Precursory patterns to vortex nucleation in stirred Bose-Einstein condensates

Within the Gross-Pitaevskii theory, we study precursory pattern formations to the nucleation of vortex dipoles in a two-dimensional Bose-Einstein condensate stirred by a Gaussian potential. We introduce a smooth superfluid vorticity field and its conservative current, which capture very well the gradual process of vortex nucleation as a mechanism of topological singularities acquiring smooth cores. This is characterized by the localization of the superfluid vorticity into core regions which harbor the phase slips. For more impenetrable obstacles, we find that there are additional phase slips that do not acquire cores, thus remaining pinned as ghost vortices to the potential. We show that the vortex kinematics is slaved to the superfluid vorticity current, which determines not only the onset of nucleation but also the shedding dynamics.