Evolution of a vortex in a magnetic field

The evolution of a single vortex in an electrically-conducting liquid, subj ect 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. Th e non-linear phase of decay, wherein the Lorentz and the inertial forces ar e of the same order of magnitude, is studied in detail. As the kinetic ener gy 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, N-t, 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 co rrect not only from the values of N-t obtained in the numerical simulation, but also from the good agreement between the theoretical and numerically-o btained energy decay laws for the non-linear phase, at finite time. In addi tion, the true interaction parameter proves to be useful in estimating the minimum magnetic field strength required for stable evolution of a swirling vortex. (C) 2000 Editions scientifiques et medicales Elsevier SAS.