Bubble merger model for the nonlinear Rayleigh-Taylor instability driven by a strong blast wave

Abstract

A bubble merger model is presented for the nonlinear evolution of the Rayleigh-Taylor instability driven by a strong blast wave. Single bubble motion is determined by an extension of previous buoyancy-drag models extended to the blast wave driven case, and a simple bubble merger law in the spirit of the Sharp-Wheeler model allows for the generation of larger scales. The blast wave driven case differs in several respects from the classical case of incompressible fluids in a uniform gravitational field. Because of material decompression in the rarefaction behind the blast front, the asymptotic bubble velocity and the merger time depend on time as well as the transverse scale and the drive. For planar blast waves, this precludes the emergence of a self-similar regime independent of the initial conditions. With higher-dimensional blast waves, divergence restores the properties necessary for the establishment of the self-similar state, but its establishment requires a very high initial characteristic mode number and a high Mach number for the incident blast wave.