Vorticity-dependent and symmetry-preserving LES models

Within the Large Eddy Simulation framework, we propose a methodology based on the Lie theory to derive symmetry-preserving turbulence models. We apply this methodology to the incompressible Navier-Stokes equations.} These models explicitly depend on both the filtered strain-rate tensor and the filtered vorticity tensor. Particular emphasis is placed on models that additionally ensure stability.