Large Eddy Simulations of wall bounded turbulent flows with fixed filter width

In large eddy simulations (LES), the geometry-dependent, large, energy-carrying scales are computed, and the subgrid scales are modeled. In wall-bounded turbulence, the filter width must approach zero for LES equations to strictly hold, which leads to prohibitively expensive grid-resolution requirements at high Reynolds numbers. Further, this also leads to additional unclosed terms as this filtering operation does not commute with the differentiation.

In this work, we develop an alternative formulation of LES that employs only fixed-width filters and avoids both these difficulties. In this framework, the computation of wall-bounded turbulent flow reduces to the simultaneous solution of a set of LES equations defined in the volume and a set of two-dimensional equations for a flow along the bounding surface. This two-dimensional surface flow contains modeled terms that capture the near-wall physics, whereas the volume flow employs traditional LES methodology (such as the use of the dynamic Smagorinsky model). The derivation of this formulation will be presented from first principles along with validation of the concept from ``a posteriori" studies of some canonical flows.