Abstract
We introduce and test measures of geometric and topological complexity to quantify morphological aspects of a tangle of vortex filaments. The tangle is produced by standard numerical simulation of superfluid turbulence in Helium II. Complexity measures such as linking number, writhing number, average crossing number and helicity are computed, and their relation to the energy of the fluid is investigated.
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References
Adams, C. C. 1994 The knot book, W. H. Freeman and Co., New York, p. 14.
Barenghi, C. F., Bauer, G., Samuels, D. C. and Donnelly, R. J. 1997 Superfluid vortex lines in a model of turbulent flow. Phys. Fluids 9 2631–2643.
Barenghi, C. F. 2001 Introduction to superfluid vortices and turbulence. In Quantized vortex dynamics and superfluid turbulence (ed. C.F. Barenghi, R.J. Donnelly and W.F. Vinen), pp. 3–13. Springer Verlag.
Barenghi, C. F., Ricca, R. L. and Samuels, D. C. 2001 How tangled is a tangle? Physica D 157 197–206.
Freedman, M. H. and He, Z.-X. 1991 Divergence-free field. Energy and asymptotic crossing number. Ann. Math. 134 189–229.
Kivotides, D., Barenghi, C. F. and Samuels, D. C. 2001 Fractal nature of super-fluid turbulence. Phys. Rev. Letters 87 155301.
Koplik, J. and Levine, H. 1993 Vortex reconnections in superfluid helium. 1375–1378 (1993).
Leadbeater, M., Winiecki, T., Samuels, D. C., Barenghi, C. F. and Adams, C.S. 2001 Sound emission due to superfluid vortex reconnections. Phys. Rev. Letters 86, 1410–1413.
Maurer, J. and Tabeling, P. 1998 Local investigation of superfluid turbulence. Europhysics Letters 43 29–34.
Moffatt, H. K. 1969 The degree of knottedness of tangles vortex lines. J. Fluid Mechanics, 35 117–129.
Moffatt, H. K. and Ricca, R. L. 1992 Helicity and the Calugareanu invariant. Proc. Roy. Soc. London A 439 411–429.
Schwarz, K. W. 1988 Three dimensional vortex dynamics in superfluid 4He. Phys. Rev. B 38, 2398–2417.
Stalp, S. R., Skrbek, L. and Donnelly, R. J. 1999 Decay of grid turbulence in a finite channel. Phys. Rev. Letters 82, 4831–4834.
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© 2002 Kluwer Academic Publishers
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Barenghi, C.F., Samuels, D.C., Ricca, R.L. (2002). Complexity measures of tangled vortex filaments. In: Bajer, K., Moffatt, H.K. (eds) Tubes, Sheets and Singularities in Fluid Dynamics. Fluid Mechanics and Its Applications, vol 71. Springer, Dordrecht. https://doi.org/10.1007/0-306-48420-X_10
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DOI: https://doi.org/10.1007/0-306-48420-X_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0980-8
Online ISBN: 978-0-306-48420-9
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