Precursory patterns to vortex nucleation in stirred Bose-Einstein condensates

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