Simulation of flux expulsion and associated dynamics in a two-dimensional magnetohydrodynamic channel flow

TL;DR

This paper uses direct numerical simulations to study magnetic flux expulsion and flow bifurcations in a two-dimensional magnetohydrodynamic channel, comparing results with existing models and analyzing effects of key parameters.

Contribution

It provides a detailed numerical analysis of flux expulsion in 2D MHD flows, evaluating the validity of a classic 1D model and exploring nonlinear effects and parameter influences.

Findings

Good agreement with the 1D model in the Hartmann regime

Significant differences in the Poiseuille regime due to nonlinear effects

Identification of a two-step flux expulsion pattern during dynamic runaway

Abstract

We consider a plane channel flow of an electrically conducting fluid which is driven by a mean pressure gradient in the presence of an applied magnetic field that is streamwise periodic with zero mean. Magnetic flux expulsion and the associated bifurcation in such a configuration is explored using direct numerical simulations (DNS). The structure of the flow and magnetic fields in the Hartmann regime (where the dominant balance is through Lorentz forces) and the Poiseuille regime (where viscous effects play a significant role) are studied and detailed comparisons to the existing one-dimensional model of Kamkar and Moffatt (J. Fluid. Mech., Vol.90, pp 107-122, 1982) are drawn to evaluate the validity of the model. Comparisons show good agreement of the model with DNS in the Hartmann regime, but significant diferences arising in the Poiseuille regime when non-linear effects become important. The effects of various parameters like the magnetic Reynolds number, imposed field wavenumber etc. on the bifurcation of the flow are studied. Magnetic field line reconnections occuring during the dynamic runaway reveal a specific two-step pattern that leads to the gradual expulsion of flux in the core region.