On the amplitude and the flow force constant of steady water waves
(2021) In Journal of Fluid Mechanics 921.- Abstract
We prove a new explicit inequality for the non-dimensional flow force constant, significantly improving the Benjamin and Lighthill conjecture about irrotational steady water waves. As a corollary, we prove a bound for the wave amplitude in terms of the Bernoulli constant. We show that the amplitude decays as r−2 when r→+∞, where r is the non-dimensional Bernoulli constant. We explain that the latter limit corresponds to deep water waves and the bound for the amplitude is sharp. In terms of physical parameters the result states that the amplitude a of an arbitrary Stokes wave is bounded by Cm2g/Q2, where m is the relative mass flux, g is the gravitational constant, Q is the total head and C is an absolute constant given explicitly. In... (More)
We prove a new explicit inequality for the non-dimensional flow force constant, significantly improving the Benjamin and Lighthill conjecture about irrotational steady water waves. As a corollary, we prove a bound for the wave amplitude in terms of the Bernoulli constant. We show that the amplitude decays as r−2 when r→+∞, where r is the non-dimensional Bernoulli constant. We explain that the latter limit corresponds to deep water waves and the bound for the amplitude is sharp. In terms of physical parameters the result states that the amplitude a of an arbitrary Stokes wave is bounded by Cm2g/Q2, where m is the relative mass flux, g is the gravitational constant, Q is the total head and C is an absolute constant given explicitly. In particular, this implies that a<Cc2g−1, where c is the wave speed. The latter inequality is valid for all Stokes waves, irrespective of wavelength or amplitude, including extreme waves.
(Less)
- author
- Lokharu, Evgeniy LU
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Surface gravity waves
- in
- Journal of Fluid Mechanics
- volume
- 921
- article number
- A2
- publisher
- Cambridge University Press
- external identifiers
-
- scopus:85108519185
- ISSN
- 0022-1120
- DOI
- 10.1017/jfm.2021.471
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: ©
- id
- 339eede5-6481-4ebf-9f4f-74dc248fa903
- date added to LUP
- 2023-11-03 13:19:20
- date last changed
- 2023-12-04 16:17:42
@article{339eede5-6481-4ebf-9f4f-74dc248fa903,
abstract = {{<p>We prove a new explicit inequality for the non-dimensional flow force constant, significantly improving the Benjamin and Lighthill conjecture about irrotational steady water waves. As a corollary, we prove a bound for the wave amplitude in terms of the Bernoulli constant. We show that the amplitude decays as r−2 when r→+∞, where r is the non-dimensional Bernoulli constant. We explain that the latter limit corresponds to deep water waves and the bound for the amplitude is sharp. In terms of physical parameters the result states that the amplitude a of an arbitrary Stokes wave is bounded by Cm2g/Q2, where m is the relative mass flux, g is the gravitational constant, Q is the total head and C is an absolute constant given explicitly. In particular, this implies that a<Cc2g−1, where c is the wave speed. The latter inequality is valid for all Stokes waves, irrespective of wavelength or amplitude, including extreme waves.</p>}},
author = {{Lokharu, Evgeniy}},
issn = {{0022-1120}},
keywords = {{Surface gravity waves}},
language = {{eng}},
publisher = {{Cambridge University Press}},
series = {{Journal of Fluid Mechanics}},
title = {{On the amplitude and the flow force constant of steady water waves}},
url = {{http://dx.doi.org/10.1017/jfm.2021.471}},
doi = {{10.1017/jfm.2021.471}},
volume = {{921}},
year = {{2021}},
}