Magnetorotational Instability in Taylor-Dean Flows

The experimental demonstration of MRI in a liquid sodium Taylor-Couette experiment might be hampered by sealing problems at the two end plates whose sophisticated design could be crucial to avoid non-linear instabilities. Thus motivated, we consider alternative flow configurations with respect to their suitability to show MRI. First results for flows that are driven by azimuthal pressure gradients (Dean flows) and for combinations with Couette flows (Taylor-Dean flows) are presented. The influence of an axial magnetic field on the stability of Dean and Taylor-Dean flows with arbitrary gap spacing between the cylinders is considered. For Dean flows with magnetic Prandtl number equal to one it is found that, similar to the result for the Taylor-Couette flow, a significant decrease of the critical Reynolds number occurs for intermediate Hartmann numbers. This MRI is more pronounced for small values of the ratio of the radii of the inner and outer cylinder. For Taylor-Dean flows the onset of the instability in dependence on the ratio of azimuthal pressure gradient and cylinder rotation is investigated.