The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics

Abstract

In ideal magnetohydrodynamics MHD, the Richtmyer-Meshkov instability can be suppressed by the presence of a magnetic field. The interface still undergoes some growth, but this is bounded for a finite magnetic field. A model for this flow has been developed by considering the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This was accomplished by analytically solving the linearized initial value problem in the framework of ideal incompressible MHD. To assess the performance of the model, its predictions are compared to results obtained from numerical simulation of impulse driven linearized, shock driven linearized, and nonlinear compressible MHD for a variety of cases. It is shown that the analytical linear model collapses the data from the simulations well. The predicted interface behavior well approximates that seen in compressible linearized simulations when the shock strength, magnetic field strength, and perturbation amplitude are small. For such cases, the agreement with interface behavior that occurs in nonlinear simulations is also reasonable. The effects of increasing shock strength, magnetic field strength, and perturbation amplitude on both the flow and the performance of the model are investigated. This results in a detailed exposition of the features and behavior of the MHD Richtmyer-Meshkov flow. For strong shocks, large initial perturbation amplitudes, and strong magnetic fields, the linear model may give a rough estimate of the interface behavior, but it is not quantitatively accurate. In all cases examined the accuracy of the model is quantified and the flow physics underlying any discrepancies is examined.

Converging cylindrical shocks in ideal magnetohydrodynamics

“…The verifications tests include: linear wave propagation tests, regular shock refraction at a density interface in MHD (this example is truly a multidimensional verification of the solution in the neighborhood of shock refraction and described in thorough detail in Wheatley et al 25 ), and magnetic reconnection. 23 Furthermore, convergence tests in a variety of contexts have been presented in Wheatley et al 17,26 For completeness, we present the equations and numerical method below.…”

Effects of seed magnetic fields on magnetohydrodynamic implosion structure and dynamics

“…13 Samtaney 14 showed that growth of the MHD RMI is suppressed under a magnetic field normal to the material interface in certain planar flow configurations and Wheatley et al [15][16][17] subsequently investigated the mechanism of this suppression. Further research also examined the suppression of the RMI by transverse 18,19 and oblique 20 seed fields for planar MHD flows. Characterizing the dynamics of MHD implosions under the effect of seed fields would assist in a fundamental investigation of the MHD RMI in cylindrical or spherical converging flows, to complement the literature [21][22][23][24] on its hydrodynamic counterpart.…”

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

“…These equations are already expressed in non-dimensional form by choosing a reference density, pressure, and length scale (for example, see Wheatley et al 12 for the non-dimensionalization). F(U), G(U), and H(U) are the fluxes of mass, momentum, magnetic flux, and energy in the r, θ, and z directions given as…”

“…In these MHD investigations, the initial seed magnetic field was parallel to the incident shock front. Wheatley et al 12 investigated the case where the magnetic field was parallel to the interface, i.e., there was no normal component of the magnetic field at the interface, and found oscillatory solutions with the RMI still being suppressed. In these prior MHD investigations of RMI, the geometry was planar.…”