  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 to the diffusive transport of the magnetic field 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.
