Simple Model for the Nonlinear Evolution of the Rayleigh-Taylor Instability

A simple Lagrangean extrapolation scheme for modeling of the nonlinear development of the Rayleigh-Taylor instability is suggested. The model incorporates Whitham's small-amplitude formulas, given up to the cube of the wave amplitude, and extends them such that multivalued contours are obtained after a while and a bubble eventually detaches itself from the fluid. The initial stages of the bubble evolution found in this way are very similar to those recently obtained numerically by other authors.