Local Three-dimensional Magnetohydrodynamic Simulations of Accretion Disks

We have performed three-dimensional magnetohydrodynamic numerical simulations of an accretion disk to study the nonlinear development of the magnetorotational instability. We use a disk model that is local in the sense that it incorporates tidal and Coriolis forces but neglects background gradients in pressure and density. For simplicity we omit the vertical component of gravity and employ periodic boundary conditions in the vertical and azimuthal directions, and shearing-periodic boundary conditions in the radial direction. Our numerical method is an implementation of the "method of characteristics-constrained transport" algorithm. Most of the simulations begin with either a purely vertical or purely azimuthal magnetic field. Our major result is that turbulence is initiated and sustained by the magnetic instability. We provide a detailed characterization of the saturated turbulent state. The turbulence is anisotropic in a sense that implies an outward flux of angular momentum. The turbulent energy and angular momentum flux is dominated by magnetic stress rather than Reynolds stress. Most of the energy and angular momentum flux is concentrated at the largest scales. We find that the magnetic energy density in the saturated state is proportional to the product of the size of the simulation box and the initial field strength and is independent of the sound speed.