On the Merger of Shielded Vortices

We investigate the merger of two identical two-dimensional vortices, individually surrounded by a ring of opposite-signed vorticity ( shielded vortices ). The novelty of this problem resides in the competition between the concentration of vorticity resulting from coalescence and its dipolar fragmentation due to barotropic instability. We describe the rich phenomenology and give a quantitative criterion for the critical merger distance. We account for the various nonlinear regimes: merging vs. breaking, "inverted merger" or fusion of the vortex peripheries (when the total circulation is negative), formation of "figure-eight" equilibria, dipoles, tripoles and quadrupoles.