  Vortex structures in dilute quantum fluids are studied using the
Gross-Pitaevskii equation. The velocity and momentum of multiply quantized
vortex rings are determined and their core structures analysed. For flow past a
spherical object, we study the encircling and pinned ring solutions, and
determine their excitation energies as a function of the flow velocity for both
penetrable and impenetrable objects. The ring and laminar flow solutions
converge at a critical velocity, which decreases with increasing object size.
We also study the vortex solutions associated with flow past a surface bump
which indicate that surface roughness also reduces the critical velocity. This
effect may have important implications for the threshold of dissipation in
superfluids and superconductors.
