  We present the results of high-resolution, three-dimensional (3D)
hydrodynamic simulations of the dynamics and formation of coherent, long-lived
vortices in stably-stratified protoplanetary disks. Tall, columnar vortices
that extend vertically through many scale heights in the disk are unstable to
small perturbations; such vortices cannot maintain vertical alignment over more
than a couple scale heights and are ripped apart by the Keplerian shear. Short,
finite-height vortices that extend only one scale height above and below the
midplane are also unstable, but for a different reason: we have isolated an
antisymmetric (with respect to the midplane) eigenmode that grows with an
e-folding time of only a few orbital periods; the nonlinear evolution of this
instability leads to the destruction of the vortex. Serendipitously, we observe
the formation of 3D vortices that are centered not in the midplane, but at one
to three scale heights above and below. Breaking internal gravity waves create
vorticity; anticyclonic regions of vorticity roll-up and coalesce into new
vortices, whereas cyclonic regions shear into thin azimuthal bands. Unlike the
midplane-centered vortices that were placed ad hoc in the disk and turned out
to be linearly unstable, the off-midplane vortices form naturally out of
perturbations in the disk, and are stable and robust for many hundreds of
orbits.
