A simple extension to eddy-viscosity models for Large Eddy Simulations based on tensor decompositions.

Using tensor decompositions theorems and a nonlinear tensor formed by the Lie product of the strain rate and the rate of rotation tensor we form a simple 2-element tensorial basis set to model the residual stress tensor attributing specific roles to each tensor.  The strain rate tensor is responsible for reproducing the correct energy transfer from the resolved to the unresolved scales, while the nonlinear term is responsible for the correct energy redistribution among the resolved scales.  The coefficients multiplying each tensor are uncoupled, so the nonlinear term can be added to any commonly used version of eddy viscosity model without the need for rethinking the eddy viscosity modeling.

We apply the extension to the Smagorinsky-Lilly model and to Germano's dynamic model for large eddy simulation of forced homogeneous axisymmetric stratified turbulence. The filter width used on the simulations is grater than the Ozmidov length, so the energy transfer rate between the resolved and unresolved scales is anisotropic.  We compare the results of the original and the extended models to fully resolved direct numerical simulation of the same flow configuration.