DNS Data of Subgrid Scale Stress and Its Wall Asymptotic Behaviour

Abstract

The objective of this study is to specify the wall asymptotic behaviour on the subgrid scale stress for LES of incompressible flows. To this end, GS and SGS turbulent statistics were extracted from the DNS data of plane channel flow at the Reynolds number 300, based on the friction velocity and channel half width. The statistics were computed corresponding to various LES filters, that is, plane (two-dimensional) and three-dimensional filters with different filter lengths. Then, the components of the subgrid scale stress, τij, were arranged along with the analytical results with Taylor expansion.The main results for the wall asymptotic behaviour on the SGS shear stress, τ12, are as follows : (1) Taylor expansion analysis estimates different wall asymptotic behaviours of the SGS stress for plane and three-dimensional filters. (2) The behaviour with the plane filter isτ12∝ O (y3), where y is the distance from the wall. This is the same behaviour as the Reynolds shear stress and the Taylor expansion result for the filter. (3) The Taylor expansion result for the three-dimensional filter, τ12∝O (Δ2yy), is not realized on the standard wall normal grid configuration (Δ+y≥1) of LES. (4) Generally, the wall asymptotic behaviour on the Reynolds stress, which has been assumed for the SGS modeling, is not correct for the SGS stress with the three-dimensional filter.