## AN ANALYSIS OF THE RAPID PRESSURE-STRAIN CORRELATION IN COMPRESSIBLE SHEAR FLOW
## RésuméThe 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 M, 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 _{g}M, 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_{t} M is considerably larger for the mixing layer than for the boundary layer.
_{g}/M_{t} |

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