Effects of pressure fluctuations on turbulence growth in compressible homogeneous shear flow

Abstract

Direct numerical simulation results are used to study compressibility effects on turbulent energy growth in homogeneous shear flow. Normalized amplitude of the pressure fluctuations is shown to decrease as the turbulent Mach number increases. This decrease causes the reduction in the pressure–strain term, changes the anisotropy of the Reynolds stress, and reduces the growth rate of turbulent kinetic energy as is the case of mixing layers. The transport equation for the pressure variance is examined in detail. It is shown that when the turbulent Mach number is high the pressure-variance dissipation term is not negligible and contributes to the reduction in the pressure fluctuations. The pressure-variance dissipation is closely related to the high-wavenumber part of the pressure-variance spectrum. Profile of the spectrum is observed to depend on the turbulent Mach number. A statistical theory called the two-scale direct-interaction approximation is applied to obtain model expressions for pressure-related terms. The pressure–dilatation correlation is a dominant term in the pressure-variance equation; its model expression as derived contains the material derivative of turbulent kinetic energy. This quantity represents nonequilibrium properties of turbulent field and can explain the very small value of the pressure dilatation in boundary layers and channel flows. The model expression for the pressure–strain correlation is also derived; the normalized pressure variance can be a parameter that describes compressibility effect on the pressure strain.