  We examine the effects of density stratification on magnetohydrodynamic
turbulence driven by the magnetorotational instability in local simulations
that adopt the shearing box approximation. Our primary result is that, even in
the absence of explicit dissipation, the addition of vertical gravity leads to
convergence in the turbulent energy densities and stresses as the resolution
increases, contrary to results for zero net flux, unstratified boxes. The ratio
of total stress to midplane pressure has a mean of ~0.01, although there can be
significant fluctuations on long (>~50 orbit) timescales. We find that the time
averaged stresses are largely insensitive to both the radial or vertical aspect
ratio of our simulation domain. For simulations with explicit dissipation, we
find that stratification extends the range of Reynolds and magnetic Prandtl
numbers for which turbulence is sustained. Confirming the results of previous
studies, we find oscillations in the large scale toroidal field with periods of
~10 orbits and describe the dynamo process that underlies these cycles.
