Interaction between Kirchhoff vortices and point vortices in an ideal fluid

Details Interaction between Kirchhoff vortices and point vortices in an ideal fluid Interaction between Kirchhoff vortices and point vortices in an ideal fluid

2005-10-04

arxiv.org/abs/nlin/0510006v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, 7 figures

Scientific paper

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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