Notable effect of the subgrid-scale stress anisotropy on mean-velocity prediction through budget of the grid-scale Reynolds-shear stress

Abstract

In large eddy simulation (LES), the mean-velocity distribution in wall turbulence depends strongly on the distribution of the ensemble-averaged Reynolds (Re) shear stress, which consists of two parts: the resolved grid-scale (GS) and unresolved subgrid-scale (SGS) components. As the grid resolution becomes coarser, the GS component decreases and thus the SGS component must increase to compensate for this. The GS decrease is originally caused by filtering, through which the power spectrum is cut off mainly in the high-wavenumber region. Therefore, the SGS model has been discussed mostly in terms of the energy transfer between the GS and SGS components. Recently, however, some studies have found that the SGS-stress anisotropy directly influences instantaneous GS vortex motions. This also means that the SGS stress may have a large effect on the ensemble-averaged GS Re stress because the instantaneous fluctuation of the SGS stress correlates with that of the velocity gradient in the GS budget. In this study, we investigate in detail the effect of the SGS stress on predicting the resolved GS Re shear stress through its budget. For this purpose, we perform a priori tests with highly resolved LES data of a plane channel flow. The knowledge obtained is then confirmed by a posteriori tests for various grid resolutions and Reynolds numbers. It is found that the SGS-stress anisotropy is very important for providing a reasonable trend of the GS Re shear stress, leading to more accurate prediction of the mean velocity for coarse-grid resolutions.