| In this thesis we present two separate perturbation expansions modeling the effects of a twice-shocked interface in cartesian coordinates, and those of a singly-shocked interface in spherical coordinates. These are performed using computer algebra software, and within the confines of the impulsive, incompressible, and irrotational flow model.; The reshocking problem consists of a comparison between a singly-shocked interface of unit shock strength, and one in which two half-strength shocks are introduced, separated by varying time intervals. We find for the case of positive Atwood number, that two half-strength shocks magnify the instability over the single shock case, while for negative Atwood number the instability can be substantially suppressed. For this latter case, we propose a means whereby the instability may be minimized by choosing an appropriate time interval between the incidences of the first and second shocks.; The instability is also studied in spherical coordinates via a two term perturbation expansion, with the hopes of shedding some light on the effects of spherical curvature on the amplitudes of the spike and bubble. |
