  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.
