The Dynamic Expulsion of Magnetic Flux by Vortices

We study numerically the dynamical evolution of two different vorticity arrays with an initially uniform magnetic field in two-dimensional incompressible magnetohydrodynamics. We concentrate particularly on the role of the strength of the background magnetic field, which is always assumed weak in the sense that its energy is much less than the kinetic energy of the vortical flows. Within the context of a weak background field, we are able to identify four distinct regimes. When the field is so weak that the back-reaction of the Lorentz force can be ignored (the kinematic regime), classical flux expulsion occurs. As the field strength is increased, the first signs of the dynamical influence of the small-scale field generated is in the disruption of vortex filaments, with flux expulsion still occurring in the vortex cores. A further increase in field strength leads to the regime of vortex disruption, in which the magnetic field is expelled, but is then of sufficient strength to disrupt or destroy the vortices. For yet stronger fields, even the large-scale field can be sufficiently strong to be dynamically active; flux expulsion is then prevented and the field is dynamically active throughout the evolution. Furthermore, in the case of a row of vortices, we show that the orientation of the background field significantly influences the evolution, especially at higher field strengths.