Effect of shocklets on the velocity gradients in highly compressible isotropic turbulence

Abstract

The effect of randomly generated shocklets on velocity gradients in a three-dimensional compressible isotropic turbulence was systematically studied. The forced flows obtained from high-resolution simulations had a turbulent Mach number of 1.0 and a Taylor microscale Reynolds number around 180. The shock detection algorithm developed by Samtaney et al. [“Direct numerical simulation of decaying compressible turbulence and shocklet statistics,” Phys. Fluids 13, 1415 (2001)] was applied to extract the shocklets. Using reference frames moving with the detected shocks, we obtained statistical properties of velocity and its gradients both upstream and downstream of the shocks. It was shown that the shocks induced flow modulation at a wide range of length scales, including the inertial subrange scales. The shocks intensified enstrophy in the shock regions and this enhanced enstrophy production was partially redistributed over various scales and dissipated by straining and viscous effects outside the shock regions. We also found that both the strain rate eigenvectors and eigenvalues were significantly altered by shocks. Furthermore, local modulation effects by the shocklets enlarged with the shocklet strength. The Helmholtz decomposition was performed to show that most statistics associated with the solenoidal component of velocity derivatives were insensitive to the formation of shocks, but those associated with the compressive component of velocity derivatives depended strongly on the shock formation and shock strength.