GALCIT Colloquium (PhD thesis talk)

The Richtmyer-Meshkov instability (RMI) describes the unstable behavior developed after the interaction of a perturbed interface separating two materials of different densities with a compression shock. This phenomenon has been observed in multiple fields, such as magneto-hydrodynamics, astrophysics, and nuclear fusion. An investigation of the RMI for both planar and converging geometries will be presented for the case in which at least one of the materials is an elastic-plastic solid. Analytical and computational techniques based on an Eulerian formulation of the equations of motion will be discussed. Topics covered will include the application of Whitham's shock dynamics in solid media to converging shocks in cylindrical and spherical geometries, an analytical model describing the effect of impulsive acceleration on a perturbed interface separating different elastic materials, and RM flow for elastic-plastic materials in both planar and converging geometries using numerical simulations. For the latter flow, simulations suggest an initial growth rate of interface perturbations that is similar in parameter-dependency and value to that of a gas-gas interface, whereas the long-term behavior depends largely on the material properties and initial parameters. As the shock strength increases or the material strength decreases, the interface behaves in an unstable manner, similar to a fluid. In some cases, formation of ejecta is observed. As the strength of the material increases, the interface amplitude can saturate at long times, exhibiting a behavior similar to the elastic case.