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

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.