Evolution of a vortex in a magnetic field

Abstract

The evolution of a single vortex in an electrically-conducting liquid, subject to a uniform magnetic field acting parallel to the axis of the vortex, is investigated by an order-of-magnitude analysis and a numerical model. The non-linear phase of decay, wherein the Lorentz and the inertial forces are of the same order of magnitude, is studied in detail. As the kinetic energy decays primarily due to Joule dissipation, the vortex evolves in such a way that the component of angular momentum parallel to the direction of the magnetic field is conserved. If the true interaction parameter, Nt , which denotes the actual ratio of the Lorentz to the inertial forces, is assumed to be a constant of order unity in the non-linear regime, the evolution of the vortex can be fully described. The above assumption is proven to be correct not only from the values of Nt obtained in the numerical simulation, but also from the good agreement between the theoretical and numerically-obtained energy decay laws for the non-linear phase, at finite time. In addition, the true interaction parameter proves to be useful in estimating the minimum magnetic field strength required for stable evolution of a swirling vortex.