  We theoretically explore the annihilation of vortex dipoles, generated when
an obstacle moves through an oblate Bose-Einstein condensate, and examine the
energetics of the annihilation event. We show that the gray soliton, which
results from the vortex dipole annihilation, is lower in energy than the vortex
dipole. We also investigate the annihilation events numerically and observe
that the annihilation occurs only when the vortex dipole overtakes the obstacle
and comes closer than the coherence length. Furthermore, we find that the noise
reduces the probability of annihilation events. This may explain the lack of
annihilation events in experimental realizations.
