Single-mode dynamics of the Rayleigh-Taylor instability at any density ratio.

The behavior of a periodic array of Rayleigh-Taylor bubbles (and spikes) of wavelength lambda is investigated at different density ratios using three-dimensional numerical simulations. The scaled bubble and spike velocities (v(b,s)/sqrt[Aglambda/2]), are found to vary with the Atwood number A, and are compared with recent potential flow theories. Simulations at different grid resolutions reveal that the convergence rates of bubble velocities improve with increasing A, while the converse holds true for spike velocities. The asymptotic radius of curvature at the bubble tip is found to be independent of A, consistent with potential flow theory. These results are useful in validating potential flow theory models of the nonlinear stage of the Rayleigh-Taylor instability.