Experimental investigation of the return flow instability in magnetic spherical Couette flow

TL;DR

This study experimentally explores the return flow instability in magnetic spherical Couette flow using GaInSn, revealing multistability of rotating waves and their dependence on initial conditions and magnetic field parameters.

Contribution

It provides the first detailed experimental investigation of rotating wave multistability and their dependence on initial conditions in magnetic spherical Couette flow.

Findings

Rotating waves with azimuthal wavenumbers 2, 3, 4 observed.

Multistability of rotating waves demonstrated.

Rotation frequencies match nonlinear stability analysis results.

Abstract

We conduct magnetic spherical Couette (MSC) flow experiments in the return flow instability regime with GaInSn as the working fluid, and the ratio of the inner to the outer sphere radii $r_{\rm i}/r_{\rm o} = 0.5$, the Reynolds number ${\rm Re} = 1000$, and the Hartmann number ${\rm Ha} \in [27.5,40]$. Rotating waves with different azimuthal wavenumbers $m \in \{2, 3, 4\}$ manifest in certain ranges of ${\rm Ha}$ in the experiments, depending on whether the values of ${\rm Ha}$ were fixed or varied from different initial values. These observations demonstrate the multistability of rotating waves, which we attribute to the dynamical system representing the state of the MSC flow tending to move along the same solution branch of the bifurcation diagram when ${\rm Ha}$ is varied. In experiments with both fixed and varying ${\rm Ha}$, the rotation frequencies of the rotating waves are consistent with the results of nonlinear stability analysis. A brief numerical investigation shows that differences in the azimuthal wavenumbers of the rotating waves that develop in the flow also depend on the azimuthal modes that are initially excited.