Material barriers to the diffusive magnetic flux in magnetohydrodynamics

Abstract

Recent work has identified objective (frame-indifferent) material barriers that inhibit the transport of dynamically active vectorial quantities (such as linear momentum, angular momentum and vorticity) in Navier–Stokes flows. In magnetohydrodynamics (MHD), a similar setting arises: the magnetic field vector impacts the evolution of the velocity field through the Lorentz force and hence is a dynamically active vector field. Here, we extend the theory of active material barriers from Navier–Stokes flows to MHD flows in order to locate frame-indifferent barriers that minimize the diffusive magnetic flux in turbulent two-dimensional and three-dimensional MHD flows. From this approach we obtain an algorithm for the automated extraction of such barriers from MHD turbulence data. Our findings suggest that the identified barriers inhibit magnetic diffusion, separate electric current sheets and organize the transport of the magnetic energy.