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Nelin. Dinam., 2006, Volume 2, Number 2, Pages 199–213 (Mi nd163)  

Interaction between Kirchhoff vortices and point vortices in an ideal fluid

A. V. Borisovab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science

Abstract: We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is found. A reduced form of equations for two Kirchhoff vortices is proposed and used to analyze their regular and chaotic behavior.

Keywords: Kirchhoff vortices, integrability, Hamiltonian, stability, point vortex.

Full text: PDF file (535 kB)

Document Type: Article
UDC: 532.517
MSC: 76ј23

Citation: A. V. Borisov, I. S. Mamaev, “Interaction between Kirchhoff vortices and point vortices in an ideal fluid”, Nelin. Dinam., 2:2 (2006), 199–213

Citation in format AMSBIB
\Bibitem{BorMam06}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Interaction between Kirchhoff vortices and point vortices in an ideal fluid
\jour Nelin. Dinam.
\yr 2006
\vol 2
\issue 2
\pages 199--213
\mathnet{http://mi.mathnet.ru/nd163}


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