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

Abstract

We derive from first principles analytic relations for the second- and third-order moments of $\boldsymbol{\mathsf{m}}$ , the spatial gradient of fluid velocity $\boldsymbol{u}$ , $\boldsymbol{\mathsf{m}} = \nabla \boldsymbol{u}$ , 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-order moments of the velocity gradient experimentally for isotropic compressible turbulence.