The response of sheared turbulence to additional distortion

Abstract

In unidirectional flows, the ratios of Reynolds shear stress to total intensity (except near positions of zero stress) remain remarkably constant from one flow to another, but curvature or strong divergence of the mean flow causes very considerable changes in the stress ratios. A scheme for calculating the changes is described, based on the rapid-distortion approximation of the equations of motion. The results depend to some extent on the effective history of distortion of the turbulence and on the magnitude of an eddy viscosity that models the effect of nonlinear transfer of energy to smaller eddies of the dissipation sequence, but the correspondence with measured values in a distorted wake and in a curved mixing layer is fairly good. In particular, the curious behaviour of stress ratios in the curved mixing-layer can be reproduced qualitatively without any difficulty. Small perturbations of wall turbulence provide a simple application, and earlier calculations of the energy transfer between wind and water waves have been repeated including the changes in the stress ratios predicted by the scheme. In the latter case, very large changes in the distributions of pressure and shear stress are found, and the rates of energy transfer are much larger and in better agreement with observations.