Trapped modes in a fluid with three layers topped by a rigid lid
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.21/16056 |
Resumo: | We consider trapping of linear water waves by a submerged horizontal cylinder in a three-layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary-value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given. |
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Trapped modes in a fluid with three layers topped by a rigid lidSpectral problemThree-layer fluidTrapped modesWe consider trapping of linear water waves by a submerged horizontal cylinder in a three-layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary-value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given.WileyRCIPLCal, FilipeDias, Gonçalo A. S.Pereira, Bruno M. M.2023-05-17T11:53:07Z2022-11-152022-11-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/16056engCAL, Filipe S.; DIAS, Gonçalo A. S.; PEREIRA, Bruno M. A. M. – Trapped modes in a fluid with three layers topped by a rigid lid. Mathematical Methods in the Applied Sciences. ISSN0170-4214. Vol. 45, N.º 16 (2022), pp. 9928-9944.0170-421410.1002/mma.8347.1099-1476metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T10:14:18Zoai:repositorio.ipl.pt:10400.21/16056Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:23:39.717214Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Trapped modes in a fluid with three layers topped by a rigid lid |
title |
Trapped modes in a fluid with three layers topped by a rigid lid |
spellingShingle |
Trapped modes in a fluid with three layers topped by a rigid lid Cal, Filipe Spectral problem Three-layer fluid Trapped modes |
title_short |
Trapped modes in a fluid with three layers topped by a rigid lid |
title_full |
Trapped modes in a fluid with three layers topped by a rigid lid |
title_fullStr |
Trapped modes in a fluid with three layers topped by a rigid lid |
title_full_unstemmed |
Trapped modes in a fluid with three layers topped by a rigid lid |
title_sort |
Trapped modes in a fluid with three layers topped by a rigid lid |
author |
Cal, Filipe |
author_facet |
Cal, Filipe Dias, Gonçalo A. S. Pereira, Bruno M. M. |
author_role |
author |
author2 |
Dias, Gonçalo A. S. Pereira, Bruno M. M. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Cal, Filipe Dias, Gonçalo A. S. Pereira, Bruno M. M. |
dc.subject.por.fl_str_mv |
Spectral problem Three-layer fluid Trapped modes |
topic |
Spectral problem Three-layer fluid Trapped modes |
description |
We consider trapping of linear water waves by a submerged horizontal cylinder in a three-layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary-value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-11-15 2022-11-15T00:00:00Z 2023-05-17T11:53:07Z |
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://hdl.handle.net/10400.21/16056 |
url |
http://hdl.handle.net/10400.21/16056 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
CAL, Filipe S.; DIAS, Gonçalo A. S.; PEREIRA, Bruno M. A. M. – Trapped modes in a fluid with three layers topped by a rigid lid. Mathematical Methods in the Applied Sciences. ISSN0170-4214. Vol. 45, N.º 16 (2022), pp. 9928-9944. 0170-4214 10.1002/mma.8347. 1099-1476 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
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metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Wiley |
publisher.none.fl_str_mv |
Wiley |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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