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Trefoil knot timescales for reconnection and helicity
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Kerr, Robert M. (2018) Trefoil knot timescales for reconnection and helicity. Fluid Dynamics Research, 50 . 011422. doi:10.1088/1873-7005/aa8163 ISSN 0169-5983.
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WRAP-trefoil-knot-timescales-reconnection-helicity-Kerr-2017.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (2128Kb) | Preview |
Official URL: https://doi.org/10.1088/1873-7005/aa8163
Abstract
Three-dimensional images of evolving numerical trefoil vortex knots are used to study thegrowth and decay of the enstrophy and helicity. Negative helicity density ($h<0$) plays several roles. First, during anti-parallel reconnection, sheets of oppositely-signed helicity dissipation of equal magnitude on either side of the maximum of the enstrophy dissipation allow the global helicity ${\cal H}$ to be preserved through the first reconnection, as suggested theoretically Laing et al (2015) and observed experimentally Scheeler et al (2014). Next, to maintain the growth of the enstrophy and positive helicity within the trefoil while ${\cal H}$ is preserved, $h<0$ forms in the outer parts of the trefoil so long as the periodic boundaries do not interfere. To prevent that, the domain size $\ell$ is increased as the viscosity $\nu\to0$. Combined, this allows two sets of trefoils to form a new scaling regime with linearly decreasing $(\sqrt{\nu}Z(t))^{-1/2}$ up to common $\nu$-independent times $t_x$ that the graphics show is when the first reconnection ends. During this phase there is good correspondence between the evolution of the simulated vortices and the reconnecting experimental trefoil of Kleckner and Irvine (2013) when time is scaled by their respective nonlinear timescales $t_f$. The timescales $t_f$ are based upon by the radii $r_f$ of the trefoils and their circulations $\Gamma$, so long as the strong camber of the experimental hydrofoil models is used to correct the published experimental circulations $\Gamma$ that use only the flat-plate approximation.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QC Physics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Fluid dynamics, Turbulence | |||||||||
Journal or Publication Title: | Fluid Dynamics Research | |||||||||
Publisher: | Institute of Physics Publishing Ltd. | |||||||||
ISSN: | 0169-5983 | |||||||||
Official Date: | 16 January 2018 | |||||||||
Dates: |
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Volume: | 50 | |||||||||
Article Number: | 011422 | |||||||||
DOI: | 10.1088/1873-7005/aa8163 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 10 January 2018 | |||||||||
Date of first compliant Open Access: | 21 July 2018 | |||||||||
RIOXX Funder/Project Grant: |
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