An analytical model of the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers $\left(A_T\right)$ 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 $(A_T=1\mathrm{})$. The model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime when the bubble velocity saturates at $U_b=\sqrt{{2A}_T/\left({1+A}_T\right)\left({g/C}_{g}k\right)}$, where $k$ is the perturbation wave number, $g$ is the interface acceleration, and $C_g=3\mathrm{}$ and $C_g=1\mathrm{}$ for the two-dimensional and three-dimensional geometries, respectively.

• Received 16 November 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.134502