Formal Derivation and Stability Analysis of Boundary Layer Models in MHD

TL;DR

This paper systematically derives boundary layer models in magnetohydrodynamics, analyzing their stability and highlighting the magnetic field's stabilizing effects, including classical and nonlinear models.

Contribution

It introduces a unified derivation of classical and nonlinear boundary layer models in MHD and analyzes their linear stability with magnetic stabilization effects.

Findings

Classical Hartmann and Shercliff layer models recovered.

Nonlinear magnetic Prandtl models derived.

Magnetic field shown to have a stabilizing effect.

Abstract

We provide a systematic derivation of boundary layer models in magnetohydrodynamics (MHD), through an asymptotic analysis of the incompressible MHD system. We recover classical linear models, related to the famous Hartmann and Shercliff layers, as well as nonlinear ones, that we call magnetic Prandtl models. We perform their linear stability analysis, emphasizing the stabilizing effect of the magnetic field.