Global Magnetorotational Instability with Inflow. II. The Nonlinear Development of Axisymmetric Wall Modes

We investigate numerically the global, nonlinear behavior of magnetorotational instabilities in accretion disks by considering our previously formulated model of a cylindrical, dissipative disk with permeable boundaries. We extend the linear theory to follow the development of unstable, axisymmetric, magnetorotational modes into the nonlinear regime to determine the saturation mechanism. In each case parameters are chosen so that the most unstable mode is localized close to the inner boundary. We conduct an extensive parameter survey and find that the nonlinear behavior is mediated by the formation of a coherent radial jet that transports vertical magnetic flux within the disk. The mechanism for saturation depends critically on the strength of this jet. Different scenarios for saturation are explored in detail. The instability can either saturate in a nonlinear steady or oscillatory, non-Keplerian state, or relax back to a Keplerian state via the removal of flux from the disk by the jet.