On a stochastic approach to Eddy Viscosity Models for turbulent flows

The aim of this note is twofold: we review some basic results which are at the basis of the derivation of eddy viscosity methods for large eddy simulation (LES) and we also try to combine them with the Stochastic approach to the Navier-Stokes equations. In particular, we propose a stochastic approach to the introduction of eddy viscosity LES methods and we evaluate by means of probabilistic techniques generalizations of the Lilly's constant. Next, we propose some heuristic for alternate modeling of sub-grid-scale terms and we apply scaling techniques to the derivation of a model for channel flows