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Role of internal structures within a vortex in helicity dynamics

Published online by Cambridge University Press:  04 September 2023

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: yyg@pku.edu.cn
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Abstract

Helicity, an invariant under ideal-fluid (Euler) evolution, has a topological interpretation in terms of writhe and twist for a closed vortex tube, but accurately quantifying twist is challenging in viscous flows. With a novel helicity decomposition, we present a framework to construct the differential twist that establishes the theoretical relation between the total twisting number and the local twist rate of each vortex surface. This framework can characterize coiling vortex lines and internal structures within a vortex – important in laminar–turbulence transition, and in vortex instability, reconnection and breakdown. As a typical example, we explore the dynamics of vortex rings with differential twist via direct numerical simulation (DNS) of the Navier–Stokes equations. Two twist waves with opposite chiralities propagate towards each other along the ring and then collide whence the local twist rate rapidly surges. Local vortex surfaces are squeezed into a disk-like dipole structure containing coiled vortex lines, leading to vortex bursting. We derive a Burgers-equation-like model to quantify this process, which predicts a bursting time that agrees well with DNS.

JFM classification

Mathematical Foundations: Topological fluid dynamics Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 970 , 10 September 2023 , A26
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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