Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers

An analytical model of the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers (A(T)) is presented. The model is based on an extension of Layzer's theory Astrophys. J. 122, 1 (1955) previously applied only to the fluid-vacuum interfaces (A(T) = 1). The model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime when the bubble velocity saturates at U(b) = square root of 2A(T)/(1+A(T)) (g/C(g)k), where k is the perturbation wave number, g is the interface acceleration, and C(g) = 3 and C(g) = 1 for the two-dimensional and three-dimensional geometries, respectively.