A coaxial vortex ring model for vortex breakdown

Denis Blackmore; Morten Brøns; Arnaud Goullet

doi:10.1016/j.physd.2008.05.012

A coaxial vortex ring model for vortex breakdown

Denis Blackmore, Morten Brøns, Arnaud Goullet

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A simple-yet plausible-model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.

Original language	English (US)
Pages (from-to)	2817-2844
Number of pages	28
Journal	Physica D: Nonlinear Phenomena
Volume	237
Issue number	22
DOIs	https://doi.org/10.1016/j.physd.2008.05.012
State	Published - Nov 15 2008

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Keywords

Advection
Chaos
Melnikov functions
Poincaré maps
Shilnikov chaos
Swirl
Vortex ring dynamics and kinematics

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10.1016/j.physd.2008.05.012

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title = "A coaxial vortex ring model for vortex breakdown",

abstract = "A simple-yet plausible-model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.",

keywords = "Advection, Chaos, Melnikov functions, Poincar{\'e} maps, Shilnikov chaos, Swirl, Vortex ring dynamics and kinematics",

author = "Denis Blackmore and Morten Br{\o}ns and Arnaud Goullet",

note = "Funding Information: The main part of this paper was completed while D. Blackmore was a visiting professor at the Technical University of Denmark (DTU), with the M. Br{\o}ns serving as his immediate host and principal scientific collaborator. D. Blackmore wants to especially thank his hosts at DTU for providing him with such a stimulating and intellectually rich environment, along with a chance to enjoy the extraordinary Danish hospitality, and a wonderful opportunity to reconnect with his roots. He also wishes to acknowledge the generous support from the The Villum Kann Rasmussen Foundation during his visit to DTU. Debts of gratitude are also owed by D. Blackmore to Egon Krause for many insightful conversations and much encouragement that were instrumental in the formulation of the vortex breakdown model, and to Lu Ting and Omar Knio for sharing their considerable expertise and wisdom regarding the work in this paper. Finally, the authors would like to thank a reviewer for some insightful constructive criticism that led to this improvement of the original manuscript.",

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AU - Brøns, Morten

AU - Goullet, Arnaud

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PY - 2008/11/15

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N2 - A simple-yet plausible-model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.

AB - A simple-yet plausible-model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.

KW - Advection

KW - Chaos

KW - Melnikov functions

KW - Poincaré maps

KW - Shilnikov chaos

KW - Swirl

KW - Vortex ring dynamics and kinematics

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A coaxial vortex ring model for vortex breakdown

Abstract

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Keywords

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