Computational solutions to the Rayleigh–Taylor fluid mixing problem, as modeled by the two‐fluid two‐dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a renormalization group analysis. The computations, carried out with the front tracking method on an Intel iPSC/860, are highly resolved and statistical convergence of ensemble averages is achieved. The computations are consistent with the experimentally observed growth rates for nearly incompressible flows. The dynamics of the interior portion of the mixing zone is simplified by the use of scaling variables. The size of the mixing zone 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 also 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 predicted from a renormalization group fixed‐point model are in a reasonable agreement with the results of the exact numerical simulations, even for flows outside of the incompressible limit.