A Powerful Local Shear Instability in Weakly Magnetized Disks. II. Nonlinear Evolution

We consider the dynamical evolution of an accretion disk undergoing Keplerian shear flow in the presence of a weak magnetic field. A linear perturbation analysis presented in a companion paper shows that such a flow is dynamically unstable; here we consider some nonlinear consequences of this instability. We solve the equations of compressible magnetohydrodynamics using a two-dimensional finite-difference code. The Keplerian disk is threaded with a weak magnetic field that has a magnetic energy density much less than the thermal pressure. When perturbations are small, the numerical results are consistent with linear perturbation theory. We demonstrate the scaling relation between the instability's wavenumber and the Alfvén velocity that was found in the companion paper, and confirm that the maximum growth rate is independent of magnetic field strength. Neither compressibility nor the presence of toroidal field have a significant effect on the evolution of unstable modes. The most important dynamic effect is the redistribution of angular momentum leading to a strong interchange instability. The resulting radial motions produce field geometries that are conducive to reconnection, suggesting a possible mechanism for mode saturation. Even for very weak fields, whose most unstable wavelengths are small, nonlinear evolution results in the growth of structure on large scales. Total magnetic field energy increases by about one order of magnitude over the course of the simulations.