RAPID DISTORTION ANALYSIS AND DIRECT SIMULATION OF COMPRESSIBLE HOMOGENEOUS TURBULENCE AT FINITE MACH NUMBER

The effect of rapid mean compression on compressible turbulence at a r ange of turbulent Mach numbers is investigated. Rapid distortion theor y (RDT) and direct numerical simulation results for the case of axial (one-dimensional) compression are used to illustrate the existence of two distinct rapid compression regimes. These regimes - the nearly sol enoidal and the 'pressure-released' - are defined by a single paramete r involving the timescales of the mean distortion, the turbulence, and the speed of sound. A general RDT formulation is developed and is pro posed as a means of improving turbulence models for compressible flows . In contrast to the well-documented observation that 'compressibility ' (measured, for example, by the turbulent Mach number) is often assoc iated with a decrease in the growth rate of turbulent kinetic energy, we find that under rapid distortion compressibility can produce an amp lification of the kinetic energy growth rate. We also find that as the compressibility increases, the magnitude of the pressure-dilation cor relation increases, in absolute terms, but its relative importance dec reases compared to the magnitude of the kinetic energy production.