On the Benjamin-Lighthill conjecture for water waves with vorticity
(2017) In Journal of Fluid Mechanics 825. p.961-1001- Abstract
We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin-Lighthill conjecture for flows with values of Bernoulli's constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values... (More)
We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin-Lighthill conjecture for flows with values of Bernoulli's constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.
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- author
- Kozlov, V. ; Kuznetsov, N. and Lokharu, E. LU
- publishing date
- 2017-08-25
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- surface gravity waves, waves/free-surface flows
- in
- Journal of Fluid Mechanics
- volume
- 825
- pages
- 41 pages
- publisher
- Cambridge University Press
- external identifiers
-
- scopus:85026363545
- ISSN
- 0022-1120
- DOI
- 10.1017/jfm.2017.361
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2017 Cambridge University Press.
- id
- 8e81b0cf-e2b5-4948-a911-c8a138e4b6cb
- date added to LUP
- 2023-11-03 13:21:44
- date last changed
- 2024-03-07 06:45:50
@article{8e81b0cf-e2b5-4948-a911-c8a138e4b6cb,
abstract = {{<p>We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin-Lighthill conjecture for flows with values of Bernoulli's constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.</p>}},
author = {{Kozlov, V. and Kuznetsov, N. and Lokharu, E.}},
issn = {{0022-1120}},
keywords = {{surface gravity waves; waves/free-surface flows}},
language = {{eng}},
month = {{08}},
pages = {{961--1001}},
publisher = {{Cambridge University Press}},
series = {{Journal of Fluid Mechanics}},
title = {{On the Benjamin-Lighthill conjecture for water waves with vorticity}},
url = {{http://dx.doi.org/10.1017/jfm.2017.361}},
doi = {{10.1017/jfm.2017.361}},
volume = {{825}},
year = {{2017}},
}