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    Mikhail Sokolovskiy

    3 Gubkina Street, 119333, Moscow
    Institute of Water Problems of the RAS


    Sokolovskiy M. A., Verron J.
    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 $A\geqslant2$, 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, point vortex, vortex structures, choreography, phase portrait
    Citation: Sokolovskiy M. A., Verron J.,  Some properties of motion of $A+1$ vortices in a two-layer rotating fluid, Rus. J. Nonlin. Dyn., 2006, Vol. 2, No. 1, pp.  27-54

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