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 Regul. Chaotic Dyn.: Год: Том: Выпуск: Страница: Найти

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 Regul. Chaotic Dyn., 2018, том 23, выпуск 5, страницы 530–550 (Mi rcd343)

Finite-time Collapse of Three Point Vortices in the Plane

Vikas S. Krishnamurthya, Mark A. Stremlerb

a Erwin Schrodinger International Institute for Mathematics and Physics, Boltzmangasse 9, 1090 Vienna, Austria
b Department of Biomedical Engineering and Mechanics, 460 Turner Street NE, Suite 304, Blacksburg, VA 24061, USA

Аннотация: We investigate the finite-time collapse of three point vortices in the plane utilizing the geometric formulation of three-vortexmotion from Krishnamurthy, Aref and Stremler (2018) Phys. Rev. Fluids 3, 024702. In this approach, the vortex system is described in terms of the interior angles of the triangle joining the vortices, the circle that circumscribes that triangle, and the orientation of the triangle. Symmetries in the governing geometric equations of motion for the general three-vortex problem allow us to consider a reduced parameter space in the relative vortex strengths. The well-known conditions for three-vortex collapse are reproduced in this formulation, and we show that these conditions are necessary and sufficient for the vortex motion to consist of collapsing or expanding self-similar motion. The geometric formulation enables a new perspective on the details of this motion. Relationships are determined between the interior angles of the triangle, the vortex strength ratios, the (finite) system energy, the time of collapse, and the distance traveled by the configuration prior to collapse. Several illustrative examples of both collapsing and expanding motion are given.

Ключевые слова: ideal flow, vortex dynamics, point vortices

 Финансовая поддержка V.S.K. acknowledges financial support from CAPES/Brazil through a Science Without Borders postdoctoral program during his stay at the Federal University of Pernambuco, and the ESI Junior Research Fellowship Program during his stay at the Erwin Schrödinger International Institute for Mathematics and Physics, University of Vienna.

DOI: https://doi.org/10.1134/S1560354718050040

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Тип публикации: Статья
MSC: 70F07, 70K99, 76B47
Поступила в редакцию: 08.07.2018
Принята в печать:18.08.2018
Язык публикации: английский

Образец цитирования: Vikas S. Krishnamurthy, Mark A. Stremler, “Finite-time Collapse of Three Point Vortices in the Plane”, Regul. Chaotic Dyn., 23:5 (2018), 530–550

Цитирование в формате AMSBIB
\RBibitem{KriStr18} \by Vikas S. Krishnamurthy, Mark A. Stremler \paper Finite-time Collapse of Three Point Vortices in the Plane \jour Regul. Chaotic Dyn. \yr 2018 \vol 23 \issue 5 \pages 530--550 \mathnet{http://mi.mathnet.ru/rcd343} \crossref{https://doi.org/10.1134/S1560354718050040} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000447268600004} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054605889} 

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