  We consider the modeling of the effect of unresolved scales, for
two-dimensional and geophysical flows. We first show that the effect of small
scales on a coarse-grained field, can be approximated at leading order, by the
effect of the strain tensor on the gradient of the vorticity, which exactly
conserves the energy. We show that this approximation would lead to unstable
numerical code. In order to propose a stable parameterization, while taking
into account of these dynamical properties, we apply a maximum entropy
production principle. The parameterization acts as a selective diffusion
proportional to the mean strain, in the contraction direction, while conserving
the energy. We show on numerical computation that the obtained
\foreignlanguage{french}{anisotropic relaxation equations} give an important
predictability improvement, with respect to Navier-Stokes, Smagorinsky or
hyperviscous parameterizations.
