Dynamic expulsion of magnetic flux by vortices

We study the evolution of an initially uniform magnetic field in vortical flows at high magnetic Reynolds numbers. By including the magnetic field's back-reaction on the flow, we extend the kinematic theory of flux expulsion into the dynamical regime. Using an incompressible two-dimensional magnetohydrodynamic model with various vortex configurations and magnetic field strengths, we identify four distinct dynamical regimes. Our results suggest that even a very weak magnetic field can influence flow dynamics, indicating that purely hydrodynamic models may be inadequate for some astrophysical systems.