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Separation scaling for viscous vortex reconnection

Published online by Cambridge University Press:  06 August 2020

Jie Yao Open the ORCID record for Jie Yao [Opens in a new window]  and
Fazle Hussain Open the ORCID record for Fazle Hussain [Opens in a new window]
Jie Yao
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX79409, USA
Fazle Hussain*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX79409, USA
*
†Email address for correspondence: fazle.hussain@ttu.edu
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Abstract

Reconnection plays a significant role in the dynamics of plasmas, polymers and macromolecules, as well as in numerous laminar and turbulent flow phenomena in both classical and quantum fluids. Extensive studies in quantum vortex reconnection show that the minimum separation distance $\delta$ between interacting vortices follows a $\delta(t) \sim t^{1/2}$ scaling. Due to the complex nature of the dynamics (e.g. the formation of bridges and threads as well as successive reconnections and avalanche), such scaling has never been reported for (classical) viscous vortex reconnection. Using direct numerical simulation of the Navier–Stokes equations, we study viscous reconnection of slender vortices, whose core size is much smaller than the radius of the vortex curvature. For separations that are large compared to the vortex core size, we discover that $\delta (t)$ between the two interacting viscous vortices surprisingly also follows the 1/2-power scaling for both pre- and post-reconnection events. The prefactors in this 1/2-power law are found to depend not only on the initial configuration but also on the vortex Reynolds number (or viscosity). Our finding in viscous reconnection, complementing numerous works on quantum vortex reconnection, suggests that there is indeed a universal route for reconnection – an essential result for understanding the various facets of the vortex reconnection phenomena and their potential modelling, as well as possibly explaining turbulence cascade physics.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex interactions
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , R4
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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Yao and Hussainy supplementary movie 1

Evolution of flow structures for reconnection of colliding vortex rings at Re Γ = 2000 using direct numerical simulation of Naiver-Stokes equation. The radius of the vortex ring is R=1 and the initial minimum distance between two rings is δ0 = 0.2. The flow structures are represented by vorticity isosurface at 5% of maximum initial vorticity |ω| = 0.05ω0.

Download Yao and Hussainy supplementary movie 1(Video)
Video 7.1 MB

Yao and Hussainy supplementary movie 2

Evolution of vortex axis for reconnection of colliding vortex rings at ReΓ = 2000

Download Yao and Hussainy supplementary movie 2(Video)
Video 1.4 MB

Yao and Hussainy supplementary movie 3

Evolution of vortex axis for reconnection of colliding vortex rings at ReΓ = 2000

Download Yao and Hussainy supplementary movie 3(Video)
Video 3.1 MB

Yao and Hussainy supplementary movie 4

Evolution of vortex axis for reconnection of orthogonal straight vortex tubes at ReΓ= 2000.

Download Yao and Hussainy supplementary movie 4(Video)
Video 1.4 MB

Yao and Hussainy supplementary movie 5

Evolution of flow structures for reconnection of vortex ring with a straight tube at ReΓ= 2000 using direct numerical simulation of Naiver-Stokes equation. The radius of the vortex ring is R = 1 and the initial minimum distance is δ0 = 0.4. The flow structures are represented by vorticity isosurface at 5% of maximum initial vorticity |ω| = 0.05ω0 .

Download Yao and Hussainy supplementary movie 5(Video)
Video 7.4 MB

Yao and Hussainy supplementary movie 6

Evolution of vortex axis for reconnection of vortex ring with a straight tube at ReΓ= 2000

Download Yao and Hussainy supplementary movie 6(Video)
Video 2.6 MB
Supplementary material: PDF

Yao and Hussainy supplementary material

Supplementary data

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