The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study

摘要

The influence of compressibility upon the structure of homogeneous sheared turbulenceis investigated. For the case in which the rate of shear is much larger than therate of nonlinear interactions of the turbulence, the modification caused by compressibilityto the amplification of turbulent kinetic energy by the mean shear is found to beprimarily reflected in pressure-strain correlations and related to the anisotropy of theReynolds stress tensor, rather than in explicit dilatational terms such as the pressure-dilatation correlation or the dilatational dissipation. The central role of a `distortionMach number' Md = S?=a, where S is the mean strain or shear rate, ? a lengthscaleof energetic structures, and a the sonic speed, is demonstrated. This parameter hasappeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation(DNS) studies; in order to generalize the previous analyses, the quasi-isentropiccompressible RDT equations are numerically solved for homogeneous turbulencesubjected to spherical (isotropic) compression, one-dimensional (axial) compressionand pure shear. For pure-shear flow at finite Mach number, the RDT results displayqualitatively different behaviour at large and small non-dimensional times St:when St < 4 the kinetic energy growth rate increases as the distortion Mach numberincreases; for St > 4 the inverse occurs, which is consistent with the frequently observedtendency for compressibility to stabilize a turbulent shear flow. This `crossover'behaviour, which is not present when the mean distortion is irrotational, is due to thekinematic distortion and the mean-shear-induced linear coupling of the dilatationaland solenoidal fields. The relevance of the RDT is illustrated by comparison to therecent DNS results of Sarkar (1995), as well as new DNS data, both of which wereobtained by solving the fully nonlinear compressible Navier-Stokes equations. Thelinear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in goodgeneral agreement over a wide range of parameters; this agreement gives new insightinto the stabilizing and destabilizing effects of compressibility, and reveals the extentto which linear processes are responsible for modifying the structure of compressibleturbulence.