Manifolds of vortex loops as coadjoint orbits

TL;DR

This paper investigates the geometric structure of vortex loops as coadjoint orbits of the area-preserving diffeomorphism group, providing insights into their mathematical properties and potential applications in fluid dynamics.

Contribution

It introduces a new class of coadjoint orbits characterized by vortex loops with zero vorticity densities, expanding the understanding of the geometric and algebraic structure of fluid flows.

Findings

Characterization of vortex loops as coadjoint orbits.

Analysis of the geometric properties of these orbits.

Potential implications for fluid dynamics and vortex behavior.

Abstract

We study a class of coadjoint orbits of the area preserving diffeomorphism group of the plane consisting of vortex loops, namely closed curves in the plane decorated with one-forms (vorticity densities) allowed to have zeros.