Geodesic
Some properties of motion of $A+1$ vortices in a two-layer rotating fluid
Russian journal of nonlinear dynamics, Tome 2 (2006) no. 1, pp. 27-54.

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The paper explores the properties of motion of $A+1$ point vortices with $A$ planes of symmetry immersed into a two-layer fluid. The central vortex is supposed to be in the upper layer while the other $A$ vortices have equal intensity and form a regular $A$-gon configuration in the lower layer. For $A\ge 2$, we study possible stationary motions. For $A=2$, using methods of qualitative analysis, we classify the motions of this vortical structure and obtain preliminary numerical results concerned with stability of symmetrical configurations.
Keywords: two-layer fluid, choreography
Mots-clés : point vortex, vortex structures, phase portrait. 
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     author = {M. A. Sokolovskiy and J. Verron},
     title = {Some properties of motion of $A+1$ vortices in a two-layer rotating fluid},
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M. A. Sokolovskiy; J. Verron. Some properties of motion of $A+1$ vortices in a two-layer rotating fluid. Russian journal of nonlinear dynamics, Tome 2 (2006) no. 1, pp. 27-54. http://geodesic.mathdoc.fr/item/ND_2006_2_1_a1/