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Helicity dynamics in reconnection events of topologically complex vortex flows

Published online by Cambridge University Press:  11 June 2021

Xinran Zhao Open the ORCID record for Xinran Zhao [Opens in a new window]  and
Carlo Scalo Open the ORCID record for Carlo Scalo [Opens in a new window]
Xinran Zhao*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN47907, USA
Carlo Scalo
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN47907, USA
*
†Email address for correspondence: zhao596@purdue.edu
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Abstract

In this paper, we address the question of whether total helicity is conserved through viscous reconnection events in topologically complex vortex flows. To answer this question, we performed direct numerical simulations (DNS) focused on two complex vortex flow problems: (1) a trefoil knot and (2) a two-ring link, both simulated for various vortex core radii. The DNS framework relies on a block-structured adaptive mesh refinement (AMR) technique. A third simulation of a colliding pair of unlinked vortex rings, which exhibit no total helicity change, is also performed to serve as a reference case. The results show that a well-defined total helicity jump occurs during the unknotting/unlinking events of cases (1) and (2), which arises from the annihilation of the local helicity density content in the reconnection regions. Changes in total helicity become steeper as thinner core radii are considered for both cases (1) and (2). Finally, an analytical derivation based on the reconnection of two infinitesimal anti-parallel vortex filaments is provided that quantitatively links helicity annihilation and viscous circulation transfer processes, which unveils the fundamental hydrodynamic mechanisms responsible for production/destruction of total helicity during reconnection events.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex breakdown Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A30
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Zhao and Scalo supplementary movie 1

Movie 1: trefoil knot vortex

Download Zhao and Scalo supplementary movie 1(Video)
Video 7.6 MB

Zhao and Scalo supplementary movie 2

Movie 2: two-ring link vortex

Download Zhao and Scalo supplementary movie 2(Video)
Video 5.5 MB