Self-similar solutions of asymmetric Rayleigh-Taylor mixing

Abstract

The late nonlinear phase of the Rayleigh-Taylor instability is characterised by the self-similar expansion of the instability mixing layer given at late times by h ≈ αAgt2 . In this paper we present a new model of this mixing layer, based on a piecewise step function approximation where the main constraint imposed is conservation of mass. This model is used to predict the structuring of the mean density of the layer and the asymmetry of the layer for a given Atwood number. By comparing to experimental data and simulation results we confirmed the predictions of the model for the asymmetry of the α values. Our model leads to a simple correction to the formulation of the expansion of the mixing layer which is consistent with an α for a given system that is independent of the density difference for both immiscible fluids and miscible fluids with low mass diffusion. As the model predicts the mean density profile, it can be used to state the energy released by the instability