Effect of compressibility on small scale statistics in homogeneous shear turbulence

The effect of compressibility on the small scale properties of stationary homogeneous shear turbulence (HST) is studied in a rectangular domain of size 4π × 2π × 2π by numerical simulations at four turbulent Mach numbers of M_t = 0.14, 0.2, 0.4, and 0.6. Compared to the compressible homogeneous isotropic turbulence (HIT), the small scale properties of HST are more sensitive to Mach number change and the velocity derivatives show a clear deviation from isotropy. At M_t = 0.14, the preferred eigenvalue ratio of the strain rate tensor is very close to -4:1:3 reported in incompressible turbulence. As M_t increases, the conditional probability density functions of the normalized eigenvalues become more dependent on the dilatation, and its ratio tends to -1:0:0 in the strong compression regions at M_t = 0.6, indicating the sheet-like structures of localized shock waves. The alignments between vorticity and eigenvectors are similar to the observations in HIT. After the Helmholtz decomposition, it is found that the compressible vortex stretching term is the primary cause for the enhancement of enstrophy production at high turbulent Mach numbers.