Magnetorotational instability and angular momentum transport in magnetized Taylor- Couette flows

The magnetorotational instability (MRI) is probably the main cause of turbulence and accretion in sufficiently ionized astrophysical disks. Despite much theoretical and computational work, however, nonlinear MRI is imperfectly understood. We present non-ideal magnetohydrodynamic simulations of MRI in the geometry of the Princeton MRI experiment. MRI saturates in a resistive current-sheet with significant reduction of the mean shear, and with poloidal circulation scaling as the square root of resistivity. Angular momentum transport scales as the reciprocal square root of viscosity but hardly depends on resistivity [1]. Separately, we have studied MRI in the presence of a a current-free combination of toroidal and axial magnetic field. The new mode (HMRI) persists to smaller magnetic Reynolds number and Lundquist number than standard MRI, which relies on axial field alone. This would seem to make HMRI attractive for experiments and perhaps for application to resistive astrophysical disks. In vertically infinite or periodic cylinders, resistive HMRI is a weakly destabilized hydrodynamic inertial oscillation propagating axially along the background Poynting flux [2]. Growth rates are small, however, and require large axial currents. Furthermore, highly resistive HMRI is stabilized in finite cylinders with insulating endcaps, and also in keplerian flow profiles regardless of end conditions. In both of these studies, comparison of models and measurements is used to validate our theoretical tools, which we will apply to nonlinear saturation of resistive MRI in astrophysical systems. Theoretical modeling has already played a major role in the design of the MRI experiment, and the physics of these modes may be of interest for fluid dynamics and geophysics as well as astrophysics. {[1]} Wei Liu, Jeremy Goodman and Hantao Ji, ApJ, 643, 306. {[2]} Wei Liu, Jeremy Goodman, Hantao Ji and Isom Herron, submitted to PRE. Supported by DoE, NASA and NSF.