Direct simulations of the turbulent shear layer are performed for subsonic to supersonic
Mach numbers. Fully developed turbulence is achieved with profiles of mean
velocity and turbulence intensities that agree well with laboratory experiments. The
thickness growth rate of the shear layer exhibits a large reduction with increasing
values of the convective Mach number, Mc. In agreement with previous investigations,
it is found that the normalized pressure–strain term decreases with increasing Mc,
which leads to inhibited energy transfer from the streamwise to cross-stream fluctuations,
to the reduced turbulence production observed in DNS, and, finally, to reduced
turbulence levels as well as reduced growth rate of the shear layer. An analysis, based
on the wave equation for pressure, with supporting DNS is performed with the result
that the pressure–strain term decreases monotonically with increasing Mach number.
The gradient Mach number, which is the ratio of the acoustic time scale to the flow
distortion time scale, is shown explicitly by the analysis to be the key quantity that
determines the reduction of the pressure–strain term in compressible shear flows. The
physical explanation is that the finite speed of sound in compressible flow introduces
a finite time delay in the transmission of pressure signals from one point to an
adjacent point and the resultant increase in decorrelation leads to a reduction in the
pressure–strain correlation.The dependence of turbulence intensities on the convective Mach number is investigated.
It is found that all components decrease with increasing Mc and so does the
shear stress.DNS is also used to study the effect of different free-stream densities parameterized
by the density ratio, s = ρ2/ρ1, in the high-speed case. It is found that changes in the
temporal growth rate of the vorticity thickness are smaller than the changes observed
in momentum thickness growth rate. The momentum thickness growth rate decreases
substantially with increasing departure from the reference case, s = 1. The peak value
of the shear stress, uv, shows only small changes as a function of s. The dividing
streamline of the shear layer is observed to move into the low-density stream. An
analysis is performed to explain this shift and the consequent reduction in momentum
thickness growth rate.
Turbulent shear-layer mixing: growth-rate compressibility scaling
