Elements of rigorous subgrid modeling in large-eddy simulation

In this review the filtering approach to large-eddy simulation of turbulent flow will be presented. Nonuniform filtering of the Navier-Stokes equations is described and the central closure problem for the turbulent stress tensor is identified. The filter-operator induces the mathematical smoothing properties associated with the turbulent stress tensor and should be explicitly accounted for in actual, so-called subgrid models representing this tensor. We describe two basic, rigorous features of the closure problem to illustrate the central role of the spatial filter that is adopted and their consequences for subgrid modeling. Closure of the filtered equations is traditionally based on subgrid models motivated by physical intuition, such as dissipation and dispersion properties. In contrast, regularization principles may be put forward which provide a method for systematically deriving the implied subgrid model. These regularization principles may be designed such that the closed fluid description is guaranteed to possess a unique, strong solution with controlled smoothing compared to the unfiltered turbulent solution. Regularization maintains the central transport structure of the governing equations. We illustrate the approach with Leray regularization and the Lagrangian averaged Navier-Stokes-a model. The regularization models constitute a rigorous large-eddy modeling which will be compared with traditional dynamic subgrid models in turbulent mixing flow