Simulated mixing rates of the Rayleigh-Taylor instability for miscible fluids with physical mass diffusion are shown to agree with experiment; for immiscible fluids with physical values of surface tension the numerical data lie in the center of the range of experimental values. The simulations are based on an improved front tracking algorithm to control numerical surface tension and on improved physical modeling to allow physical values of mass diffusion or surface tension. Compressibility, after correction for variable density effects, has also been shown to have a strong influence on mixing rates. In summary, we find significant dependence of the mixing rates on scale breaking phenomena. We introduce tools to analyze the bubble merger process and confirm that bubble interactions, as in a bubble merger model, drive the mixing growth rate.

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.

Simulations not seen before compare turbulent mixing rates for ideal fluids and for real immiscible fluids with experimental values for the surface tension. The simulated real fluid mixing rates lie near the center of the range of experimental values. A comparison to theoretical predictions relating the mixing rate, the bubble width, and the bubble height fluctuations based on bubble merger models shows good agreement with experiment. The ideal fluid mixing rate is some 50% larger, providing an example of the sensitivity of the mixing rate to physical scale breaking interfacial phenomena; we also observe this sensitivity to numerical scale-breaking artifacts.