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Regul. Chaotic Dyn., 2016, Volume 21, Issue 3, Pages 367–376 (Mi rcd83)  

This article is cited in 5 scientific papers (total in 5 papers)

The Dynamics of Vortex Sources in a Deformation Flow

Ivan A. Bizyaeva, Alexey V. Borisova, Ivan S. Mamaevab

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, Ekaterinburg, 620990, Russia

Abstract: This paper is concerned with the dynamics of vortex sources in a deformation flow. The case of two vortex sources is shown to be integrable by quadratures. In addition, the relative equilibria (of the reduced system) are examined in detail and it is shown that in this case the trajectory of vortex sources is an ellipse.

Keywords: integrability, vortex sources, reduction, deformation flow

Funding Agency Grant Number
Russian Science Foundation 15-12-20035
Russian Foundation for Basic Research 14-01-00395-a
15-38-20879 mol_a_ved
Dynasty Foundation
The work of I. A. Bizyaev (Section 3) was carried out within the framework of the state assignment for institutions of higher education and partially supported by the Dynasty Foundation. The work of A. V. Borisov (Sections 1, 2) was supported by the Russian Science Foundation (project No. 15-12-20035). The work of I. S. Mamaev (Sections 4, 5) was supported by the RFBR grants Nos. 14-01-00395-a and 15-38-20879 mol_a_ved.


DOI: https://doi.org/10.1134/S1560354716030084

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 76M23
Received: 01.04.2016
Accepted:26.04.2016
Language: English

Citation: Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Vortex Sources in a Deformation Flow”, Regul. Chaotic Dyn., 21:3 (2016), 367–376

Citation in format AMSBIB
\Bibitem{BizBorMam16}
\by Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
\paper The Dynamics of Vortex Sources in a Deformation Flow
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 3
\pages 367--376
\mathnet{http://mi.mathnet.ru/rcd83}
\crossref{https://doi.org/10.1134/S1560354716030084}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3508237}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000377616400008}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84975824499}


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

    This publication is cited in the following articles:
    1. Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266  mathnet  crossref  mathscinet
    2. Evgeny V. Vetchanin, Ivan S. Mamaev, “Dynamics of Two Point Vortices in an External Compressible Shear Flow”, Regul. Chaotic Dyn., 22:8 (2017), 893–908  mathnet  crossref
    3. Sergei V. Sokolov, Pavel E. Ryabov, “Bifurcation Analysis of the Dynamics of Two Vortices in a Bose Einstein Condensate. The Case of Intensities of Opposite Signs”, Regul. Chaotic Dyn., 22:8 (2017), 976–995  mathnet  crossref
    4. Yu. M. Grishin, M. Long, “Numerical simulation of the argon-hydrogen plasma flow in the channel of RF inductively coupled plasma torch”, International Conference Problems of Thermal Physics and Power Engineering (PTPPE-2017), Journal of Physics Conference Series, 891, IOP Publishing Ltd, 2017, UNSP 012302  crossref  isi  scopus
    5. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636  mathnet  crossref
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