Velocity-gradient dynamics in compressible turbulence: influence of Mach number and dilatation rate

Abstract

The onset of compressibility effects brings about profound changes in the nature of pressure and its consequent influence on velocity-gradient evolution in turbulent flows. In this work we examine the changing action of pressure on velocity-gradient evolution with varying levels of compressibility in decaying isotropic turbulence. The degree of departure from incompressibility is characterized in one of the following three ways: (1) local turbulent Mach number, which is indicative of local balance between inertial and pressure effects; (2) local relative dilatation, which is a measure of the level of compression/expansion rate of a fluid element and (3) global turbulent Mach number, which is a global measure of compressibility of a homogeneous turbulent flow field. It is found that the pressure-Hessian inhibits velocity-gradient steepening at incompressible and subsonic local Mach numbers. In contrast, at higher local Mach numbers, the pressure-Hessian becomes the dominant driver of gradient steepening. Expanding fluid elements (positive dilatation) are generally associated with gentler overall gradients than contracting (negative dilatation) elements. With increasing local turbulent Mach number, the disparity increases as the gradients of contracting elements become steeper. Overall, this work provides important insight into the velocity-gradient dynamics in compressible flows.