Scattering of Line-Ring Vortices in a Superfluid

Abstract

We study the scattering of vortex rings by a superfluid line vortex using the Gross–Pitaevskii equation in a parameter regime where a hydrodynamic description based on a vortex filament approximation is applicable. The scattering of a vortex ring by a line vortex is characterised by the initial offset of the centre of the ring from the axis of the vortex. We find that a strong asymmetry exists in the scattering of a ring as a function of this initial scattering parameter. Using a vortex extraction algorithm, we are able to track the location of the vortex ring as a function of time. We then show that the scattering of the vortex ring in our Gross–Pitaevskii simulations is well captured by the local induction approximation of a vortex filament model for a wide range of impact parameters. In contrast, the absorption of the ring by the line vortex is not predicted by the local induction approximation.

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Acknowledgments

The authors would like to thank A. Baggaley, G. Krstulovic, J. Laurie, D. Maestrini, and the anonymous referees for helpful suggestions and discussions. The research presented in this paper was carried out on the High Performance Computing Cluster supported by the Research and Specialist Computing Support service at the University of East Anglia.

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Correspondence to Hayder Salman.

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Villois, A., Salman, H. & Proment, D. Scattering of Line-Ring Vortices in a Superfluid. J Low Temp Phys 180, 68–81 (2015). https://doi.org/10.1007/s10909-015-1293-y

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Keywords

  • Superfluids
  • Biot-Savart filament model
  • Local induction approximation
  • Gross–Pitaevskii model
  • Topological defects
  • Scattering theory