Pointed vortex loops in ideal 2D fluids

Abstract

We study a special kind of singular vorticities in ideal 2D fluids that combine features of point vortices and vortex sheets, namely pointed vortex loops. We focus on the coadjoint orbits of the area-preserving diffeomorphism group of ${\mathbb{R}}^2$ determined by them. We show that a polarization subgroup consists of diffeomorphisms that preserve the loop as a set, thus the configuration space is the space of loops that enclose a fixed area, without information on vorticity distribution and attached points.

14 pages

References in corpus (1)

• Geometric Structures on Spaces of Weighted Submanifolds

Cited by in corpus (3)

• Weighted nonlinear flag manifolds as coadjoint orbits
• A dual pair for the group of volume preserving diffeomorphisms
• Manifolds of vortex loops as coadjoint orbits