Exact solutions for steadily translating deep water waves carrying hollow vortices
File(s)
Author(s)
Crowdy, Darren
Type
Journal Article
Abstract
This paper reports analytical solutions for steadily travelling two-dimensional water waves on deep water, without gravity or surface tension, carrying a cotravelling periodic row of hollow vortices. The solutions are hollow-vortex regularisations of the exact solutions of Crowdy & Roenby (Fluid Dyn. Res., vol. 46, 2014, 031424) for the analogous waves carrying a submerged point-vortex row, the free-surface shapes of which coincide with those for pure capillary waves and, like those, exhibit steady pinchoff at a critical wave amplitude. The same pinchoff phenomenon is shown to occur for the hollow-vortex regularisations. The new wave solutions are likely to provide a useful basis for perturbative, asymptotic or numerical studies when additional effects such as gravity, capillarity or compressibility are incorporated.
Date Issued
2026-02-25
Date Acceptance
2026-01-11
Citation
Journal of Fluid Mechanics, 2026, 1029
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
1029
Copyright Statement
© The Author(s), 2026. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Publication Status
Published
Article Number
A21
Date Publish Online
2026-02-16