Proposal for a Taylor-Dean experiment to investigate the magnetorotational instability

The magnetorotational instability (MRI) is one of the most promising candidates to explain why accretion disks, which exhibit a Keplerian flow profile and should therefore be hydrodynamically stable, allow for a rate of angular transport which cannot be attributed to the molecular viscosity of the disk. Like the dynamo effect, MRI occurs only at large magnetic Reynolds numbers, making its laboratory investigation rather expensive. Recently, there are strong activities to study MRI in a liquid metal Taylor-Couette flow, and it might be that MRI has already been found in a spherical Couette flow of liquid sodium. We propose an alternative experimental configuration which is based on the Taylor-Dean flow. This flow is a combination of the usual cylindrical Couette flow and an additional Dean flow which is driven by an azimuthal force. This force can be realized in the form of an externally applied pressure gradient or, more elegantly, by a Lorentz force due to a radial current and an axial magnetic field. Our main idea is that, for a well adjusted ratio of Dean flow to Taylor-Couette flow, one gets an angular velocity that is decreasing with the radius and an angular momentum that is increasing with the radius, hence a situation that is prone to the study of MRI. Our main focus is on a particular configuration in which the outer and inner cylinders rotate at the same angular velocity. Evidently, this would simplify the mechanical part of the experiment dramatically. We find that, for sufficiently small values of the ratio of inner to outer radius, such an experiment seems indeed feasible.