A RENORMALIZATION-GROUP SCALING ANALYSIS FOR COMPRESSIBLE 2-PHASE FLOW

Computational solutions to the Rayleigh-Taylor fluid mixing problem, a s modeled by the two-fluid two-dimensional Euler equations, are presen ted. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a renorma lization group analysis. The computations, carried out with the front tracking method on an Intel iPSC/860, are highly resolved and statisti cal convergence of ensemble averages is achieved. The computations are consistent with the experimentally observed growth rates for nearly i ncompressible flows. The dynamics of the interior portion of the mixin g zone is simplified by the use of scaling variables. The size of the mixing Lone suggests fixed-point behavior. The profile of statistical quantities within the mixing zone exhibit self-similarity under fixed- point scaling to a limited degree. The effect of compressibility is al so examined. It is found that, for even moderate compressibility, the growth rates fail to satisfy universal scaling, and moreover, increase significantly with increasing compressibility. The growth rates predi cted from a renormalization group fixed-point model are in a reasonabl e agreement with the results of the exact numerical simulations, even for flows outside of the incompressible limit.