Magnetorotational instability in electrically driven fluids

TL;DR

This paper investigates the linear stability of electrically driven liquid metal flows in circular channels under vertical magnetic fields, revealing that magnetorotational instability governs the flow's stability threshold, independent of fluid type at low magnetic Prandtl numbers.

Contribution

It demonstrates that magnetorotational instability determines the flow stability threshold in electrically driven liquid metal flows, aligning numerical results with experimental data.

Findings

Instability threshold is set by magnetorotational instability.

Threshold is independent of fluid type at low magnetic Prandtl numbers.

Numerical results agree with experimental data.

Abstract

The linear stability of electrically driven flow of liquid metal in circular channel in the presence of vertical magnetic field is studied. It is shown that the instability threshold of such flow is determined by magnetorotational instability of non-axisymmetric modes ($m\neq0$) and does not depend on the type of the fluid if magnetic Prandtl number is small $\Pr\ll1$. Our numerical results are found to be in a good agreement with available experimental data from Grenoble High Magnetic Field Laboratory, France [P. Moresco and T. Alboussi\`{e}re, J. Fluid Mech. \textbf{504}, 167 (2004)].