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Reduction and chaotic behavior of point vortices on a plane and a sphere

Pages: 100 - 109, Issue Special, August 2005

 Abstract        Full Text (396.5K)              

A.V. Borisov - Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation (email)
A.A. Kilin - Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation (email)
I.S. Mamaev - Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation (email)

Abstract: We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied to the vortex dynamics, it requires substantial modification. Reduction of four vortices on a sphere is given in more detail. We also use the Poincaré surface-of-section technique to perform the reduction a four-vortex system on a sphere.

Keywords:  Vortex dynamics, reduction, Poincar¶e map, point vortices.
Mathematics Subject Classification:  37N10, 76B47.

Received: September 2004;      Revised: April 2005;      Published: September 2005.