Material Barriers to the Diffusion of Magnetic Field Lines

Recent work has identified objective (frame-indifferent) material barriers that inhibit the flux of dynamically active vectorial quantities (i.e. linear momentum, angular momentum and vorticity) in Navier-Stokes flows. In the context of magnetohydrodynamics (MHD) the magnetic field vector is directly coupled to the evolution of the velocity field through the Lorentz force and therefore qualifies as a dynamically active vector field. In this work, we identify active Eulerian and Lagrangian barriers that block the diffusion of magnetic field lines in two-dimensional (2D) and three-dimensional (3D) MHD turbulence. These distinguished material surfaces provide physics-based and frame-indifferent active magnetic coherent structures that locally divide the space into two regions with minimal diffusion of magnetic field lines. In 2D, these barriers are directly connected to the electric current density. We propose an algorithm for the automated identification of such barriers from 2D and 3D numerical data of MHD turbulence simulations.