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Interaction between Kirchhoff vortices and point vortices in an ideal fluid

Alexey V. Borisov·Ivan S. Mamaev
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Abstract

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.

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Alexey V. Borisov, Ivan S. Mamaev. 2005-10-04. Interaction between Kirchhoff vortices and point vortices in an ideal fluid. https://arxiv.org/abs/nlin/0510006

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