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Abstract 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.