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We have developed a theoretical analysis to systematically study thelate-time evolution of the Rayleigh-Taylor instability in a finite-sizedspatial domain. The nonlinear dynamics of fluids with similar and contrastingdensities are considered for two-dimensional flows driven by sustainedacceleration. The flows are periodic in the plane normal to the direction ofacceleration and have no external mass sources. Group theory analysis isapplied to accurately account for the mode coupling. Asymptotic nonlinearsolutions are found to describe the inter-facial dynamics far from and near theboundaries. The influence of the size of the domain on the diagnosticparameters of the flow is identified. In particular, it is shown that in afinite-sized domain the flow is slower compared to the spatially extended case.The direct link between the multiplicity of solutions and the inter-facialshear function is explored. It is suggested that the inter-facial shearfunction acts as a natural parameter to the family of analytic solutions.

Early- and late-time evolution of Rayleigh-Taylor instability in a finite-sized domain by means of group theory analysisAnnie Naveh