UMR 5519, CNRS, BP 53 38041, Grenoble
Laboratoire des Ecoulements, Geophysiques et Industriels, CNRS
Sokolovskiy M. A., Verron J.
Some properties of motion of $A+1$ vortices in a two-layer rotating fluid
2006, Vol. 2, No. 1, pp. 27-54
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.