From generation to chaotic motion of a ring configuration of vortex structures on a sphere

This is a review article of recent research developments on the motion of a polygonal ring configuration of vortex structures with singular vorticity distributions in incompressible and inviscid flows on a non-rotating sphere. Numerical computation of a single vortex sheet reveals that the Kelvin-Helmholtz instability gives rise to the formation of a polygonal ring arrangement of rolling-up spirals. An application of methods of Hamiltonian dynamics to the N-vortex problem on the sphere shows that the motion of the ring configuration of homogeneous point vortices, which is a simple model for the rolling-up spirals, becomes chaotic after a long time evolution. Some remarks on an extension of the present research and a generic non-self-similar collapse are also provided.