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This article is cited in 21 scientific papers (total in 21 papers)
Four-Vortex Motion in the Two Layer Approximation: Integrable Case
M. A. Sokolovskiya, J. Verronb a Institute of Water Problems of the
Russian Academy of Sciences,
3 Gubkina Str., 117735, Moscow, GSP-1, Russia
b Laboratoire des Ecoulements,
Géophysiques et Industriels,
UMR 5519, CNRS, BP53 X,
38041 Grenoble Cedex, France
Abstract:
The problem of four vortex lines with zero total circulation and zero impulse on a unlimited fluid plane, as it is known [1,3,4,16], is reduced to a problem of three point vortices and is integrated in quadratures. In the given work these results are transferred on a case of four vortices in a two-layer rotating liquid. The analysis of phase trajectories of relative motion of vortices is made, and the singularities of absolute motion on an example of a head-on, off-center collision of two two-layer vortex pairs are studied. In particular, the new class of quasistationary solutions for the given type of motions is obtained. The problems of interaction of the distributed (or finite-core) two-layer vortices are discussed.
Received: 16.11.2000
Citation:
M. A. Sokolovskiy, J. Verron, “Four-Vortex Motion in the Two Layer Approximation: Integrable Case”, Regul. Chaotic Dyn., 5:4 (2000), 413–436
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https://www.mathnet.ru/eng/rcd888 https://www.mathnet.ru/eng/rcd/v5/i4/p413
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