Vortex disruption by magnetohydrodynamic feedback

In an electrically conducting fluid, vortices stretch out a weak, large-scale magnetic field to form strong current sheets on their edges. Associated with these current sheets are magnetic stresses, which are subsequently released through reconnection, leading to vortex disruption, and possibly even destruction. This disruption phenomenon is investigated here in the context of two-dimensional, homogeneous, incompressible magnetohydrodynamics. We derive a simple order of magnitude estimate for the magnetic stresses --- and thus the degree of disruption --- that depends on the strength of the background magnetic field (measured by the parameter $M$, a ratio between the Alfv\'en speed and a typical flow speed) and on the magnetic diffusivity (measured by the magnetic Reynolds number $\mbox{Rm}$). The resulting estimate suggests that significant disruption occurs when $M^{2}\mbox{Rm} = O(1)$. To test our prediction, we analyse direct numerical simulations of vortices generated by the breakup of unstable shear flows with an initially weak background magnetic field. Using the Okubo--Weiss vortex coherence criterion, we introduce a vortex disruption measure, and show that it is consistent with our predicted scaling, for vortices generated by instabilities of both a shear layer and a jet.