Modeling of compressible effects on the Reynolds stress using a Markovianized two-scale method

Compressibility effects on the Reynolds stress are modeled using a Markovianized two-scale method. These effects occur twofold. One is the effect on the turbulent viscosity, which is expressed in terms of the ratio of the normalized density variance to the squared turbulent Mach number. Another comes from the deviation of the Reynolds stress from a turbulent-viscosity representation, which is written using the Langrange derivative of the mean velocity and the spatial derivatives of the mean density and internal energy. A simple model with the former compressibility effect incorporated is applied to fully developed free-shear layers and is shown to capture the steep decrease in the growth rate with the increasing convective Mach number.