Stable and runaway bubble merger in a model for Rayleigh-Taylor unstable interfaces

A statistical model for the growth of bubbles in a Rayleigh-Taylor unstable interface is analyzed. Runaway and uniform growth regimes are observed. Starting from a random configuration, in which neighboring bubbles are uncorrelated, runaway is found to be the expected initial transient with velocities and accelerations growing exponentially. However neighboring bubble correlations develop dynamically, which may lead to a self-limiting regime of uniform growth and constant acceleration. The observed constant acceleration rate is non-universal.