Helicoids and vortices
Differential Geometry
2022-12-06 v4 Fluid Dynamics
Abstract
We point out an interesting connection between fluid dynamics and minimal surface theory: When gluing helicoids into a minimal surface, the limit positions of the helicoids correspond to a "vortex crystal", an equilibrium of point vortices in 2D fluid that move together as a rigid body. While vortex crystals have been studied for almost 150 years, the gluing construction of minimal surfaces is relatively new. As a consequence of the connection, we obtain many new minimal surfaces and some new vortex crystals by simply comparing notes.
Keywords
Cite
@article{arxiv.2201.13091,
title = {Helicoids and vortices},
author = {Hao Chen and Daniel Freese},
journal= {arXiv preprint arXiv:2201.13091},
year = {2022}
}
Comments
18 pages, 5 figures. Add converse statements as required by referees. Otherwise minor revision. Final before publishing