The stabilization of a viscous interface stressed by an oscillating
magnetic field is investigated. Account is taken of the influence of free-surface
currents on the effective solidly rotating fluid column. Only azimuthal modes
are considered in the linear perturbation. The dispersion relation with or
without free-surface currents is obtained in the form of a linear Mathieu
equation with complex coefficients. It is found that there is a nonlinear relation
between the surface current density and both the stratified viscosity and the
stratified azimuthal magnetic field. The surface currents disappear on the
interface of the fluid column when the stratified magnetic field has the value of
unity. At this value, a coupled parametric resonance occurs in the absence of
angular velocity. The magnetic field plays a stabilizing role. This role increases
with increasing surface currents. The angular velocity plays a destabilizing role,
while the field frequency plays a stabilizing role and acts against the angular
velocity. The stratified viscosity plays a damping role in the presence of the
surface current density, while, in the absence of a surface current, it plays two
opposite roles corresponding to the presence or absence of the field frequency.
A set of graphs are used to illustrate the relation between the presence of free-surface
currents and both the viscosity and the azimuthal magnetic field.
Steady flow of one uniformly rotating fluid layer above another immiscible uniformly rotating fluid layer
