Аннотация:
We consider the problem of motion of axisymmetric vortex rings in an ideal incompressible fluid. Using the topological approach, we present a method for complete qualitative analysis of the dynamics of a system of two vortex rings. In particular, we completely solve the problem of describing the conditions for the onset of leapfrogging motion of vortex rings. In addition, for the system of two vortex rings we find new families of motions where the relative distances remain finite (we call them pseudo-leapfrogging). We also find solutions for the problem of three vortex rings, which describe both the regular and chaotic leapfrogging motion of vortex rings.
This research was supported by the RFBR grant 11-01-91056-NTsNI_a, the Target Programme “Development of Scientific Potential of Higher Schools” (State contract 1.2953.2011, 2012–2014); the Federal Target Programme “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (State contract 14.B37.21.1935, 2009–2013); grant of leading scientific schools NSh-2519.2012.1. A. A. Kilin’s research was supported by the grant of the President of the Russian Federation for the Support of Young Russian Scientists–Candidates of Science (MK-8428.2010.1).
Поступила в редакцию: 19.09.2012 Принята в печать: 21.12.2012
Образец цитирования:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The Dynamics of Vortex Rings: Leapfrogging, Choreographies and the Stability Problem”, Regul. Chaotic Dyn., 18:1-2 (2013), 33–62
\RBibitem{BorKilMam13}
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper The Dynamics of Vortex Rings: Leapfrogging, Choreographies and the Stability Problem
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 33--62
\mathnet{http://mi.mathnet.ru/rcd94}
\crossref{https://doi.org/10.1134/S1560354713010036}
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\zmath{https://zbmath.org/?q=an:1273.76067}
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Цитирование в формате AMSBIB
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