Objective Transport Barriers to the Magnetic Flux and Electromagnetic Energy in Magnetohydrodynamics

Recent work has identified objective (frame-indifferent) material barriers that inhibit the flux of dynamically active vectorial quantities (i.e. linear momentum and vorticity) in Navier-Stokes flows. In the context of magnetohydrodynamics (MHD), the magnetic field is directly coupled to the evolution of the velocity field through the Lorentz force and therefore qualifies as a dynamically active vector field. Here, we propose to identify material barriers to the transport of active vectorial quantities in MHD such as the electromagnetic energy, i.e. poynting vector. We additionally identify material surfaces that pointwise inhibit the magnetic flux over some time-interval. A general data-driven algorithm is developed for locating objective barriers that minimize the flux of these vectorial quantities. The identified hidden coherent structures highlight important pathways in MHD responsible for the energy transport in the magnetic field. We illustrate the results on three-dimensional homogenous isotropic MHD simulations from the John Hopkins Turbulence Database. The transport barriers resulting from the magnetic field are finally compared to advective and active kinematic barriers.