Sustained oscillating regime in the two-dimensional magnetic Rayleigh–Taylor instability

Abstract

There exists an oscillating stable solution to the single-mode two-dimensional Rayleigh–Taylor instability when a mean magnetic field B0 is imposed parallel to the interface, within the Boussinesq approximation. The characteristic frequency Ω and averaged deformation amplitude of the interface L¯ can be predicted by analyzing the stability of a background piecewise density profile. Comparisons with direct numerical simulations of the Navier–Stokes equations, under the magnetohydrodynamics approximation, yield satisfactory results, with deviations of ±5% for Ω and ±20% for L¯. By combining these theoretical predictions with numerical observations, simplified models are proposed to estimate the averaged amplitude and characteristic frequency of the oscillating solution.