Nonlinear Rayleigh--Taylor stability with mass and heat transfer

The nonlinear Rayleigh-Taylor stability of a liquid-vapor system was studied using a simplified formulation of the problem. The method of multiple scale expansion was employed for the investigation. It was found that when the heat transfer rate is strong enough, the classically unstable system is stabilized by the nonlinear effect and the effect of mass and heat transfer across the interface. The size of the bubbles detached from the interface can also be estimated when the heat transfer rate is moderately strong. The problem was also studied by the variational method, which corroborates basically the same conclusion