Local numerical models of turbulent accretion flows

Magnetohydrodynamical (MHD) turbulence induced by magnetorotational instability (MRI) is the most promising candidate for driving angular momentum transport in accretion disks. This work provides a comprehensive study of MHD turbulent accretion flow using shearing box simulations.;To evaluate the limitations of global axisymmetric models, I first studied the evolution of MHD turbulence in an axisymmetric local model using HAM, a nonrelativistic version of HARM. I have demonstrated that a suite of 2D models can produce outcomes quite different from a comparable 3D model, depending on the resolution and initial field strength.;We have developed a novel numerical scheme "orbital advection" for integrating super-fast MHD shear flows. In our code mthreed we have modified ZEUS to include "orbital advection" with a magnetic field, which greatly improves the integration speed and accuracy. mthreed has passed a series of linear and non-linear codes tests. With mthreed we are able to carry out shearing box simulations with radial extents much larger than the disk scale height H.;The first application of mthreed was to study the saturation and structures of MHD turbulence in a 3D, unstratified accretion disk. We have demonstrated that: (1) in models with zero net magnetic flux, the dimensionless shear stress alpha is proportional to the grid scale; for mean toroidal field models which are more relevant to astrophysical disks, alpha increases weakly with resolution; (2) the two-point correlation function of turbulent fields is composed of narrow filaments swept back by the shear; (3) MHD turbulence in isothermal disks is localized with correlation length ≲ H; (4) the magnetic turbulent Prandtl number in disks is ∼ 1. This result suggests a net vertical field in the disk will most likely diffuse outward before it can be advected inward by accretion.;We then used mthreed to study 3D stratified disk models with domain sizes much larger than H. We have found that in a saturated state: (1) the disk consists of a turbulent inner region at |z| ≤ 2H and a magnetically dominated corona at |z| > 2H; (2) the disk is dominated by a toroidal field and alpha ∼ 0.01--0.02; (3) central |z| ≤ 2H part of the disk is dominated by small scale (≤ H) turbulence, statistically similar to what has been observed in unstratified disk models; for the corona, magnetic fields are correlated on scales of ∼ 10H, implying the existence of meso-scale structures, although transport through corona is small; (4) quasi-periodic oscillations of the vertical magnetic energy profile ("the butterfly diagrams") persist in all our models with a period ∼ 5 orbits.