M. A. Sokolovskiy, J. Verron, “Four-Vortex Motion in the Two Layer Approximation: Integrable Case”, Regul. Chaotic Dyn., 5:4 (2000), 413

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Regular and Chaotic Dynamics, 2000, Volume 5, Issue 4, Pages 413–436
DOI: https://doi.org/10.1070/RD2000v005n04ABEH000157 (Mi rcd888)

This article is cited in 21 scientific papers (total in 21 papers)

Four-Vortex Motion in the Two Layer Approximation: Integrable Case

M. A. Sokolovskiy^a, J. Verron^b

^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

Citations (21)

DOI: https://doi.org/10.1070/RD2000v005n04ABEH000157

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

Bibliographic databases:

Document Type: Article

MSC: 76C05

Language: English

Citation: M. A. Sokolovskiy, J. Verron, “Four-Vortex Motion in the Two Layer Approximation: Integrable Case”, Regul. Chaotic Dyn., 5:4 (2000), 413–436

Citation in format AMSBIB

\Bibitem{SokVer00}

\by M. A. Sokolovskiy, J. Verron

\paper Four-Vortex Motion in the Two Layer Approximation: Integrable Case

\jour Regul. Chaotic Dyn.

\yr 2000

\vol 5

\issue 4

\pages 413--436

\mathnet{http://mi.mathnet.ru/rcd888}

\crossref{https://doi.org/10.1070/RD2000v005n04ABEH000157}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1810624}

\zmath{https://zbmath.org/?q=an:0973.76018}

Linking options:

https://www.mathnet.ru/eng/rcd888

https://www.mathnet.ru/eng/rcd/v5/i4/p413

This publication is cited in the following 21 articles:

Sokolovskiy M.A. Koshel K.V. Dritschel D.G. Reinaud J.N., “N-Symmetric Interaction of N Hetons. i. Analysis of the Case N=2”, Phys. Fluids, 32:9 (2020), 096601
Sokolovskiy M.A. Carton X.J. Filyushkin B.N., “Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 1: Point-Vortex Approach”, Mathematics, 8:8 (2020), 1228
Koshel K.V. Ryzhov E.A. Carton X.J., “Vortex Interactions Subjected to Deformation Flows: a Review”, Fluids, 4:1 (2019), 14
J. N. Reinaud, M. A. Sokolovskiy, X. Carton, “Hetonic quartets in a two-layer quasi-geostrophic flow: V-states and stability”, Physics of Fluids, 30:5 (2018)
Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
X. Carton, D. Ciani, J. Verron, J. Reinaud, M. Sokolovskiy, “Vortex merger in surface quasi-geostrophy”, Geophysical & Astrophysical Fluid Dynamics, 110:1 (2016), 1
Jean N. Reinaud, Xavier Carton, “Head-on collisions between two quasi-geostrophic hetons in a continuously stratified fluid”, J. Fluid Mech., 779 (2015), 144
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 1
M.I. Jamaloodeen, “Integrable two layer point vortex motion on the half plane”, Journal of Geometry and Physics, 84 (2014), 55
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 37
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 317
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 179
M. A. Sokolovskiy, K. V. Koshel, J. Verron, “Three-vortex quasi-geostrophic dynamics in a two-layer fluid. Part 1. Analysis of relative and absolute motions”, J. Fluid Mech., 717 (2013), 232
K. V. Koshel, M. A. Sokolovskiy, J. Verron, “Three-vortex quasi-geostrophic dynamics in a two-layer fluid. Part 2. Regular and chaotic advection around the perturbed steady states”, J. Fluid Mech., 717 (2013), 255
A. I. Shavlyugin, “Two-layer quasi-geostrophic model of contour dynamics for a round basin”, Izv. Atmos. Ocean. Phys., 47:5 (2011), 619
Ziv Kizner, “Stability of point-vortex multipoles revisited”, Physics of Fluids, 23:6 (2011)
Mikhail A Sokolovskiy, Xavier J Carton, “Baroclinic multipole formation from heton interaction”, Fluid Dyn. Res., 42:4 (2010), 045501
GREGORY REZNIK, ZIV KIZNER, “Two-layer quasi-geostrophic singular vortices embedded in a regular flow. Part 1. Invariants of motion and stability of vortex pairs”, J. Fluid Mech., 584 (2007), 185
Denis Blackmore, Lu Ting, Omar Knio, “Studies of perturbed three vortex dynamics”, Journal of Mathematical Physics, 48:6 (2007)
Mohamed I. Jamaloodeen, Paul K. Newton, “Two-layer quasigeostrophic potential vorticity model”, Journal of Mathematical Physics, 48:6 (2007)

Citing articles in Google Scholar: Russian citations, English citations
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