When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥ , where denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size < are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than ; and (b) damp any disturbances having a scale of size smaller than initially. From this we deduce that the eddy viscosity νe has to depend on the invariants q = 2 tr(S2) and r =− 3 tr(S3) of the (filtered) strain rate tensor S. The simplest model is then given by νe = 2 ( /π)2|r|/q. This model is successfully tested for a turbulent channel flow (Reτ = 590).