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

We have developed a theoretical analysis to systematically study the late-time evolution of the Rayleigh-Taylor instability in a finite-sized spatial domain. The nonlinear dynamics of fluids with similar and contrasting densities are considered for two-dimensional flows driven by sustained acceleration. The flows are periodic in the plane normal to the direction of acceleration and have no external mass sources. Group theory analysis is applied to accurately account for the mode coupling. Asymptotic nonlinear solutions are found to describe the inter-facial dynamics far from and near the boundaries. The influence of the size of the domain on the diagnostic parameters of the flow is identified. In particular, it is shown that in a finite-sized domain the flow is slower compared to the spatially extended case. The direct link between the multiplicity of solutions and the inter-facial shear function is explored. It is suggested that the inter-facial shear function acts as a natural parameter to the family of analytic solutions.