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Influence of winding number on vortex knots dynamics
In this paper we determine the effects of winding number on the dynamics of vortex torus knots and unknots in the context of classical, ideal fluid mechanics. We prove that the winding number — a topological invariant of torus knots — has a primary effect on vortex motion. This is done by applying t...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6872556/ https://www.ncbi.nlm.nih.gov/pubmed/31754143 http://dx.doi.org/10.1038/s41598-019-53548-w |
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author | Oberti, Chiara Ricca, Renzo L. |
author_facet | Oberti, Chiara Ricca, Renzo L. |
author_sort | Oberti, Chiara |
collection | PubMed |
description | In this paper we determine the effects of winding number on the dynamics of vortex torus knots and unknots in the context of classical, ideal fluid mechanics. We prove that the winding number — a topological invariant of torus knots — has a primary effect on vortex motion. This is done by applying the Moore-Saffman desingularization technique to the full Biot-Savart induction law, determining the influence of winding number on the 3 components of the induced velocity. Results have been obtained for 56 knots and unknots up to 51 crossings. In agreement with previous numerical results we prove that in general the propagation speed increases with the number of toroidal coils, but we notice that the number of poloidal coils may greatly modify the motion. Indeed we prove that for increasing aspect ratio and number of poloidal coils vortex motion can be even reversed, in agreement with previous numerical observations. These results demonstrate the importance of three-dimensional features in vortex dynamics and find useful applications to understand helicity and energy transfers across scales in vortical flows. |
format | Online Article Text |
id | pubmed-6872556 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-68725562019-12-04 Influence of winding number on vortex knots dynamics Oberti, Chiara Ricca, Renzo L. Sci Rep Article In this paper we determine the effects of winding number on the dynamics of vortex torus knots and unknots in the context of classical, ideal fluid mechanics. We prove that the winding number — a topological invariant of torus knots — has a primary effect on vortex motion. This is done by applying the Moore-Saffman desingularization technique to the full Biot-Savart induction law, determining the influence of winding number on the 3 components of the induced velocity. Results have been obtained for 56 knots and unknots up to 51 crossings. In agreement with previous numerical results we prove that in general the propagation speed increases with the number of toroidal coils, but we notice that the number of poloidal coils may greatly modify the motion. Indeed we prove that for increasing aspect ratio and number of poloidal coils vortex motion can be even reversed, in agreement with previous numerical observations. These results demonstrate the importance of three-dimensional features in vortex dynamics and find useful applications to understand helicity and energy transfers across scales in vortical flows. Nature Publishing Group UK 2019-11-21 /pmc/articles/PMC6872556/ /pubmed/31754143 http://dx.doi.org/10.1038/s41598-019-53548-w Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Oberti, Chiara Ricca, Renzo L. Influence of winding number on vortex knots dynamics |
title | Influence of winding number on vortex knots dynamics |
title_full | Influence of winding number on vortex knots dynamics |
title_fullStr | Influence of winding number on vortex knots dynamics |
title_full_unstemmed | Influence of winding number on vortex knots dynamics |
title_short | Influence of winding number on vortex knots dynamics |
title_sort | influence of winding number on vortex knots dynamics |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6872556/ https://www.ncbi.nlm.nih.gov/pubmed/31754143 http://dx.doi.org/10.1038/s41598-019-53548-w |
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