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Nelin. Dinam., 2006, Volume 2, Number 4, Pages 435–443 (Mi nd182)  

This article is cited in 2 scientific papers (total in 2 papers)

On the motion of two mass vortices in perfect fluid

S. M. Ramodanov

Institute of Cryptography, Communications and Informatics

Abstract: The system of two interacting dynamically 2D rigid circular cylinders in an infinite volume of perfect fluid was considered in [4, 5], while the pioneering contribution is due to Hicks [1, 2]. An allied problem, the motion of two spheres in perfect fluid, was studied by Stokes, Hicks, Carl and Vilhelm Bjerknes, Kirhhoff, and Joukowski (the references can be found in [3] and [7]). Assuming the circulations around the cylinders to be constant and making the radii of the cylinders infinitely small result in new 2D hydrodynamic objects called mass vortices [5]. The equations of motion for mass vortices expand upon the classical Kirhhoff equations governing the motion of ordinary point vortices. In this paper the motion of two mass vortices is examined in greater detail (some results have been obtained already in [5]. A reduction of order is performed; using the Poincaré surfae-of-section technique the system is shown to be generally non-integrable. Some integrable cases are indicated. In conclusion the motion of a single mass vortex and the motion of cylinder in a half plane are briefly investigated.

Keywords: motion of circular cylinders, mass vortices, reduction of order, vortices in a domain.

Full text: PDF file (617 kB)

Document Type: Article
UDC: 532.517
MSC: 76M23

Citation: S. M. Ramodanov, “On the motion of two mass vortices in perfect fluid”, Nelin. Dinam., 2:4 (2006), 435–443

Citation in format AMSBIB
\Bibitem{Ram06}
\by S.~M.~Ramodanov
\paper On the motion of two mass vortices in perfect fluid
\jour Nelin. Dinam.
\yr 2006
\vol 2
\issue 4
\pages 435--443
\mathnet{http://mi.mathnet.ru/nd182}


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    This publication is cited in the following articles:
    1. Borisov A.V., Mamaev I.S., Ramodanov S.M., “Basic principles and models of dynamic advection”, Dokl. Phys., 55:5 (2010), 223–227  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Dinamicheskaya advektsiya”, Nelineinaya dinam., 6:3 (2010), 521–530  mathnet  elib
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