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.
Goncharov
V N
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Laboratory for Laser Energetics, Department of Mechanical Engineering, University of Rochester, New York 14623-1299, USA.