Tensorial volume of turbulence revisited

Abstract

A corrected tensorial turbulent volume transport equation, which is exact for uniform density flows, is derived from the Navier-Stokes equations. For homogeneous turbulence, the new terms appearing in the correct equation account for the effect of the pressure velocity correlation and of the mean velocity gradient. The correct tensorial volume equation is closed only for the case of isotropic homogeneous turbulence. To solve the equation for the anisotropic case a model for the velocity spectrum is required. When applied to the cases of isotropic expansion, incompressible axisymmetric contraction, and shearing of initially isotropic turbulence, the correct equation predicts the same time evolution for the tensorial volume that rapid distortion theory does. © 1990 American Institute of Physics.