  Simulations of the magnetorotational instability (MRI) in 'unstratified'
shearing boxes exhibit powerful coherent flows, whereby the fluid vertically
splits into countermoving planar jets or `channels'. Channel flows correspond
to certain axisymmetric linear MRI modes, and their preponderance follows from
the remarkable fact that they are approximate nonlinear solutions of the MHD
equations in the limit of weak magnetic fields. We show in this paper,
analytically and with one-dimensional numerical simulations, that this property
is also shared by certain axisymmetric MRI modes in vertically-stratified
shearing boxes. These channel flows rapidly capture significant amounts of
magnetic and kinetic energy, and thus are vulnerable to secondary shear
instabilities. We examine these parasites in the vertically stratified context,
and estimate the maximum amplitudes that channels attain before they are
destroyed. These estimates suggest that a dominant channel flow will usually
drive the disk's magnetic field to thermal strengths. The prominence of these
flows and their destruction place enormous demands on simulations, but channels
in their initial stages also offer a useful check on numerical codes. These
benchmarks are especially valuable given the increasing interest in the
saturation of the stratified MRI. Lastly we speculate on the potential
connection between 'run-away' channel flows and outburst behaviour in
protostellar and dwarf nova disks.
