Statistical analysis of compressible turbulent shear flows with special emphasis on turbulence modeling

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Abstract
Compressible turbulent shear flows are analyzed using a two-scale direct-interaction (propagator-renormalization) approximation with the density, velocity, and internal energy as the primitive variables. This method elucidates the effects of fluid compressibility on various important correlation functions that appear in the equations for the mean field. Specifically, density fluctuations are confirmed to be closely linked with compressibility effects. These results show that the current one-point turbulence model based on mass-weighted averaging, which is widely used in aeronautical studies, obscures many important features of fluid compressibility. On this basis, modeling based on the combined use of ensemble averaging and primitive variables is recommended as the one-point turbulence modeling applicable to the study of aerospace and astrophysical phenomena.