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Scattering of Line-Ring Vortices in a Superfluid

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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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References

  1. S. Fujiyama, A. Mitani, M. Tsubota, Generation, evolution, and decay of pure quantum turbulence: a full Biot-Savart simulation. Phys. Rev. B 81, 180512(R) (2010)

    Article  ADS  Google Scholar 

  2. P. Walmsley, A. Golov, Quantum and quasiclassical types of superfluid turbulence. Phys. Rev. Lett. 100, 245301 (2008)

    Article  ADS  Google Scholar 

  3. E. Kozik, B. Svistunov, Theory of decay of superfluid turbulence in the low-temperature limit. J. Low Temp. Phys. 156(3–6), 215–267 (2009)

    Article  ADS  Google Scholar 

  4. V. L’vov, S. Nazarenko, O. Rudenko, Bottleneck crossover between classical and quantum superfluid turbulence. Phys. Rev. B 76, 024520 (2007)

    Article  ADS  Google Scholar 

  5. D. Bradley, D. Clubb, S. Fisher, A. Guénault, R. Haley, C. Matthews, G. Pickett, V. Tsepelin, K. Zaki, Emission of discrete vortex rings by a vibrating grid in superfluid \(^3\)He-\(B\): a precursor to quantum turbulence. Phys. Rev. Lett. 95, 035302 (2005)

    Article  ADS  Google Scholar 

  6. M. Walmsley, P.A. Tompsett, D.E. Zmeev, A.I. Golov, Reconnections of quantized vortex rings in superfluid \({}^{4}\)He at very low temperatures. Phys. Rev. Lett. 113, 125302 (2014)

    Article  ADS  Google Scholar 

  7. M. Leadbeater, T. Winiecki, D.C. Samuels, C.F. Barenghi, C.S. Adams, Sound emission due to superfluid vortex reconnections. Phys. Rev. Lett. 86, 1410–1413 (2001)

    Article  ADS  Google Scholar 

  8. R. Caplan, J. Talley, R. Carretero-González, P. Kevrekidis, Scattering and leapfrogging of vortex rings in a superfluid. Phys. Fluids 26(9), 097101 (2014)

    Article  ADS  Google Scholar 

  9. Z. Sultan, A. Youd, C. Barenghi, Reconnection of superfluid vortex bundles. Phys. Rev. Lett. 101, 215302 (2008)

    Article  ADS  Google Scholar 

  10. R.J. Arms, F.R. Hama, Localized-induction concept on a curved vortex and motion of an elliptic vortex ring. Phys. Fluids (1958–1988) 8(4), 553–559 (1965)

    Article  ADS  Google Scholar 

  11. C. Nore, M. Abid, M. Brachet, Decaying Kolmogorov turbulence in a model of superflow. Phys. Fluids 9(9), 2644–2669 (1997)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. R. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991). Books Online

    Google Scholar 

  13. P. Saffman, Vortex Dynamics (Cambridge University Press, Cambridge, 1993). Books Online

    Book  Google Scholar 

  14. N. Berloff, Padé approximations of solitary wave solutions of the Gross–Pitaevskii equation. J. Phys. A 37(5), 1617 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. D. Proment, M. Onorato, C.F. Barenghi, Torus quantum vortex knots in the Gross–Pitaevskii model for Bose–Einstein condensates. J. Phys.: Conf. Ser. 544(1), 012022 (2014)

    ADS  Google Scholar 

  16. G. Krstulovic, Kelvin-wave cascade and dissipation in low-temperature superfluid vortices. Phys. Rev. E 86(5), 055301 (2012)

    Article  ADS  Google Scholar 

  17. R. Hänninen, Dissipation enhancement from a single vortex reconnection in superfluid helium. Phys. Rev. B 88, 054511 (2013)

    Article  ADS  Google Scholar 

  18. K.W. Schwarz, Interaction of quantized vortex rings with quantized vortex lines in rotating He II. Phys. Rev. 165, 323–334 (1968)

    Article  ADS  Google Scholar 

  19. L. Kiknadze, Y. Mamaladze, The waves on the vortex ring in HeII. J. Low Temp. Phys. 126(1–2), 321–326 (2002)

    Article  ADS  Google Scholar 

  20. J.L. Helm, C.F. Barenghi, A.J. Youd, Slowing down of vortex rings in Bose–Einstein condensates. Phys. Rev. A 83, 045601 (2011)

    Article  ADS  Google Scholar 

  21. G. Krstulovic, M. Brachet, Energy cascade with small-scale thermalization, counterflow metastability, and anomalous velocity of vortex rings in Fourier-truncated Gross–Pitaevskii equation. Phys. Rev. E 83, 066311 (2011)

    Article  ADS  Google Scholar 

  22. H. Hasimoto, A soliton on a vortex filament. J. Fluid Mech. 51, 477 (1972)

    Article  ADS  MATH  Google Scholar 

  23. J. Laurie, A.W. Baggaley, A note on the propagation of quantized vortex rings through a quantum turbulence tangle: energy transport or energy dissipation? J. Low Temp. Phys. (2015). doi:10.1007/s10909-015-1287-9

  24. B. Svistunov, Superfluid turbulence in the low-temperature limit. Phys. Rev. B 52, 3647 (1995)

    Article  ADS  Google Scholar 

  25. H. Salman, Breathers on quantized superfluid vortices. Phys. Rev. Lett. 111, 165301 (2013)

    Article  ADS  Google Scholar 

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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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  1. School of Mathematics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK

    Alberto Villois, Hayder Salman & Davide Proment

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  1. Alberto Villois
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  2. Hayder Salman
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  3. Davide Proment
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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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  • DOI: https://doi.org/10.1007/s10909-015-1293-y

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