Material Barriers to the Diffusive Magnetic Flux in Magnetohydrodynamics

TL;DR

This paper extends the concept of frame-indifferent material barriers from Navier-Stokes flows to magnetohydrodynamics, identifying barriers that inhibit magnetic flux diffusion in turbulent MHD flows and providing an algorithm for their extraction.

Contribution

It introduces a novel theoretical framework for active material barriers in MHD flows and develops an algorithm to extract these barriers from turbulence data.

Findings

Identified frame-indifferent barriers to magnetic flux diffusion in MHD.

Extended active barrier theory from Navier-Stokes to MHD flows.

Developed an algorithm for barrier extraction from turbulence data.

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 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.