A Sharp Version of the Benjamin and Lighthill Conjecture for Steady Waves with Vorticity
(2024) In Journal of Mathematical Fluid Mechanics 26(2).- Abstract
We give a complete proof of the classical Benjamin and Lighthill conjecture for arbitrary two-dimensional steady water waves with vorticity. We show that the flow force constant of an arbitrary smooth solution is bounded by the flow force constants for the corresponding conjugate laminar flows. We prove these inequalities without any assumptions on the geometry of the surface profile and put no restrictions on the wave amplitude. Furthermore, we give a complete description of all cases when the equalities can occur. In particular, that excludes the existence of one-sided bores and multi-hump solitary waves. Our conclusions are new already for Stokes waves with a constant vorticity, while the case of equalities is new even in the... (More)
We give a complete proof of the classical Benjamin and Lighthill conjecture for arbitrary two-dimensional steady water waves with vorticity. We show that the flow force constant of an arbitrary smooth solution is bounded by the flow force constants for the corresponding conjugate laminar flows. We prove these inequalities without any assumptions on the geometry of the surface profile and put no restrictions on the wave amplitude. Furthermore, we give a complete description of all cases when the equalities can occur. In particular, that excludes the existence of one-sided bores and multi-hump solitary waves. Our conclusions are new already for Stokes waves with a constant vorticity, while the case of equalities is new even in the classical setting of irrotational waves.
(Less)
- author
- Lokharu, Evgeniy LU
- organization
- publishing date
- 2024-05
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Flow force, Gravity waves, Steady waves, Vorticity
- in
- Journal of Mathematical Fluid Mechanics
- volume
- 26
- issue
- 2
- article number
- 31
- publisher
- Birkhäuser Verlag
- external identifiers
-
- scopus:85189643942
- ISSN
- 1422-6928
- DOI
- 10.1007/s00021-024-00859-2
- language
- English
- LU publication?
- yes
- id
- 6f3dba1a-d652-418b-ae38-ec657cb43a01
- date added to LUP
- 2024-04-23 09:13:15
- date last changed
- 2024-04-23 09:14:05
@article{6f3dba1a-d652-418b-ae38-ec657cb43a01,
abstract = {{<p>We give a complete proof of the classical Benjamin and Lighthill conjecture for arbitrary two-dimensional steady water waves with vorticity. We show that the flow force constant of an arbitrary smooth solution is bounded by the flow force constants for the corresponding conjugate laminar flows. We prove these inequalities without any assumptions on the geometry of the surface profile and put no restrictions on the wave amplitude. Furthermore, we give a complete description of all cases when the equalities can occur. In particular, that excludes the existence of one-sided bores and multi-hump solitary waves. Our conclusions are new already for Stokes waves with a constant vorticity, while the case of equalities is new even in the classical setting of irrotational waves.</p>}},
author = {{Lokharu, Evgeniy}},
issn = {{1422-6928}},
keywords = {{Flow force; Gravity waves; Steady waves; Vorticity}},
language = {{eng}},
number = {{2}},
publisher = {{Birkhäuser Verlag}},
series = {{Journal of Mathematical Fluid Mechanics}},
title = {{A Sharp Version of the Benjamin and Lighthill Conjecture for Steady Waves with Vorticity}},
url = {{http://dx.doi.org/10.1007/s00021-024-00859-2}},
doi = {{10.1007/s00021-024-00859-2}},
volume = {{26}},
year = {{2024}},
}