Bubble Motion in the Nonlinear Rayleigh-Taylor Instability

An approximate description of Rayleigh-Taylor bubble motion is given in terms of a Fourier series expansion of the velocity potential. Consistent predictions for the steady-state velocity, the bubble curvature, and the first three Fourier coefficients are obtained. A simple model of nonsteady bubble motion is developed. It is found that an exponential amplitude dependence is responsible for a rapid transition to the steady-state regime when the amplitude becomes larger than $\sim \frac{\lambda }{6\pi }$.