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.