Linear analysis of magnetohydrodynamic Richtmyer–Meshkov instability in cylindrical geometry for double interfaces in the presence of an azimuthal magnetic field

Abstract

Richtmyer–Meshkov instability (RMI) occurs when a shock wave impulsively accelerates a perturbed density interface between different fluids. The present work investigates the suppression of RMI of double interfaces in terms of linear analysis in cylindrical geometry. An exponential increase/decrease in a growth rate is related to the Rayleigh–Taylor instability that occurs without a magnetic field as the lighter fluid penetrates the heavier one. The research program of inertial confinement fusion is one of the advanced applications where fluid mixing is the main mechanize of producing energy. The investigations represent the effects of different Atwood numbers or magnetic strengths on the suppression of the instabilities. Three different cases are considered with the hydrodynamics and magnetohydrodynamics (MHD). In the MHD case, the instability's growth rate reduces proportion to the Atwood ratios or the strength of the magnetic field. Two waves are interfering and running parallel and anti-parallel to the interfaces and transport the generated vorticity at the interfaces, causing the perturbed interfaces' growth rate to oscillate in time, which is the essential suppression mechanism.