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We present two high-order potential flow models for the evolution of the interface in the Rayleigh-Taylor instability in two dimensions. One is the source-flow model and the other is the Layzer-type model which is based on an analytic potential. The late-time asymptotic solution of the source-flow model for arbitrary density jump is obtained. The asymptotic bubble curvature is found to be independent to the density jump of the fluids. We also give the time- evolution solutions of the two models by integrating equations numerically. We show that the two high-order models give more accurate solutions for the bubble evolution than their low- order models, but the solution of the source-flow model agrees much better with the numerical solution than the Layzer model.

HIGH-ORDER POTENTIAL FLOW MODELS FOR HYDRODYNAMIC UNSTABLE INTERFACE