Self-similarity of Rayleigh–Taylor mixing rates

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We establish a renormalized self-similar scaling law for fluid mixing in the deeply compressible regime. Compressibility introduces a new length scale into the mixing but our time dependent analysis of the density contrast largely removes the effects of this length scale, so that self-similarity is maintained. Dynamically induced density changes lead to a dynamic Atwood number to measure density contrasts. We improve previous density renormalizations to allow a unified treatment of mass diffusion and compressible density stratification in a range of weakly to strongly compressible three-dimensional multimode Rayleigh–Taylor simulations. Some of these simulations use front tracking to prevent numerical interfacial mass diffusion, while the others are untracked and diffusive. Using the dynamic Atwood number A(t) as opposed to the customary t=0 Atwood number A=A(t=0) to define growth rate constants, approximate universality of the mixing rate constant αb is obtained at low compressibility. Furthermore, earlier results giving consistent simulation, experiment and theory for nearly incompressible mixing, are now extended to show renormalized self-similar scaling with increases in the mixing rates for simulations of highly compressible mixing. The renormalized (i.e., dynamic Atwood number corrected) mixing rates of the diffusive and nondiffusive simulations agree, and show very similar compressibility dependence, with self-similar mixing rates tripling as compressibility becomes strong.