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 a single-charged particle on the surface with a charge of order $1/\varepsilon ^{2}$ in an magnetic field $B$ that is everywhere normal to the surface and of strength $|B|=\Gamma _{1} +\Gamma… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.