A New Integrable Problem of Motion of Point Vortices on The Sphere
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.
KeywordsHydrodynamics ideal fluid vortex dynamics point vortex reduction bifurcation analysis
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