The magnetohydrodynamic Richtmyer-Meshkov instability: The transverse field case

The Richtmyer-Meshkov instability occurs when a perturbed interface between fluids of different densities is impulsively accelerated, typically by a shock wave. It is important in a number of applications including inertial confinement fusion, astrophysical phenomena and fuel-air mixing in scramjets. When the materials involved are in the plasma state, it has been shown that the instability can be suppressed by a magnetic field normal to the interface. The linearized case where the magnetic field is parallel to the interface has also been modelled analytically, but utilising a non-equilibrium initial condition. Here, we present an alternative model based on solving the linearized incompressible initial value problem with an equilibrium initial condition. This results in a simpler model for the interface behaviour that illustrates the effect of the impulsive acceleration only. The flow predicted by the incompressible model is compared to the results of two-dimensional, impulsively accelerated, compressible magnetohydrodynamic (MHD) simulations, which was not done previously for the parallel field case. The instability is found to also be suppressed in the parallel field case. The vortex sheet that is present on the interface immediately after the impulse breaks up into waves travelling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves, as they propagate, causes the perturbation amplitude of the interface to oscillate in time. This interface behaviour is accurately predicted by the linear model for the conditions investigated.