Simone, A., Coleman, G.N. and Cambon, C.
The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study.
Journal of Fluid Mechanics, 330, . (doi:10.1017/S0022112096003837).
The influence of compressibility upon the structure of homogeneous sheared turbulence
is investigated. For the case in which the rate of shear is much larger than the
rate of nonlinear interactions of the turbulence, the modification caused by compressibility
to the amplification of turbulent kinetic energy by the mean shear is found to be
primarily reflected in pressure-strain correlations and related to the anisotropy of the
Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure-
dilatation correlation or the dilatational dissipation. The central role of a `distortion
Mach number' Md = Sℓ=a, where S is the mean strain or shear rate, ℓ a lengthscale
of energetic structures, and a the sonic speed, is demonstrated. This parameter has
appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation
(DNS) studies; in order to generalize the previous analyses, the quasi-isentropic
compressible RDT equations are numerically solved for homogeneous turbulence
subjected to spherical (isotropic) compression, one-dimensional (axial) compression
and pure shear. For pure-shear flow at finite Mach number, the RDT results display
qualitatively different behaviour at large and small non-dimensional times St:
when St < 4 the kinetic energy growth rate increases as the distortion Mach number
increases; for St > 4 the inverse occurs, which is consistent 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
kinematic distortion and the mean-shear-induced linear coupling of the dilatational
and solenoidal fields. The relevance of the RDT is illustrated by comparison to the
recent DNS results of Sarkar (1995), as well as new DNS data, both of which were
obtained by solving the fully nonlinear compressible Navier-Stokes equations. The
linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good
general agreement over a wide range of parameters; this agreement gives new insight
into the stabilizing and destabilizing effects of compressibility, and reveals the extent
to which linear processes are responsible for modifying the structure of compressible
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