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