Pressure Effects in Compressible Flows at the Rapid Distortion Limit

We investigate the role of pressure in rapidly sheared homogeneous compressible turbulence using the Rapid Distortion Theory (RDT). Our objective is to develop a simple dynamical model that reproduces the 3-stage turbulent kinetic energy evolution observed in compressible RDT calculations. The three stages of turbulent kinetic energy evolution are: (1) initial growth at a rate higher than equivalent incompressible flow; (2) an intermediate period of stabilization where the turbulent kinetic energy grows very slowly or not at all; and (3) final period of growth at a rate similar to incompressible flows. The dynamical model is a function of gradient and turbulent Mach numbers and attempts to shed light on the pressure-strain correlation process in compressible flows.