Numerical simulations of an effective two-dimensional model for flows with a transverse magnetic field

TL;DR

This paper introduces and tests a 2D MHD flow model with inertial effects, showing it accurately predicts flow behavior and recirculations under laminar Hartmann layers through numerical simulations and comparison with experiments.

Contribution

The paper develops a numerical implementation of an extended 2D MHD flow model that includes inertial effects, improving accuracy over previous models for flows with a transverse magnetic field.

Findings

Model accurately reproduces experimental velocity profiles.

Global angular momentum is closely matched by simulations.

Recirculations significantly influence flow structure and dissipation.

Abstract

This paper presents simulations of the 2d model developed by Poth\'erat at al (\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strong transverse homogeneous and steady magnetic field, accounting for moderate inertial effects in Hartmann layers. We first show analytically how the additional terms in the equations of motion accounting for inertia, soften velocity gradients in the horizontal plane, and then we implement the model on a code to carry out numerical simulations to be compared with available experimental results. This comparison shows that the new model can give very accurate results as long as the Hartmann layer remains laminar. Both experimental velocity profiles and global angular momentum measurements are closely recovered, and local and global Ekman recirculations are shown to alter significantly the aspect of the flow as well as the global dissipation.