Effect of heat source on statistics and scaling in compressible homogeneous shear turbulence

Abstract

The effects of heat sources on the velocity and pressure spectra, Mach number scaling of one-point statistics, and small-scale structures of compressible homogeneous shear turbulence are numerically studied. The dilatational components of flow fields are significantly enhanced by a strong heat source at low turbulent Mach numbers Mt and are dominated by an acoustic mode, leading to a strong acoustic equilibrium between the dilatational velocity and pressure. As the magnitude of the heat source increases, the scaling behaviors of the dilatational components of kinetic energy and dissipation rate change from Mt4 and approach a state that is nearly independent of the turbulent Mach number. Furthermore, a strong heat source has a significant effect on small-scale structures at low turbulent Mach numbers. The conditional probability density functions of the normalized eigenvalues of a strain rate tensor become more dependent on the dilatation owing to the effect of the heat source. For low turbulent Mach numbers with strong heat sources, the ratio of the normalized eigenvalues of the strain rate tensor tends to −1:0:0 and −0.2:0.25:1 in the strong compression and strong expansion regions, respectively, and the dilatational vortex stretching term can significantly enhance the enstrophy production.