Instability of waves in deep water — A discrete Hamiltonian approach
The stability of waves in deep water has classically been approached via linear stability analysis, with various model equations, such as the nonlinear Schrödinger equation, serving as points of departure. Some of the most well-studied instabilities involve the interaction of four waves – so called...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/42132
- Acceso en línea:
- https://repository.urosario.edu.co/handle/10336/42132
- Palabra clave:
- Water waves
Wave–wave interaction
Weakly-nonlinear surface waves
Instability
Hamiltonian systems
- Rights
- License
- Attribution 4.0 International
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49a0984b-c3ad-4c03-980b-b1c49c56cd2b2024-01-31T18:27:29Z2024-01-31T18:27:29Z2023-09-012023The stability of waves in deep water has classically been approached via linear stability analysis, with various model equations, such as the nonlinear Schrödinger equation, serving as points of departure. Some of the most well-studied instabilities involve the interaction of four waves – so called Type I instabilities – or five waves – Type II instabilities. A unified description of four and five wave interaction can be provided by the reduced Hamiltonian derived by Krasitskii (1994). Exploiting additional conservation laws, the discretised Hamiltonian may be used to shed light on these four and five wave instabilities without restrictions on spectral bandwidth. We derive equivalent autonomous, planar dynamical systems which allow for straightforward insight into the emergence of instability and the long time dynamics. They also yield new steady-state solutions, as well as discrete breathers associated with heteroclinic orbits in the phase space.application/pdf10.1016/j.euromechflu.2023.06.0080997-7546https://repository.urosario.edu.co/handle/10336/42132engUniversidad del Rosariohttps://www.sciencedirect.com/science/article/pii/S0997754623000857/pdfft?md5=32969424efe2d390829a14837818aa16&pid=1-s2.0-S0997754623000857-main.pdfAttribution 4.0 InternationalAbierto (Texto Completo)https://creativecommons.org/licenses/by/4.0/http://purl.org/coar/access_right/c_abf2European Journal of Mechanics, B/Fluidsinstname:Universidad del Rosarioreponame:Repositorio Institucional EdocURWater wavesWave–wave interactionWeakly-nonlinear surface wavesInstabilityHamiltonian systemsInstability of waves in deep water — A discrete Hamiltonian approacharticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501David Andrade,Raphael StuhlmeierORIGINALInstability of waves in deep water A discrete Hamiltonian approach.pdfapplication/pdf4069354https://repository.urosario.edu.co/bitstreams/049403b9-aa11-43fd-859d-1d671938dcb8/download7e5b0247924d6e9020f44ebbc824bdbdMD51TEXTInstability of waves in deep water A discrete Hamiltonian approach.pdf.txtInstability of waves in deep water A discrete Hamiltonian approach.pdf.txtExtracted texttext/plain85781https://repository.urosario.edu.co/bitstreams/be926297-ebb9-4c7d-96b8-20cdc1b243dd/downloadc120ff35e72b64169f683da7060bcebdMD52THUMBNAILInstability of waves in deep water A discrete Hamiltonian approach.pdf.jpgInstability of waves in deep water A discrete Hamiltonian approach.pdf.jpgGenerated Thumbnailimage/jpeg5119https://repository.urosario.edu.co/bitstreams/1ed12c2e-ecdd-47f2-8d71-e44963e56725/download9da461af549427868984b7436fe09a73MD5310336/42132oai:repository.urosario.edu.co:10336/421322024-02-01 03:00:52.423https://creativecommons.org/licenses/by/4.0/Attribution 4.0 Internationalhttps://repository.urosario.edu.coRepositorio institucional EdocURedocur@urosario.edu.co |
dc.title.spa.fl_str_mv |
Instability of waves in deep water — A discrete Hamiltonian approach |
title |
Instability of waves in deep water — A discrete Hamiltonian approach |
spellingShingle |
Instability of waves in deep water — A discrete Hamiltonian approach Water waves Wave–wave interaction Weakly-nonlinear surface waves Instability Hamiltonian systems |
title_short |
Instability of waves in deep water — A discrete Hamiltonian approach |
title_full |
Instability of waves in deep water — A discrete Hamiltonian approach |
title_fullStr |
Instability of waves in deep water — A discrete Hamiltonian approach |
title_full_unstemmed |
Instability of waves in deep water — A discrete Hamiltonian approach |
title_sort |
Instability of waves in deep water — A discrete Hamiltonian approach |
dc.subject.spa.fl_str_mv |
Water waves Wave–wave interaction Weakly-nonlinear surface waves Instability Hamiltonian systems |
topic |
Water waves Wave–wave interaction Weakly-nonlinear surface waves Instability Hamiltonian systems |
description |
The stability of waves in deep water has classically been approached via linear stability analysis, with various model equations, such as the nonlinear Schrödinger equation, serving as points of departure. Some of the most well-studied instabilities involve the interaction of four waves – so called Type I instabilities – or five waves – Type II instabilities. A unified description of four and five wave interaction can be provided by the reduced Hamiltonian derived by Krasitskii (1994). Exploiting additional conservation laws, the discretised Hamiltonian may be used to shed light on these four and five wave instabilities without restrictions on spectral bandwidth. We derive equivalent autonomous, planar dynamical systems which allow for straightforward insight into the emergence of instability and the long time dynamics. They also yield new steady-state solutions, as well as discrete breathers associated with heteroclinic orbits in the phase space. |
publishDate |
2023 |
dc.date.created.spa.fl_str_mv |
2023-09-01 |
dc.date.issued.spa.fl_str_mv |
2023 |
dc.date.accessioned.none.fl_str_mv |
2024-01-31T18:27:29Z |
dc.date.available.none.fl_str_mv |
2024-01-31T18:27:29Z |
dc.type.spa.fl_str_mv |
article |
dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
dc.type.spa.spa.fl_str_mv |
Artículo |
dc.identifier.doi.spa.fl_str_mv |
10.1016/j.euromechflu.2023.06.008 |
dc.identifier.issn.spa.fl_str_mv |
0997-7546 |
dc.identifier.uri.none.fl_str_mv |
https://repository.urosario.edu.co/handle/10336/42132 |
identifier_str_mv |
10.1016/j.euromechflu.2023.06.008 0997-7546 |
url |
https://repository.urosario.edu.co/handle/10336/42132 |
dc.language.iso.spa.fl_str_mv |
eng |
language |
eng |
dc.relation.uri.spa.fl_str_mv |
https://www.sciencedirect.com/science/article/pii/S0997754623000857/pdfft?md5=32969424efe2d390829a14837818aa16&pid=1-s2.0-S0997754623000857-main.pdf |
dc.rights.spa.fl_str_mv |
Attribution 4.0 International |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
dc.rights.acceso.spa.fl_str_mv |
Abierto (Texto Completo) |
dc.rights.uri.spa.fl_str_mv |
https://creativecommons.org/licenses/by/4.0/ |
rights_invalid_str_mv |
Attribution 4.0 International Abierto (Texto Completo) https://creativecommons.org/licenses/by/4.0/ http://purl.org/coar/access_right/c_abf2 |
dc.format.mimetype.spa.fl_str_mv |
application/pdf |
dc.publisher.spa.fl_str_mv |
Universidad del Rosario |
dc.source.spa.fl_str_mv |
European Journal of Mechanics, B/Fluids |
institution |
Universidad del Rosario |
dc.source.instname.spa.fl_str_mv |
instname:Universidad del Rosario |
dc.source.reponame.spa.fl_str_mv |
reponame:Repositorio Institucional EdocUR |
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