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Mixing of passive scalars in compressible turbulence does not obey the sameclassical Reynolds number scaling as its incompressible counterpart. We firstshow from a large database of direct numerical simulations that even thesolenoidal part of the velocity field fails to follow the classicalincompressible scaling when the forcing includes a substantial dilatationalcomponent. Though the dilatational effects on the flow remain significant, ourmain results are that both the solenoidal energy spectrum and the passivescalar spectrum scale assume incompressible forms, and that the scalar gradientaligns with the most compressive eigenvalue of the solenoidal part, providedthat only the solenoidal components are used for scaling in a consistentmanner. Minor modifications to this statement are also pointed out.

Solenoidal scaling laws for compressible mixing