Evolution of a vortex in a rotating conducting fluid

In this paper we examine the evolution of an isolated vortex in a rotating conducting fluid which is threaded by a uniform magnetic field. Magnetic and rotation forces dominate over nonlinear and viscous effects and the flow is incompressible. The study is formulated in terms of an unbounded initial value problem with emphasis on the asymptotic solutions at large time. When the homogeneous imposed magnetic field is normal to the rotation axis it is observed that inertial waves, induced by the prescribed initial condition, transport energy on planes perpendicular to the magnetic field to form a series of counter-rotating travelling eddies. Transport along magnetic field lines occurs by pseudo-diffusion, common at low magnetic Reynolds numbers, and by wave propagation from those inertial waves that survive the strong magnetic damping.