On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows

Abstract

The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation (LES) of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress (SGS) tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation (DNS). It is shown that the SGS tensor, for the case of inhomogeneous flow, where the filtering operation is necessarily performed in physical space, contains two components: a rapid part that depends explicitly on the mean velocity gradient and a slow part that does not. The characterization, rapid and slow, is adopted by analogy to that used in the modeling of the pressure–strain in the Reynolds-averaged Navier–Stokes equations. In the absence of mean flow gradients, the slow part is the only nonzero component and has been the subject of much theoretical study. However, the rapid part can be important in the inhomogeneous flows that are often encountered in practice. An analytical estimate of the relative magnitude of the rapid and slow components is derived and the distinct role of each component in the energy transfer between the resolved grid scales and the unresolved subgrid scales is identified. Results that quantify this new decomposition are obtained from DNS data of a turbulent mixing layer. The rapid part is shown to play an important role when the turbulence is in a nonequilibrium state with turbulence production much larger than dissipation or when the filter size is not very small compared to the characteristic integral scale of the turbulence, as in the case of practical LES applications. More importantly, the SGS is observed to be highly anisotropic due to the close connection of the rapid part with the mean shear. The Smagorinsky eddy viscosity and the scale-similarity models are tested by performing a priori tests with data from DNS of the mixing layer. It is found that the scale-similarity model correctly represents the anisotropic energy transfer between grid and subgrid scales that is associated with the rapid part, while the eddy viscosity model captures the dissipation associated with the slow part. This may be a physical reason for the recent successes of the mixed model (Smagorinsky plus scale similarity) reported in the literature.