Аннотация:
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 is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is found by the variable separation method . A reduced form of equations for two Kirchhoff vortices is proposed and used to analyze their regular and chaotic behavior.
Ключевые слова:
vortex patch, point vortex, integrability.
Поступила в редакцию: 01.03.2005 Принята в печать: 14.01.2006
Образец цитирования:
A. V. Borisov, I. S. Mamaev, “Interaction between Kirchhoff vortices and point vortices in an ideal fluid”, Regul. Chaotic Dyn., 12:1 (2007), 68–80
\RBibitem{BorMam07}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Interaction between Kirchhoff vortices and point vortices in an ideal fluid
\jour Regul. Chaotic Dyn.
\yr 2007
\vol 12
\issue 1
\pages 68--80
\mathnet{http://mi.mathnet.ru/rcd612}
\crossref{https://doi.org/10.1134/S1560354707010066}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2350297}
\zmath{https://zbmath.org/?q=an:1229.37108}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd612
https://www.mathnet.ru/rus/rcd/v12/i1/p68
Эта публикация цитируется в следующих 2 статьяx:
Eugene A. Ryzhov, “Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 27:11 (2017)
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface”, Regul. Chaotic Dyn., 15:4 (2010), 440–461
Цитирование в формате AMSBIB
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