Effect of compressibility on turbulent velocity gradients and small-scale structure

Abstract

The effect of compressibility on turbulent velocity gradients is studied by performing direct numerical simulations of decaying compressible turbulence at various turbulent Mach (0.059–0.885) and Reynolds (55, 110) numbers. When examined as a function of turbulent Mach number, compressibility effects on velocity gradients are masked by dominant solenoidal fluctuations. To isolate the compressibility effects, we investigate velocity-gradient behavior conditioned on the local dilatation level. The main conclusions valid for the parameter range of the study are as follows (1) kinetic energy and dissipation rate depend weakly on the turbulent Mach number, but strongly on the Reynolds number. (2) The dilatation level increases progressively with turbulent Mach number but still constitutes only a small fraction of total fluctuations in all cases considered. (3) Intermittency increases with turbulent Mach number. (4) Strain-rate eigenvalue distribution depends strongly on dilatation level. It is found that at extreme dilatation levels, the flow field may experience isotropic expansion or isotropic compression. (5) The preferential alignment between vorticity and strain-rate eigenvectors weakens in strong dilatation region as vorticity itself starts to vanish. It must be emphasized that these observations are valid only for the range of Reynolds and Mach numbers considered in the study.