Kevin A. O'Neil, “Clustered Equilibria of Point Vortices”, Regul. Chaotic Dyn., 16:6 (2011), 555

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Regular and Chaotic Dynamics, 2011, Volume 16, Issue 6, Pages 555–561
DOI: https://doi.org/10.1134/S1560354711060013 (Mi rcd456)

This article is cited in 8 scientific papers (total in 8 papers)

Clustered Equilibria of Point Vortices

Kevin A. O'Neil

Department of Mathematical and Computer Sciences, The University of Tulsa, 800 S. Tucker Dr., Tulsa OK 74104 USA

Citations (8)

DOI: https://doi.org/10.1134/S1560354711060013

Abstract: Point vortex equilibria in which the vortices are arranged in clusters are examined. The vortex velocities in these configurations are all equal. Necessary conditions for their existence are established that relate the circulations within the clusters to the cluster radius. A method for generating these configurations by singular continuation is proved to be valid for the generic case. Finally, a partial analysis of exceptional cases is given and their connection to the existence of parametrized families of equilibria is described.

Keywords: point vortex, equilibrium, singular continuation.

Received: 24.03.2011
Accepted: 22.07.2011

Document Type: Article

MSC: 76B47, 70F10

Language: English

Citation: Kevin A. O'Neil, “Clustered Equilibria of Point Vortices”, Regul. Chaotic Dyn., 16:6 (2011), 555–561

Citation in format AMSBIB

\Bibitem{One11}

\by Kevin A. O'Neil

\paper Clustered Equilibria of Point Vortices

\jour Regul. Chaotic Dyn.

\yr 2011

\vol 16

\issue 6

\pages 555--561

\mathnet{http://mi.mathnet.ru/rcd456}

\crossref{https://doi.org/10.1134/S1560354711060013}

Linking options:

https://www.mathnet.ru/eng/rcd456

https://www.mathnet.ru/eng/rcd/v16/i6/p555

This publication is cited in the following 8 articles:

Ya-Lun Tsai, “Exploring circulations yielding no vortex equilibria”, Journal of Symbolic Computation, 114 (2023), 231
Sreethin Sreedharan Kallyadan, Priyanka Shukla, “Self-similar vortex configurations: Collapse, expansion, and rigid-vortex motion”, Phys. Rev. Fluids, 7:11 (2022)
Tsai Ya.-L., “Bifurcation of Point Vortex Equilibria: Four-Vortex Translating Configurations and Five-Vortex Stationary Configurations”, Nonlinearity, 33:12 (2020), 6564–6589
Dariya V. Safonova, Maria V. Demina, Nikolai A. Kudryashov, “Stationary Configurations of Point Vortices on a Cylinder”, Regul. Chaotic Dyn., 23:5 (2018), 569–579
M. V. Demina, N. A. Kudryashov, “Rotation, collapse, and scattering of point vortices”, Theor. Comput. Fluid Dyn., 28:3 (2014), 357
Kevin A O'Neil, “Singular continuation of point vortex relative equilibria on the plane and sphere”, Nonlinearity, 26:3 (2013), 777
Maria V. Demina, Nikolai A. Kudryashov, “Point Vortices and Classical Orthogonal Polynomials”, Regul. Chaotic Dyn., 17:5 (2012), 371–384
Alexey V. Bolsinov, Alexey V. Borisov, Ivan S. Mamaev, “The Bifurcation Analysis and the Conley Index in Mechanics”, Regul. Chaotic Dyn., 17:5 (2012), 451–478

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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