A POWERFUL LOCAL SHEAR INSTABILITY IN WEAKLY MAGNETIZED DISKS .3. LONG-TERM EVOLUTION IN A SHEARING SHEET

We investigate the nonlinear evolution of the recently identified accretion disk magnetic shear instability through a series of numerical simulations. We carry out finite-difference computations of the equations of compressible magnetohydrodynamics on an axisymmetric shearing sheet system with periodic boundary conditions designed to approximate a local region within an accretion disk. We ignore density stratification and assume that the pressure is constant. We consider a variety of initial field strengths and geometries including uniform vertical, uniform radial, and spatially varying fields. The simulation results are in agreement with the predictions of linear perturbation theory for small amplitude perturbations. The instability amplifies the disk's magnetic energy and efficiently transports angular momentum outward. Initial field configurations that include some net vertical component evolve into a nonlinear, exponentially growing solution with large poloidal velocities and magnetic fields with energies comparable to the thermal energy density. Other initial field configurations lead to unsteady flows that transport net angular momentum through the shearing sheet. These simulations demonstrate the importance of the instability and the shortcomings of laminar hydrodynamic disk models.