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...

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Fecha de publicación:
2023
Institución:
Universidad del Rosario
Repositorio:
Repositorio EdocUR - U. Rosario
Idioma:
eng
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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
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spelling 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
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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
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http://purl.org/coar/access_right/c_abf2
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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
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