A dynamic eddy - viscosity model based on the invariants of the rate - of - strain

Large-eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. By construction, the LES solution contains only scales of size ≥ ∆, where ∆ denotes some user-chosen length scale of the spatial filter. A large-eddy simulation based on an eddy-viscosity model and a Navier-Stokes simulation differ only in diffusion coefficient. Therefore, we focus on the question: “When does eddy diffusivity reduce a turbulent flow to eddies of size ≥ ∆?”. It is deduced that the eddy viscosity νe has to depend on the two invariants q and r of the filtered rate-of-strain tensor. We present a dynamic version of the resultant eddy-viscosity model and present results from LES of isotropic turbulence and turbulent channel flow.