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Knot spectrum of turbulence

Lookup NU author(s): Robert Cooper, Mae Mesgarnezhad, Dr Andrew BaggaleyORCiD, Professor Carlo Barenghi



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2019, The Author(s).Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the discrete (quantized) nature of vorticity can be exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose degree characterizes the topology of that vortex loop. By numerically simulating the dynamics of a tangle of quantum vortex lines, we find that this quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing and reforming, creating a distribution of topologies which we quantify in terms of a knot spectrum and its scaling law. We also find results analogous to those in the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the vortex length, as for macromolecules, and saturates above a characteristic length, as found for tumbled strings.

Publication metadata

Author(s): Cooper RG, Mesgarnezhad M, Baggaley AW, Barenghi CF

Publication type: Article

Publication status: Published

Journal: Scientific Reports

Year: 2019

Volume: 9

Issue: 1

Online publication date: 22/07/2019

Acceptance date: 05/07/2019

Date deposited: 09/09/2019

ISSN (print): 1571-0645

ISSN (electronic): 1873-1457

Publisher: Nature Publishing Group


DOI: 10.1038/s41598-019-47103-w


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