Simulations of Vortex Evolution and Phase Slip in Oscillatory Potential   Flow of the Superfluid Component of Helium-4 Through an Aperture
  The evolution of semicircular quantum vortex loops in oscillating potential flow emerging from an aperture is simulated in some highly symmetrical cases. As the frequency of potential flow oscillation increases, vortex loops that are evolving so as eventually to cross all of the streamlines of potential flow are drawn back toward the aperture when the flow reverses. As a result, the escape size of the vortex loops, and hence the net energy transferred from potential flow to vortex flow in such 2 Pi phase-slip events, decreases as the oscillation frequency increases. Above some aperture-dependent and flow-dependent threshold frequency, vortex loops are drawn back into the aperture. Simulations are preformed using both radial potential flow and oblate-spheroidal potential flow. 
J. A. Flaten, C. T. Borden, C. A. Lindensmith, W. Zimmermann Jr