The role of constant vorticity on weakly nonlinear surface gravity waves
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.wavemoti.2020.102702 http://hdl.handle.net/11449/207138 |
Resumo: | This manuscript describes the derivation of systems of equations for weakly nonlinear gravity waves in shallow water in the presence of constant vorticity. The derivation is based on a multi-layer generalization of the traditional columnar Ansatz. A perturbative development in a nonlinear parameter and a dispersive parameter allow us to obtain sets of equations, for the horizontal fluid velocity and the free surface, able to describe propagation of weakly nonlinear and dispersive surface waves moving in water with some prescribed initial constant vorticity. We have shown that vorticity plays a central role on the dispersive properties of the system. When it is weak, it acts as a correction in linear and nonlinear dispersive terms. When stronger, it can also influence the nondispersive behavior of the system. Explicit steady solutions of the system corresponding to zero, weak, normal or strong vorticity are obtained. They correspond to solitary waves. Evolution of the soliton celerity, amplitude and width for these four cases are discussed. |
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Repositório Institucional da UNESP |
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The role of constant vorticity on weakly nonlinear surface gravity wavesThis manuscript describes the derivation of systems of equations for weakly nonlinear gravity waves in shallow water in the presence of constant vorticity. The derivation is based on a multi-layer generalization of the traditional columnar Ansatz. A perturbative development in a nonlinear parameter and a dispersive parameter allow us to obtain sets of equations, for the horizontal fluid velocity and the free surface, able to describe propagation of weakly nonlinear and dispersive surface waves moving in water with some prescribed initial constant vorticity. We have shown that vorticity plays a central role on the dispersive properties of the system. When it is weak, it acts as a correction in linear and nonlinear dispersive terms. When stronger, it can also influence the nondispersive behavior of the system. Explicit steady solutions of the system corresponding to zero, weak, normal or strong vorticity are obtained. They correspond to solitary waves. Evolution of the soliton celerity, amplitude and width for these four cases are discussed.Délégation Générale pour l'ArmementFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Agence Nationale de la RechercheLaboratoire Charles Coulomb (L2C) Univ. Montpellier CNRSInstitute of Technology University of Dschang, P.O. Box 134Université de Toulon Aix Marseille Univ. CNRS IRD MIOInstituto de Física Téorica-UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271 Bloco IIInstituto de Física Téorica-UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271 Bloco IIAgence Nationale de la Recherche: 13-ASTR-0007CNRSUniversity of DschangMIOUniversidade Estadual Paulista (Unesp)Manna, M. A.Noubissié, S.Touboul, J.Simon, B.Kraenkel, R. A. [UNESP]2021-06-25T10:49:35Z2021-06-25T10:49:35Z2021-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.wavemoti.2020.102702Wave Motion, v. 102.0165-2125http://hdl.handle.net/11449/20713810.1016/j.wavemoti.2020.1027022-s2.0-85099379803Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengWave Motioninfo:eu-repo/semantics/openAccess2021-10-23T16:16:11Zoai:repositorio.unesp.br:11449/207138Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:09:07.619414Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
The role of constant vorticity on weakly nonlinear surface gravity waves |
title |
The role of constant vorticity on weakly nonlinear surface gravity waves |
spellingShingle |
The role of constant vorticity on weakly nonlinear surface gravity waves Manna, M. A. |
title_short |
The role of constant vorticity on weakly nonlinear surface gravity waves |
title_full |
The role of constant vorticity on weakly nonlinear surface gravity waves |
title_fullStr |
The role of constant vorticity on weakly nonlinear surface gravity waves |
title_full_unstemmed |
The role of constant vorticity on weakly nonlinear surface gravity waves |
title_sort |
The role of constant vorticity on weakly nonlinear surface gravity waves |
author |
Manna, M. A. |
author_facet |
Manna, M. A. Noubissié, S. Touboul, J. Simon, B. Kraenkel, R. A. [UNESP] |
author_role |
author |
author2 |
Noubissié, S. Touboul, J. Simon, B. Kraenkel, R. A. [UNESP] |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
CNRS University of Dschang MIO Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Manna, M. A. Noubissié, S. Touboul, J. Simon, B. Kraenkel, R. A. [UNESP] |
description |
This manuscript describes the derivation of systems of equations for weakly nonlinear gravity waves in shallow water in the presence of constant vorticity. The derivation is based on a multi-layer generalization of the traditional columnar Ansatz. A perturbative development in a nonlinear parameter and a dispersive parameter allow us to obtain sets of equations, for the horizontal fluid velocity and the free surface, able to describe propagation of weakly nonlinear and dispersive surface waves moving in water with some prescribed initial constant vorticity. We have shown that vorticity plays a central role on the dispersive properties of the system. When it is weak, it acts as a correction in linear and nonlinear dispersive terms. When stronger, it can also influence the nondispersive behavior of the system. Explicit steady solutions of the system corresponding to zero, weak, normal or strong vorticity are obtained. They correspond to solitary waves. Evolution of the soliton celerity, amplitude and width for these four cases are discussed. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T10:49:35Z 2021-06-25T10:49:35Z 2021-04-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.wavemoti.2020.102702 Wave Motion, v. 102. 0165-2125 http://hdl.handle.net/11449/207138 10.1016/j.wavemoti.2020.102702 2-s2.0-85099379803 |
url |
http://dx.doi.org/10.1016/j.wavemoti.2020.102702 http://hdl.handle.net/11449/207138 |
identifier_str_mv |
Wave Motion, v. 102. 0165-2125 10.1016/j.wavemoti.2020.102702 2-s2.0-85099379803 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Wave Motion |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129398149218304 |