THE EFFECT OF COMPRESSIBILITY ON TURBULENT SHEAR-FLOW - A RAPID-DISTORTION-THEORY AND DIRECT-NUMERICAL-SIMULATION STUDY

The influence of compressibility upon the structure of homogeneous she ared turbulence is investigated. For the case in which the rate of she ar is much larger than the rate of nonlinear interactions of the turbu lence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primaril y reflected in pressure-strain correlations and related to the anisotr opy of the Reynolds stress tensor, rather than in explicit dilatationa l terms such as the pressure-dilatation correlation or the dilatationa l dissipation. The central role of a 'distortion Mach number' M(d) = S l/a, where S is the mean strain or shear rate, l a lengthscale of ener getic structures, and a the sonic speed, is demonstrated. This paramet er has appeared in previous rapid-distortion-theory (RDT) and direct-n umerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numeric ally solved for homogeneous turbulence subjected to spherical (isotrop ic) compression, one-dimensional (axial) compression and pure shear. F or pure-shear flow at finite Mach number, the RDT results display qual itatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the disto rtion Mach number increases; for St > 4 the inverse occurs, which is c onsistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This 'crossover behaviour, which is not present when the mean distortion is irrotational, is due to the k inematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illust rated by comparison to the recent DNS results of Sarkar (1995), as wel l as new DNS data, both of which were obtained by solving the fully no nlinear compressible Navier-Stokes equations. The linear quasi-isentro pic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new i nsight into the stabilizing and destabilizing effects of compressibili ty, and reveals the extent to which linear processes are responsible f or modifying the structure of compressible turbulence.