Locality of MHD Turbulence in Isothermal Disks
  We numerically evolve turbulence driven by the magnetorotational instability
(MRI) in a 3D, unstratified shearing box and study its structure using
two-point correlation functions. We confirm Fromang and Papaloizou's result
that shearing box models with zero net magnetic flux are not converged; the
dimensionless shear stress $\alpha$ is proportional to the grid scale. We find
that the two-point correlation of the magnetic field shows that it is composed
of narrow filaments that are swept back by differential rotation into a
trailing spiral. The correlation lengths along each of the correlation function
principal axes decrease monotonically with the grid scale. For mean azimuthal
field models, which we argue are more relevant to astrophysical disks than the
zero net field models, we find that: $\alpha$ increases weakly with increasing
resolution at fixed box size; $\alpha$ increases slightly as the box size is
increased; $\alpha$ increases linearly with net field strength, confirming
earlier results; the two-point correlation function of the magnetic field is
resolved and converged, and is composed of narrow filaments swept back by the
shear; the major axis of the two-point increases slightly as the box size is
increased; these results are code independent, based on a comparison of ATHENA
and ZEUS runs. The velocity, density, and magnetic fields decorrelate over
scales larger than $\sim H$, as do the dynamical terms in the magnetic energy
evolution equations. We conclude that MHD turbulence in disks is localized,
subject to the limitations imposed by the absence of vertical stratification,
the use of an isothermal equation of state, finite box size, finite run time,
and finite resolution
