  Magnetohydrodynamic (MHD) turbulence driven by the magnetorotational
instability can provide diffusive transport of angular momentum in
astrophysical disks, and a widely studied computational model for this process
is the ideal, stratified, isothermal shearing box. Here we report results of a
convergence study of such boxes up to a resolution of $N = 256$ zones per scale
height, performed on blue waters at NCSA with ramses-gpu. We find that the time
and vertically integrated dimensionless shear stress $\overline{\alpha} \sim
N^{-1/3}$, i.e. the shear stress is resolution dependent. We also find that the
magnetic field correlation length decreases with resolution, $\lambda \sim
N^{-1/2}$. This variation is strongest at the disk midplane. We show that our
measurements of $\alpha$ are consistent with earlier studies. We discuss
possible reasons for the lack of convergence.
