Interface instabilities and entrainment.

The highly nonlinear (late time) regime of bubble amalgamation for a Rayleigh-Taylor unstable interface is studied. The latter instability is a gravity or acceleration driven instability of an interface between two fluids of different densities. The statistical model developed by D.H. Sharp and J.A. Wheeler in 1961 is utilized. In this model the dynamics is completely specified by the motion of a single bubble and the interaction (merger) of a pair of bubbles. The qualitative behaviour of the model is discussed. Numerical solutions of the two fluid Euler equations for a gamma law gas are presented which show how to determine the parameters in the statistical model.