Three-equation modeling of inhomogeneous compressible turbulence based on a two-scale direct-interaction approximation

Abstract

Mathematical functional forms of important correlation functions in inhomogeneous compressible turbulence are investigated, with the focus on the turbulence modeling based on bulk turbulence quantities. A two-scale direct-interaction approximation (TSDIA) is applied using three fundamental variables, that is, the density, momentum, and internal energy per unit volume. This choice of variables under the ensemble-mean procedure retains the simplicity of the mean-field equations under the Favre-mean procedure. Using these theoretical results, a three-equation turbulence model is constructed, where the turbulence equations consist of the equations for the intensity of momentum fluctuation, its viscous dissipation rate, and the intensity of density fluctuation. Direct effects of compressibility on the Reynolds stress and other important correlation functions are related to the intensity of density fluctuation. These results give a clue for explaining the virtual decrease of the eddy-viscosity effect near a shock wave.