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Topology of interacting coiled vortex rings

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Kerr, Robert M. (2018) Topology of interacting coiled vortex rings. Journal of Fluid Mechanics, 854 . R2. doi:10.1017/jfm.2018.665 ISSN 0022-1120.

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Official URL: https://doi.org/10.1017/jfm.2018.665

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Abstract

Pairs of nested vortex rings, one with coils, are evolved numerically to compare their topological numbers to those of recent experiments reported in Scheeler et al. (Science, vol. 357, 2017, pp. 487–491). Included are the twist Tw , writhe Wr and self-linking LS numbers, plus centreline helicities Hc . The questions are: can the experimental numbers be validated and do these numbers have roles in the dynamics of the global helicities H and enstrophies Z with respect to cascades? Topological analysis of the experiments t=0 analytic centreline vortex trajectories validates only the writhe measurements, not their values of Tw and LS , which obey Tw≲LS=m≫Wr for m -coil rings. Not Tw≪Wr . To suggest why the large twists do not contribute to H , it is noted that the mapping of the coiled rings onto the mesh is to a first approximation a single pair of Clebsch potentials, whose self-helicity HS≡0 . Numerical rings with circulations Γ , including some single rings, show small initial helicities with H(0)≈Hc∼(1 to 2)WrΓ2 ≪LSΓ2 . For time and velocity scales that are consistent with the experiments, as the coils evolve, their Tw , Wr , LS numbers and their helicities are nearly static until reconnection. Nonetheless, Wr and Tw retain important complementary roles in the dynamics of the global helicity H and enstrophy Z , with the evolution of the torsion τ(s) profile showing the beginnings of a cascade to small scales.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Topology, Rings (Algebra)
Journal or Publication Title: Journal of Fluid Mechanics
Publisher: Cambridge University Press
ISSN: 0022-1120
Official Date: 10 November 2018
Dates:
DateEvent
10 November 2018Published
3 September 2018Available
11 August 2018Accepted
Volume: 854
Article Number: R2
DOI: 10.1017/jfm.2018.665
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): © Cambridge University Press 2018
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: Cambridge University Press
Date of first compliant deposit: 5 September 2018
Date of first compliant Open Access: 3 March 2019

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