The Rayleigh–Taylor instability in magnetic fluids and nonlinear interfacial waves

Abstract

The nonlinear evolution of a horizontal interface separating two magnetic fluids of different densities, including surface tension effects, is investigated. The fluids are considered incompressible and inviscid, being stressed by the force of gravity, the normal magnetic field, and a constant acceleration in a direction normal to the interface. The method of multiple-scale perturbations is used to obtain two nonlinear Schrödinger equations describing the behavior of the perturbed system. The stability of the perturbed system is discussed both analytically and numerically, and the stability diagrams are obtained. We also obtain the nonlinear cutoff wave number, which separates the region of stability from that of instability.