We investigate the linear, nonlinear and turbulent development of the Richtmyer-Meshkov instability in a spherically convergent geometry. The three-dimensional simulations were performed using the astrophysical FLASH code [1], with a resolution of 2560 x 512 x 512 in the radial, azimuthal and polar directions for the multimode case. The perturbations at the interface between an outer shell of light fluid and an inner shell of heavy fluid were specified according to single-mode or multimode spherical harmonic functions . A third, fictitious layer is necessary in these Eulerian calculations to simulate an external shell that sustains the incident shock, thus mimicking an implosion. The modification of the linear growth rate due to convergence was compared with the linear model of [2], while the growth rates during the nonlinear stage were verified against potential flow models. We present results from multimode initial perturbations that lead to the formation of a turbulent front at late times. The growth of the turbulent mixing layer under the effect of the reflected shock is also investigated. The validity of the above results is examined at different Atwood numbers.
[1] Fryxell, B. et al., Astrophys. J. Suppl., 131 (1), 2000, 273.
[2] Mikaelian, Karnig O., Phys. Rev. A 42 (6), 1990, 3400.
