English

Desingularization of vortex rings in 3 dimensional Euler flows: with swirl

Analysis of PDEs 2019-09-26 v3

Abstract

We study desingularization of steady vortex rings in three-dimensional axisymmetric incompressible Euler fluids with swirl. Using the variational method, we construct a two-parameter family of steady vortex rings, which constitute a desingularization of the classical circular vortex filament, in several kinds of domains. The precise localization of the asymptotic singular vortex filament is shown to depend on the circulation and the velocity at far fields of the vortex ring and the geometry of the domains. We also discuss other qualitative and asymptotic properties of these vortices.

Keywords

Cite

@article{arxiv.1909.00355,
  title  = {Desingularization of vortex rings in 3 dimensional Euler flows: with swirl},
  author = {Daomin Cao and Jie Wan and Weicheng Zhan},
  journal= {arXiv preprint arXiv:1909.00355},
  year   = {2019}
}

Comments

33 pages. arXiv admin note: text overlap with arXiv:1905.10342

R2 v1 2026-06-23T11:02:27.701Z