Nonlinear evolution of perturbations in high Mach number wall-bounded flow: Pressure–dilatation effects

Abstract

We characterize the nonlinear evolution of perturbations in a high Mach number Poiseuille flow and contrast the behavior against an equivalent incompressible flow. The focus is on the influence of pressure–dilatation on (i) internal energy evolution, (ii) kinetic–internal energy exchange, and (iii) kinetic energy spectrum evolution. We perform direct numerical simulations of plane Poiseuille flow at different Mach numbers subject to a variety of initial perturbations. In all high-speed cases considered, pressure dilatation leads to energy equipartition between wall-normal velocity fluctuations (dilatational kinetic energy) and pressure fluctuations (a measure of internal energy). However, the effect of pressure–dilatation on the kinetic energy spectral growth can be varied. In cases wherein pressure–dilatation is larger than the turbulent kinetic energy production, spectral growth is considerably slow relative to an equivalent low Mach number case. When pressure–dilatation is smaller than production, the spectral growth is only marginally affected. As a consequence, in a high-speed Poiseuille flow, the spectral growth rate varies with the wall-normal distance depending on the local pressure effects. These findings provide valuable insight into the nonlinear aspects of breakdown toward turbulence in high speed wall-bounded shear flows.