Late-time evolution of Rayleigh-Taylor instability in a domain of a finite size

We develop the theoretical analysis to systematically study the late-time evolution of Rayleigh-Taylor instability in a domain of a finite size. 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 interface dynamics far from the boundaries 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 size the domain the flow is decelerating compared to spatially extended case. A close analysis of the shear present at the interface of the fluids is also studied both for a domain of a finite size and in the limit of an infinite domain. It is shown how the interfacial
shear acts as a natural parameter to the family of solutions. The theory outcomes for the numerical modelling and design of experiments on Rayleigh-Taylor instability are discussed.