Statistical Properties of Subgrid-Scale Turbulence Models

This review examines large eddy simulation (LES) models from the perspective of their a priori statistical characteristics. The most well-known statistical characteristic of an LES subgrid-scale model is its dissipation (energy transfer to unresolved scales), and many models are directly or indirectly formulated and tuned for consistency of this characteristic. However, in complex turbulent flows, many other subgrid statistical characteristics are important. These include such quantities as mean subgrid stress, subgrid transport of resolved Reynolds stress, and dissipation anisotropy. Also important are the statistical characteristics of models that account for filters that do not commute with differentiation and of the discrete numerical operators in the LES equations. We review the known statistical characteristics of subgrid models to assess these characteristics and the importance of their a priori consistency. We hope that this analysis will be helpful in continued development of LES models.