Simulations of Magnetorotational Instability in a Magnetized Couette Flow

In preparation for an experimental study of magnetorotational instability(MRI) in liquid metal, we present non-ideal two-dimensional magnetohydrodynamicsimulations of the nonlinear evolution of MRI in the experimental geometry. Thesimulations adopt initially uniform vertical magnetic fields, conducting radialboundaries, and periodic vertical boundary conditions. No-slip conditions areimposed at the cylinders. Our linear growth rates compare well with existinglocal and global linear analyses. The MRI saturates nonlinearly with horizontalmagnetic fields comparable to the initial axial field. The rate of angularmomentum transport increases modestly but significantly over the initial state.For modest fluid and magnetic Reynolds numbers Re, Rm between 100 and 1000, thefinal state is laminar reduced mean shear except near the radial boundaries,and with poloidal circulation scaling as the square root of resistivity, inpartial agreement with the analysis of Knobloch and Julien. A sequence ofsimulations at Rm=20 and 100 < Re < 25,600 enables extrapolation to theexperimental regime (Rm ~ 20, Re ~ 10^7), albeit with unrealistic boundaryconditions. MRI should increase the experimentally measured torquesubstantially over its initial purely hydrodynamic value.Comment: 29 pages, 15 figures and 3 tables, accepted by Ap