| As an incident shock wave collides with a material interface between two fluids of different densities, the interface becomes unstable. Small disturbances at the interface start to grow. This interfacial instability is known as a Richtmyer-Meshkov instability and is the subject of this work.;The method of front tracking has been used to perform a systematic numerical study of the Richtmyer-Meshkov instability in cylindrical geometry for both the imploding and the exploding cases, including the cases of the incident shock wave imploding (exploding) from a heavy to light fluid phase or a light to heavy fluid phase.;The curved geometry complicates the system considerably. For example, the unperturbed system does not have an analytic solution; the unperturbed system in plane geometry does; the occurrence of re-acceleration or reshock at the material interface caused by the waves reflecting back from the origin is unavoidable in curved geometry. This paper addresses those issues.;In addition, a detailed study is presented of small amplitude perturbation solutions, nonlinear solutions, the effect due to the number of fingers at initialization, the effect of the initial perturbation amplitude, the phenomenon of phase inversion and twice phase inversions, the growth rate of the spikes and bubbles formed by the instability (including the overall growth rate), and the similarity scaling law for Richtmyer-Meshkov instabilities by shocks of large Mach number.;So far theoretical, numerical and experimental studies of the instability have been performed in plane geometry. In most physical applications--such as, inertial confinement fusion and supernova--the Richtmyer-Meshkov instability occurs in curved geometry.;A qualitative understanding of this system has been achieved. |
