Rayleigh–Taylor instability in the presence of an oscillating magnetic field permeating both heavier and lighter fluids

Rayleigh–Taylor instability of a heavy fluid, supported by a lighter one, in the presence of a uniform, horizontal, and oscillating magnetic field permeating both the fluids is studied. The fluids are taken as inviscid, uniform, incompressible, and infinitely conducting. The amplitude of the oscillating part of the field is taken to be small compared with its steady part. The conditions under which the model calculations are valid are obtained first. The dispersion relation is obtained in the form of a third-order differential equation, with time as the independent variable and with periodic coefficients, for the vertical displacement of the surface of separation of the two fluids from its equilibrium position. The oscillatory magnetic field of frequency ω and steady part H0 has a stabilizing influence on a mode of disturbance which is unstable in a steady field of strength H0. The oscillatory field has either no stabilizing influence or a destabilizing influence in some special cases. However, for reliable results in these cases, a more realistic model of Rayleigh–Taylor instability should be considered taking the finite conductivity of the fluid into account.