Stabilizing action of pressure in homogeneous compressible shear flows: effect of Mach number and perturbation obliqueness

Abstract

AbstractCompressibility exerts a stabilizing influence on a variety of high-speed shear flows such as turbulent mixing layers, transitioning boundary layers and homogeneously sheared turbulence. An important stabilizing feature that is common amongst all shear flows is the velocity–pressure interaction dynamics. In this study, velocity–pressure interactions of individual perturbation or fluctuation modes are investigated using direct numerical simulations and linear analysis in high-Mach-number homogeneous shear flow. For a given perturbation wave mode, the action of pressure is shown to depend on two important factors: the orientation of the perturbation wavevector with respect to the shear plane and the Mach number. It is shown that the streamwise perturbation wave mode rapidly develops a high level of kinetic energy but is self-limiting owing to the action of pressure. On the other hand, the energy of spanwise perturbation wave modes grows unaffected by pressure or Mach number. Oblique modes combine spanwise and streamwise characteristics and are shown to be chiefly responsible for stabilizing effects seen in shear flows. Three regimes of obliqueness of different linear stability characteristics are identified. The critical role of perturbation obliqueness on stabilization is established.