Dynamical model for velocity-gradient evolution in compressible turbulence

Velocity-gradient evolution in compressible turbulence is modelled with an autonomous dynamical system of equations that are able to explain important non-isentropic, Mach-number and viscous effects. This enhanced homogenized Euler equation (EHEE) model is validated against the Burgers equation and direct numerical simulation (DNS) computations at the appropriate limits of Mach number. The EHEE model qualitatively captures crucial nonlinear physical features – especially various dilatational aspects of the flow field – observed in DNS over a range of Mach, Reynolds and Prandtl numbers. The model can serve as the basis of more quantitative statistical and stochastic closure models.