Rayleigh–Taylor and Richtmyer–Meshkov instabilities in the presence of an inclined magnetic field

Abstract

A unified and analytical model is developed to study the effects of an inclined magnetic field on magneto-Rayleigh–Taylor (MRT) and magneto-Richtmyer–Meshkov (MRM) instabilities in ideal magnetohydrodynamics. Unlike either a horizontal or a vertical magnetic field is present, the decay modes possess decaying and oscillation behaviors together. The vorticity transportation is analyzed. The dispersion relations are derived, and some interesting phenomena are observed. For a small R that represents the ratio of the magnetic field strength, or equivalently, the inclination θ, the growth rate of MRT instabilities resembles the case when a vertical magnetic field is present. For a large R, the growth rate resembles to the case when a horizontal magnetic field exists. The maximum growth rate becomes strongly dependent on At instead of on R. Furthermore, analytical expression is obtained for the MRM instability by using the impulsive accelerated model. The decaying and oscillating rates of the perturbed amplitude are explicitly related to θ. For two limiting cases, with either the vertical or the horizontal magnetic field existing, our results retrieve previous one of the theoretical analyses and numerical simulations. Generally, the asymptotic amplitude becomes independent of the wave number of the initial perturbation in the MRM instability. These findings regarding magneto-hydrodynamic interfacial instabilities in an inclined magnetic field could provide physical insights for magnetically driven targets and astrophysical observations. This analytical model is easily expanded to investigate the effects of finite thickness of magnetic slab and sheared magnetic field in relevant to high-energy-density physics and to astrophysics.