Toward A Constitutive Relation in Compressible Turbulence

Abstract

In high-speed turbulent flows questions arise as to what extent compressibility affects turbulence structures, the Reynolds stress- mean velocity (constitutive) relation, and the accompanying processes of heat transfer and mixing. This paper addresses the problem of compressibility effects on the constitutive relation when the R.M.S. fluctuating Mach number is sufficiently high to cause significant coupling between the compressive and solenoidal modes. Emphasis is given to the analysis of homogeneous shear turbulence. It is found that turbulence model equations possess a compressible selfsimilar solution characterized by invariant R.M.S. Mach number and turbulence time scale (normalized by mean shear). The turbulence second- order quantities grow exponentially but at a much slower rate than in the incompressible regime.