A new canonical reduction of three-vortex motion and its application to vortex-dipole scattering
A. Anurag,
R. H. Goodman,
E. K. O'Grady
Abstract:We introduce a new reduction of the motion of three point vortices in a two-dimensional ideal fluid. This proceeds in two stages: a change of variables to Jacobi coordinates and then a Nambu reduction. The new coordinates demonstrate that the dynamics evolve on a two-dimensional manifold whose topology depends on the sign of a parameter κ2 that arises in the reduction. For κ2>0, the phase space is spherical, while for κ2<0, the dynamics are confined to the upper sheet of a two-sheeted hyperboloid… Show more
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