Compressible effects on statistics and small-scale structures in homogeneous shear turbulence*

The compressible effects on statistics and small-scale structures of stationary homogeneous shear turbulence (HST) are studied by numerical simulations in a three-dimensional rectangular domain. The results show that pseudo-sound modes dominate compressible velocity field at turbulent Mach number (M_t) less than 0.1, giving rise to a 4^th power law of M_t for normalized compressible kinetic energy and dissipation rate. As M_t grows to larger than 0.3, acoustic modes become dominate and a quadratic scaling of M_t is observed for spectra of compressible velocity and pressure. The strain rate eigenvalue ratio tends to be -1:0:0 at relative high M_t, implying the existence of sheet-like structures.  Some interesting features about vortex stretching and enstrophy production in HST are also discussed.