Statistical Analysis of the Rate of Strain Tensor in Compressible Homogeneous Turbulence

Recent analysis of direct numerical simulations of compressible homogeneous shear flow turbulence has unraveled some of the energy transfer mechanisms responsible for the decrease of kinetic energy production when the flow becomes more compressible. In this complementary study, we focus our attention on the rate of strain tensor. A Helmholtz decomposition of the velocity field leads us to consider a solenoidal and an irrotational rate of strain tensor. Their eigenvalue distributions, eigenvector orientations, and the relative alignment between the eigenvectors and the vorticity and pressure gradient vectors are examined with the use of probability density functions. The irrotational rate of strain tensor is found to have a preferred structure in regions of strong dilatation. This structure depends on the mean shear, and is quite different from that of the solenoidal rate of strain tensor. Compressibility strongly affects the orientation properties of the pressure gradient vector.