Wall Asymptotic Behavior of Subgrid Scale Stress for Large Eddy Simulation

The objective of this study is to specify the wall asymptotic behavior of the subgrid scale stress for the large eddy simulation (LES) of wall bounded turbulent flows. The grid scale (GS) and subgrid scale (SGS) turbulent statistics are extracted from the numerical data of direct numerical simulation (DNS) of the turbulent channel flow at the Reynolds number of 300, based on the friction velocity and channel half width, in order to achieve this objective. The basic equations of the DNS are the Navier-Stokes and continuity equations for incompressible flows. The GS and SGS statistics are computed corresponding to various LES filters, that is, two-dimensional (plane) and three-dimensional filters with different filter widths. The Gaussian filter is used in the periodic directions. The filtering function in the wall-normal direction is top-hat for the three-dimensional filter. Then, the components of the SGS stress are compared with the analytical results by the Taylor expansion. The results estimated by the Taylor expansion and the DNS data indicate different wall asymptotic behaviors of the SGS stress for the plane and three-dimensional filters. In particular, the wall asymptotic behavior of the Reynolds stress, which has been assumed in the SGS modeling, is not true of the SGS stress for the three-dimensional filter.