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We conduct magnetic spherical Couette (MSC) flow experiments in the returnflow instability regime with GaInSn as the working fluid, and the ratio of theinner to the outer sphere radii $r_{\rm i}/r_{\rm o} = 0.5$, the Reynoldsnumber ${\rm Re} = 1000$, 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 onwhether the values of ${\rm Ha}$ were fixed or varied from different initialvalues. These observations demonstrate the multistability of rotating waves,which we attribute to the dynamical system representing the state of the MSCflow tending to move along the same solution branch of the bifurcation diagramwhen ${\rm Ha}$ is varied. In experiments with both fixed and varying ${\rmHa}$, the rotation frequencies of the rotating waves are consistent with theresults of nonlinear stability analysis. A brief numerical investigation showsthat differences in the azimuthal wavenumbers of the rotating waves thatdevelop in the flow also depend on the azimuthal modes that are initiallyexcited.

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