Low-order moments of the velocity gradient in homogeneous compressible turbulence

TL;DR

This paper derives analytic relations for the second and third order moments of the velocity gradient in homogeneous compressible turbulence, extending incompressible flow relations and enabling experimental determination of these moments.

Contribution

It introduces new analytic relations for velocity gradient moments in compressible turbulence, generalizing incompressible flow results and applicable to experimental analysis.

Findings

Relations hold approximately for mixing layers

Provides a method to experimentally determine velocity gradient moments

Extends known incompressible flow relations to compressible turbulence

Abstract

We derive from first principles analytic relations for the second and third order moments of the velocity gradient mij = dui/dxj in compressible turbulence, which generalize known relations in incompressible flows. These relations, although derived for homogeneous flows, hold approximately for a mixing layer. We also discuss how to apply these relations to determine all the second and third moments of the velocity gradient experimentally.