Effect of compressibility on the local flow topology in homogeneous shear turbulence

The local flow topology based on the invariants of the velocity gradient tensor in stationary compressible homogeneous shear turbulence (HST) is studied by numerical simulations. In the compressible homogeneous shear turbulence, local compressibility decreases the flow volume fraction occupied by the focal, eddy, and shear flow structures both in compression regions and in strong expansion regions. The joint probability density function (pdf) of the second and third invariants of the deviatoric velocity gradient tensor exhibits a similar teardrop shape as for the homogeneous isotropic turbulence (HIT), and the tail of the joint pdf alongside the right branch of the null-discriminant curve is elongated as the turbulent Mach number increases. When conditioned on dilatation, the statistical preference for points in the fourth quadrants of the joint pdf is enhanced significantly by the compression motion. It is found that the shape of the joint pdf shows a good similarity between HST and HIT in strong compression regions, which is dependent on the root mean square dilatation, rather than the turbulent Mach number. In strong expansion regions, the shape of the joint pdf in HST has a long tail in the third quadrant, which is related to sheetlike expansion structures and does not exist in HIT. After the Helmholtz decomposition, the properties of local flow topology 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 in local dilatation and turbulent Mach number.