2D models for MHD flows

TL;DR

This paper introduces a refined 2D model for low magnetic Reynolds number MHD flows that captures small three-dimensional effects, improving upon previous models and aligning well with experimental data.

Contribution

It presents a new 2D model incorporating small 3D effects in low Rm MHD flows, enhancing accuracy over existing models like Sommeria-Moreau.

Findings

Model agrees with measurements of isolated vortices.

Captures small 3D effects due to inertia and electric coupling.

Improves understanding of turbulence in low Rm MHD flows.

Abstract

A new model is proposed for low $Rm$ MHD flows which remain turbulent even in the presence of a magnetic field. These flows minimize the Joule dissipation because of their tendency to become two-dimensional and, therefore to suppress all induction effects. However, some small three-dimensional effects, due to inertia and to the electric coupling between the core flow and the Hartmann layers, are present even within the core flow. This new model, which may be seen as an improvement of the Sommeria-Moreau 2D model, introduces this three-dimensionality as a small perturbation. It yields an equation for the average velocity over the magnetic field lines, whose solution agrees well with available measurements performed on isolated vortices.