combines rotation and stratification into one variable which offers key insights into dynamical properties for atmospheric and oceanic flows where rotation and stratification are important (i.e., large scales). However, as small scales are approached and turbulent mixing dominates the flow, potential vorticity transitions to being strongly influenced by the smallest scales, which in LES are the least reliable, unresolved, or heavily approximated processes. In this study, we present an accurate diagnosis method for potential vorticity dynamics in such models, by treating all scales associated with turbulent mixing separately, and find the corresponding larger scale potential vorticity and its governing equations.