Inhomogeneity and anisotropy effects on the redistribution term in Reynolds-averaged Navier-Stokes modelling

A channel flow DNS database at Re-tau = 590 is used to assess the validity of modelling the redistribution term in the Reynolds stress transport equat ions by elliptic relaxation. The model assumptions are found to be globally consistent with the data. However, the correlation function between the fl uctuating velocity and the Laplacian of the pressure gradient, which enters the integral equation of the redistribution term, is shown to be anisotrop ic. It is elongated in the streamwise direction and strongly asymmetric in the direction normal to the wall, in contrast to the isotropic, exponential model representation used in the original elliptic relaxation model. This discrepancy is the main cause of the slight amplification of the energy red istribution in the log layer as predicted by the elliptic relaxation equati on. New formulations of the model are proposed in order to correct this spu rious behaviour, by accounting for the rapid variations of the length scale and the asymmetrical shape of the correlation function. These formulations do not rely on the use of so-called 'wall echo' correction terms to damp t he redistribution. The belief that the damping is due to the wall echo effe ct is called into question through the present DNS analysis.