2012ApJ...744..184D

The problem of interest is the unstable growth of structure at density transitions affected by blast waves, which arise in natural environments such as core-collapse supernovae and in laboratory experiments. The resulting spikes of dense material, which penetrate the less dense material, develop broadened tips, but the degree of broadening varies substantially across both experiments and simulations. The variable broadening presumably produces variations in the drag experienced by the spike tips as they penetrate the less dense material. The present work has used semianalytic theory to address the question of how the variation in drag might affect the spike penetration, for cases in which the post-shock interface deceleration can be described by a power law in a normalized time variable. It did so by following the evolution of structure on the interface through the initial shock passage, the subsequent small-amplitude phase of Rayleigh-Taylor instability growth, and the later phase in which the spike growth involves the competition of buoyancy and drag. In all phases, the expansion of the system during its evolution was accounted for and was important. The calculated spike length is strongly affected by the drag attributed to spike tip broadening. One finds from such a calculation that it is not unreasonable for narrow spikes to keep up with the shock front of the blast wave. The implication is that the accuracy of prediction of spike penetration and consequent structure by simulations very likely depends on how accurately they treat the broadening of the spike tips and the associated drag. Experimental validation of spike morphology in simulations would be useful.