Singular Vortex Pairs Follow Magnetic Geodesics
Singular Vortex Pairs Follow Magnetic Geodesics
Abstract We consider pairs of point vortices having circulations $\Gamma _{1}$ and $\Gamma _{2}$ and confined to a two-dimensional surface $S$. In the limit of zero initial separation $\varepsilon $, we prove that they follow a magnetic geodesic in unison, if properly renormalized. Specifically, the “singular vortex pair” moves as …