Velocity gradient invariants and local flow-field topology in compressible turbulence

Abstract

The effect of compressibility on velocity gradient structure and the related flow-field patterns/topology is investigated using direct numerical simulation data. To clearly isolate compressibility effects, the behavior is investigated as a function of local level of dilatation. Importantly, dilatation-conditioned behavior is found to be independent of Mach and Reynolds numbers. Not surprisingly, at low dilatation level, velocity gradient structure and local flow topology are similar to incompressible turbulence. At high dilatation levels, however, the behavior is quite different. A recently developed velocity gradient evolution equation – Homogenized Euler Equation (HEE) – qualitatively captures many of the observed features of compressible turbulence.