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 =
S[lscr ]/a, where S is the mean strain or
shear rate, [lscr ] 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
turbulence.
NUMERICAL SIMULATION OF TURBULENT SHEAR FLOW OVER TWO-DIMENSIONAL SMOOTH TOPOGRAPHY USING UNSTEADY RANS METHOD
