MRI in Taylor-Dean flows

The magnetorotational instability (MRI) can destabilize hydrodynamically stable flows which are characterized by an angular momentum that is increasing with the radius and by an angular velocity that is decreasing with radius. Its astrophysical importance comes from the fact that the Kepler flow with Omega(r) similar to r(-3/2) shows exactly such a behaviour. In order to investigate MRI in a laboratory experiment, the Taylor-Couette flow with Omega(r) = A + Br-2 with A > 0 has been proposed as a substitute for the Kepler flow. In this paper we consider the Taylor-Dean flow as another example of a flow profile which can exhibit the necessary radial dependence. Taylor-Dean flows are a combination of the traditional Taylor-Couette flow with an additional flow that is produced by an azimuthal force. Special focus is laid on the case that the Taylor-Couette part of the flow is a rigid body rotation and the magnitude of the Dean flow is adjusted in such a way that in the outer part of the flow the conditions for MRI are fulfilled. Based on the dispersion relation derived by Ji, Kageyama and Goodman, in combination with some preliminary global instability analysis, we give some first estimates for the physical parameters of a Taylor-Dean MRI experiment with liquid sodium.