Experimental investigation of the return flow instability in magnetized spherical Couette flows

We conduct magnetized spherical Couette (MSC) flow experiments in the return flow instability regime with GaInSn as the working fluid, the ratio of the inner to the outer sphere radii r(i)/r(o) = 0.5, the Reynolds number Re = 1000, and the Hartmann number Ha is an element of [27.5, 40]. Rotating waves with different azimuthal wavenumbers m is an element of {2, 3, 4} manifest in certain ranges of Ha in the experiments, depending on whether the values of 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 Ha is varied. In experiments with both fixed and varying 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.