Subgrid parameterizations of ocean mesoscale eddies based on Germano decomposition

Abstract: Ocean models at intermediate resolution (1/4 degree), which partially resolve mesoscale eddies, can be seen as Large eddy simulations (LES) of the primitive equations, in which the effect of unresolved eddies must be parameterized. In this work, we propose new subgrid models that are consistent with the physics of two-dimensional (2D) flows. We analyze subgrid fluxes in barotropic decaying turbulence using Germano (1986) decomposition. We show that Leonard and Cross stresses are responsible for the enstrophy dissipation, while the Reynolds stress is responsible for additional kinetic energy backscatter. We utilize these findings to propose a new model, consisting of three parts, that is compared to a baseline dynamic Smagorinsky model (DSM). The three-component model accurately simulates the spectral transfer of energy and enstrophy and improves the representation of kinetic energy (KE) spectrum, resolved KE and enstrophy decay in a posteriori experiments. The backscattering component of the new model (Reynolds stress) is implemented both in quasi-geostrophic and primitive equation ocean models and improves statistical characteristics, such as the vertical profile of eddy kinetic energy, meridional overturning circulation and cascades of kinetic and potential energy.