Parametric instability of the interface between two viscous magnetic fluids

The flat interface solution between two magnetic fluids can be parametrically excited by periodically oscillating magnetic field H0(1+m cos(ωt)) oriented in direction normal to the fluids. The stability problem for the interface of two magnetic viscous fluids has been formulated. Beyond a critical value of wave number kC and a critical value mC of amplitude of excitation, the plane interface becomes unstable and standing waves appear. The solutions for standing waves are found to exist within stability bands in (k,m) plane for a given value of external frequency ω and steady magnetic field H0