Simulations of Single-mode Richtmyer-Meshkov and Rayleigh-Taylor Instabilities in Spherical Geometries

We describe recent numerical simulations of the single-mode Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities in a spherical geometry. The simulations were performed using the astrophysical FLASH code in two- and three-dimensions. Our results are compared to previously published simulation results\footnote{Sakagami, H. and Nishihara, K., Phys. Rev. Lett. 65, 432, 1990a.} and linear\footnote{K.O. Mikaelian, Phys. Rev. A., 42 (6), 3400, 1990.} and nonlinear\footnote{D. S. Clark, M. Tabak, Phys. Fluids 18, 064106, 2006.} theories. The RM problem was setup with an air-SF6 interface, subject to a Mach 1.2 shock, and a convergence ratio of 10. We studied the variation of initial amplitude, shock strength, and convergence ratio. We expect the single-mode results to inform multimode growth in applications through bubble merger and competition mechanisms.