Linear and Nonlinear Simulations of the Richtmyer- Meshkov Instability in Magnetohydrodynamics

Nonlinear ideal magnetohydrodynamics (MHD) simulations and analysis indicate that the Richtmyer-Meshkov instability (RMI) is suppressed in the presence of a magnetic field in Cartesian slab geometry. We present results of linear and nonlinear MHD simulations of RMI in cylindrical geometry. The linear simulations are performed with a numerical method that is an extension of the method proposed by Samtaney (J. Comput. Phys. 2009). In the absence of a magnetic field, linear analysis indicates that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor growth phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by $\beta={2p}/{B^2} $). For the strongest field case studied ($\beta\approx 2$) we see a significant suppression of the instability. We will present a description of the numerical methods, a complete characterization of the RMI linear stability in cylindrical geometry, and comparisons between linear and nonlinear MHD simulations for field strengths, and azimuthal and axial wavenumbers.