Two-phase flow analysis of self-similar turbulent mixing by Rayleigh–Taylor instability

The evolution of a randomly perturbed interface between unbounded incompressible fluids undergoing Rayleigh–Taylor instability is analyzed numerically and theoretically. Two-dimensional simulation results, obtained with an interface tracking code, are presented and compared with a theoretical model based on Young’s two-phase flow description of the mixing process. The simplifications implied by self-similarity and by high drag enable simple analytic results to be obtained for the profiles of the average volume fractions and velocities of the two materials as a function of penetration depth. Agreement of the analytic results with the simulation data is demonstrated for a wide range of density ratios.