Effect of compressibility on the small-scale structures in isotropic turbulence

Using a simulated highly compressible isotropic turbulence field with turbulent Mach number around 1.0, we studied the effects of local compressibility on the statistical properties and structures of velocity gradients in order to assess salient small-scale features pertaining to highly compressible turbulence against existing theories for incompressible turbulence. A variety of statistics and local flow structures conditioned on the local dilatation - a measure of local flow compressibility - are studied. The overall enstrophy production is found to be enhanced by compression motions and suppressed by expansion motions. It is further revealed that most of the enstrophy production is generated along the directions tangential to the local density isosurface in both compression and expansion regions. The dilatational contribution to enstrophy production is isotropic and dominant in highly compressible regions. The emphasis is then directed to the complicated properties of the enstrophy production by the deviatoric strain rate at various dilatation levels. In the overall flow field, the most probable eigenvalue ratio for the strain rate tensor is found to be -3:1:2.5, quantitatively different from the preferred eigenvalue ratio of -4:1:3 reported in incompressible turbulence. Furthermore, the strain rate eigenvalue ratio tends to be -1:0:0 in high compression regions, implying the dominance of sheet-like structures. The joint probability distribution function of the invariants for the deviatoric velocity gradient tensor is used to characterize local flow structures conditioned on the local dilatation as well as the distribution of enstrophy production within these flow structures. We demonstrate that strong local compression motions enhance the enstrophy production by vortex stretching, while strong local expansion motions suppress enstrophy production by vortex stretching. Despite these complications, most statistical properties associated with the solenoidal component of the velocity field are found to be very similar to those in incompressible turbulence, and are insensitive to the change of local dilatation. Therefore, a good understanding of dynamics of the compressive component of the velocity field is key to an overall accurate description of highly compressible turbulence.