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AN ANALYSIS OF THE RAPID PRESSURE-STRAIN CORRELATION IN COMPRESSIBLE SHEAR FLOW

William D. Thacker
Saint Louis University, St. Louis, MO 63156

Sutanu Sarkar
Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093

Thomas B. Gatski


Abstrakt

The influence of compressibility on the rapid pressure-strain rate correlation is investigated using the Green's function for the wave equation governing pressure fluctuations in compressible homogeneous shear flow. The solution for the Green's function is obtained as a combination of parabolic cylinder functions; it is oscillatory with monotonically increasing frequency and decreasing amplitude at large times, and anisotropic in wave-vector space. This Green's function, which depends explicitly on turbulent Mach number Mt and gradient Mach number Mg, provides a means for analyzing the influence of these two compressibility parameters on the rapid pressure term. Assuming a form for the temporal decorrelation of velocity fluctuations brought about by the turbulence, the rapid pressure-strain rate tensor is expressed exactly in terms of the energy spectrum tensor and the time integral of the Green's function times a decaying exponential. A model for the energy spectrum tensor, linear in Reynolds stress anisotropics and in mean shear, is assumed for closure. The expression for the rapid pressure-strain correlation is evaluated using parameters applicable to a mixing layer and a boundary layer. It is found that, for the same range of Mt, there is a large reduction of the pressure-strain correlation in the mixing layer but not in the boundary layer. This result is linked with the observation that Mg/Mt is considerably larger for the mixing layer than for the boundary layer.