Decomposition of the Reynolds stress from filtered data

The reconstruction of the Reynolds stress from data provided by a large-eddy simulation (LES) is commonly based on the assumption that the statistical average of the filtered LES quantities is the same as that of the unfiltered ones. As such, the Reynolds stress is given by the sum of the resolved stress associated with the large-eddy simulation and the mean subfilter scale and subgrid scale stresses. In this paper LES is considered from a purely mathematical point of view corresponding to a convolution operation applied to the Navier-Stokes equations, thus solely with subfilter scale stresses. In this context we derive and test an exact relation between the Reynolds stress and the resolved stress in order to quantify exactly the possible effect of the interference between the mean and the subfilter scale. A resolution criterion that should reinforce the independence of the scales is proposed and it is shown that the interference effect could have some relevance if the resolution is inadequate.

Duke Scholars

Author Massimo Germano Civil and Environmental Engineering