Geodesic
Interaction between Kirchhoff vortices and point vortices in an ideal fluid
Russian journal of nonlinear dynamics, Tome 2 (2006) no. 2, pp. 199-213.

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We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is found. A reduced form of equations for two Kirchhoff vortices is proposed and used to analyze their regular and chaotic behavior.
Keywords: Kirchhoff vortices, integrability, Hamiltonian, stability
Mots-clés : point vortex. 
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     author = {A. V. Borisov and I. S. Mamaev},
     title = {Interaction between {Kirchhoff} vortices and point vortices in an ideal fluid},
     journal = {Russian journal of nonlinear dynamics},
     pages = {199--213},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2006_2_2_a4/}
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A. V. Borisov; I. S. Mamaev. Interaction between Kirchhoff vortices and point vortices in an ideal fluid. Russian journal of nonlinear dynamics, Tome 2 (2006) no. 2, pp. 199-213. http://geodesic.mathdoc.fr/item/ND_2006_2_2_a4/