Scale-invariant regime in Rayleigh-Taylor bubble-front dynamics

A statistical model of Rayleigh-Taylor bubble fronts in two dimensions is introduced. Float and merger of bubbles lead to a scale-invariant regime, with a stable distribution of scaled bubble radii and a constant front acceleration. The model is solved for a simple merger law, showing that a family of such stable distributions exists. The basins of attraction of each of these are mapped. The properties of the scale-invariant distributions for various merger laws, including a merger law derived from the Sharp-Wheeler model, are analyzed. The results are in good agreement with computer simulations. Finally, it is shown that for some merger laws, a runaway bubble regime develops. A criterion for the appearance of runaway growth is presented.