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Topological transition and helicity conversion of vortex knots and links

Published online by Cambridge University Press:  16 June 2022

Weiyu Shen Open the ORCID record for Weiyu Shen [Opens in a new window] ,
Jie Yao Open the ORCID record for Jie Yao [Opens in a new window] ,
Fazle Hussain Open the ORCID record for Fazle Hussain [Opens in a new window]  and
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window]
Weiyu Shen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China
Jie Yao
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Fazle Hussain
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China HEDPS-CAPT and BIC-ESAT, Peking University, Beijing 100871, PR China
*
†Email address for correspondence: [email protected]
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Abstract

Topological transition and helicity conversion of vortex torus knots and links are studied using direct numerical simulations of the incompressible Navier–Stokes equations. We find three topological transitional routes (viz. merging, reconnection and transition to turbulence) in the evolution of vortex knots and links over a range of torus aspect ratios and winding numbers. The topological transition depends not only on the initial topology but also on the initial geometry of knots/links. For small torus aspect ratios, the initially knotted or linked vortex tube rapidly merges into a vortex ring with a complete helicity conversion from the writhe and link components to the twist. For large torus aspect ratios, the vortex knot or link is untied into upper and lower coiled loops via the first vortex reconnection, with a helicity fluctuation including loss of writhe and link, and generation of twist. Then, the relatively unstable lower loop can undergo a secondary reconnection to split into multiple small vortices with a similar helicity fluctuation. Surprisingly, for moderate torus aspect ratios, the incomplete reconnection of tangled vortex loops together with strong vortex interactions triggers transition to turbulence, in which the topological helicity decomposition fails due to the breakdown of vortex core lines.

JFM classification

Mathematical Foundations: Topological fluid dynamics Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 943 , 25 July 2022 , A41
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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