Vortex structures in dilute quantum fluids

Vortex structures in dilute quantum fluids are studied using the time-independent Gross-Pitaevskii equation. The velocity and momentum of vortex rings with multiple circulation are determined and their core structures analysed. For flow around a spherical object, we study the encircling and pinned ring solutions, and determine their excitation energies as a function of 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.