Creation and dynamics of knotted vortices

Nature Physics

Volumn 9, Issue 4, 2013, Pages 253-258

  Kleckner, Dustin ^a   Irvine, William T M ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

TOMOGRAPHY;

HIGH SPEED SCANNING; PHYSICAL FIELD; REAL FLUIDS; THEORETICAL STUDY; VORTEX LOOPS; VORTEX RECONNECTION; VORTEX RINGS;

VORTEX FLOW;

EID: 84876417245     PISSN: 17452473     EISSN: 17452481     Source Type: Journal    
DOI: 10.1038/nphys2560     Document Type: Article

References (36)

1. Witten, E. Quantum-field theory and the Jones polynomial. Commun. Math. Phys. 121, 351-399 (1989).
2. Faddeev, L. & Niemi, A. Stable knot-like structures in classical field theory. Nature 387, 58-61 (1997).
3. Manton, N. & Sutcliffe, P. M. Topological Solitons (Cambridge Univ. Press, 2004).
4. Smalyukh, I. I., Lansac, Y., Clark, N. A. & Trivedi, R. P. Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids. Nature Mater. 9, 139-145 (2010).
5. Tkalec, U. et al. Reconfigurable knots and links in chiral nematic colloids. Science 333, 62-65 (2011).
6. Irvine, W. T. M. & Bouwmeester, D. Linked and knotted beams of light. Nature Phys. 4, 716-720 (2008).
7. Irvine, W. T. M. Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields. J. Phys. A 43, 385203 (2010).
8. Dennis, M. R., King, R. P., Jack, B., O'holleran, K. & Padgett, M. Isolated optical vortex knots. Nature Phys. 6, 118-121 (2010).
9. Chandrasekhar, S. & Kendall, P. C. On force-free magnetic fields. Proc. Natl Acad. Sci. USA 42, 1-5 (1956).
10. Woltjer, L. A theorem on force-free magnetic fields. Proc. Natl Acad. Sci. USA 44, 489-491 (1958).
11. Berger, M. A. Introduction to magnetic helicity. Plasma Phys. Control. Fusion 41, B167-B175 (1999).
12. Freedman, M. H. & Berger, M. A. Combinatorial relaxation of magnetic fields. Geophys. Astrophys. Fluid Dynam. 73, 91-96 (1993).
13. Moffatt, H. K. Degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117-129 (1969).
14. Moffatt, H. K. Some developments in the theory of turbulence. J. Fluid Mech. 106, 27-47 (1981).
15. Ricca, R. L. & Berger, M. A. Topological ideas and fluid mechanics. Phys. Today 49, 28-34 (1996).
16. Barenghi, C. F. Knots and unknots in superfluid turbulence. Milan J. Math. 75, 177-196 (2007).
17. Babaev, E. Non-Meissner electrodynamics and knotted solitons in two-component superconductors. Phys. Rev. B 79, 1-6 (2009).
18. Bouligand, Y. Recherches sur les textures des états mésomorphes. 6-Dislocations coins et signification des cloisons de Grandjean-Cano dans les cholestériques. J. Physique 35, 959-981 (1974).
19. Kambe, T. & Takao, T. Motion of distorted vortex rings. J. Phys. Soc. Jpn 31, 591-599 (1971).
20. Kida, S. A vortex filament moving without change of form. J. Fluid Mech. 112, 397-409 (1981).
21. Ricca, R. L., Samuels, D. & Barenghi, C. Evolution of vortex knots. J. Fluid Mech. 391, 29-44 (1999).
22. Proment, D., Onorato, M. & Barenghi, C. Vortex knots in a Bose-Einstein condensate. Phys. Rev. E 85, 1-8 (2012).
23. Ricca, R. New developments in topological fluid mechanics. Il Nuovo Cimento. 32, 185-192 (2009).
24. Thomson, W. On vortex atoms. Phil. Mag. 34, 94-105 (1867).
25. Moffatt, H. K., Kida, S. & Ohkitani, K. Stretched vortices-the sinews of turbulence; large-Reynolds-number asymptotics. J. Fluid Mech. 259, 241-264 (1994).
26. Acheson, D. J. Elementary Fluid Dynamics (Clarendon, 1990).
27. Saffman, P. G. Vortex Dynamics (Cambridge Univ. Press, 1992).
28. Calini, A., Keith, S. F. & Lafortune, S. Squared eigenfunctions and linear stability properties of closed vortex filaments. Nonlinearity 24, 3555-3583 (2011).
29. Kida, S. & Takaoka, M. Reconnection of vortex tubes. Fluid Dynam. Res. 3, 257-261 (1988).
30. Donnelly, R. J. Vortex rings in classical and quantum systems. Fluid Dynam. Res. 41, 051401 (2009) 1-31.
31. Douady, S. & Couder, Y. Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983-986 (1991).
32. Thomson, W. XXIV. Vibrations of A Columnar Vortex 155-168 (Philosophical Magazine Series 5, Vol. 10, 1880).
33. Sethian, J. A. A fast marching level set method for monotonically advancing fronts. Proc. Natl Acad. Sci. USA 93, 1591-1595 (1996).
34. Deschamps, T. & Cohen, L. D. Minimal paths in 3D images and application to virtual endoscopy. Med. Image Anal. 5, 281-299 (2001).
35. Dengler, R. Self inductance of a wire loop as a curve integral. Preprint at http://arxiv.org/abs/1204.1486 (2012).
36. Oshima, Y., Kambe, T. & Asaka, S. Interaction of two vortex rings moving along a common axis of symmetry. J. Phys. Soc. Jpn 38, 1159-1166 (1975).