On eddy viscosity models that restrict the dynamics to the larger eddies

The very essence of large eddy simulation (LES) is that the LES-solution contains only scales of size ≥ δ, where δ is a user-chosen length scale. Therefore, in case the LES is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size < δ are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) (counter)balance the production of scales of size smaller than δ; and (b) damp any disturbances having a scale of size smaller than δ initially. From this we deduce that the eddy viscosity νe has to depend on the invariants q = ½ tr(S2) and r = −⅓ tr(S3) of the strain rate tensor S. The simplest model is then given by νe = 3/2 (δ/π)2|r|/q. This model is successfully tested for a turbulent channel flow (Reτ=590).