Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Mechanical Engineering Program
Physical Sciences and Engineering (PSE) Division
KAUST Grant NumberURF/1/2162-01
Online Publication Date2016-03-09
Print Publication Date2016-03
Permanent link to this recordhttp://hdl.handle.net/10754/601341
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AbstractNumerical simulations and analysis indicate that the Richtmyer-Meshkov instability(RMI) is suppressed in ideal magnetohydrodynamics(MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate 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 instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2p/B^2_r) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.
CitationLinear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics 2016, 28 (3):034106 Physics of Fluids
SponsorsThis work was supported by the KAUST Office of Sponsored Research under Award No. URF/1/2162-01.
JournalPhysics of Fluids