A New Integrable Problem of Motion of Point Vortices on the Sphere

Borisov A. V.; Kilin A. A.; Mamaev I. S.

A New Integrable Problem of Motion of Point Vortices on the Sphere

2007, Vol. 3, No. 2, pp. 211-223

Author(s): Borisov A. V., Kilin A. A., Mamaev I. S.

The dynamics of an antipodal vortex on a sphere (a point vortex plus its antipode with opposite circulation) is considered. It is shown that the system of n antipodal vortices can be reduced by four dimensions (two degrees of freedom). The cases n=2,3 are explored in greater detail both analytically and numerically. We discuss Thomson, collinear and isosceles configurations of antipodal vortices and study their bifurcations.

Keywords: hydrodynamics, ideal fluid, vortex dynamics, point vortex, reduction, bifurcation analysis

Citation: Borisov A. V., Kilin A. A., Mamaev I. S., A New Integrable Problem of Motion of Point Vortices on the Sphere, Rus. J. Nonlin. Dyn., 2007, Vol. 3, No. 2, pp. 211-223

DOI:10.20537/nd0702006

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