A new LES model derived from generalized Navier-Stokes equations with nonlinear viscosity

In this work, we shall propose a new approximation to this problem by applying the filter, not to the Navier-Stokes equations, but to a generalized version of these equations with nonlinear viscosity. That is, we shall introduce a nonlinear viscosity, not as a procedure to close the subgrid-scale stress tensor, but as part of the model itself (see below). Consequently, we shall need a different method to close the subgrid-scale stress tensor, and we shall use the Clark approximation, where the Taylor expansion of the subgrid-scale stress tensor is computed (see Carati et al., 2001 and Vreman et al., 1966).