Ferromagnetic rotating Couette flow: the role of magnetic viscosity

Abstract

A theory is constructed for rotating plane Couette flow of ferrofluid that is subject to the field generated by a periodic array of magnets. The system that is analysed contains a substantial lateral magnetic buoyancy, or magnetic gravity, allowing the configuration to be used in experimental studies of stratified shear flows in a connected geometry.

However, the spatial variation of the magnetic vector field of the magnet stack leads to magnetically generated wavy flows via the action of flow vorticity on the particle orientation in the suspension. The basic rotating Couette flow instabilities may also be affected by the same mechanism, which is sometimes referred to as rotational or ‘magnetic viscosity’. Theoretical calculations show that the directly excited wavy flows are generally small, for anticipated experimental conditions, except when they resonate with the natural linear instabilities of the Couette flow. A weakly nonlinear analysis is carried out in order to predict the behaviour in these cases. Magnetic effects stabilize the fundamental roll instability of rotating Couette flow by about 10% for a typical laboratory realization.