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Variational problems in the theory of hydroelastic waves
This paper outlines a mathematical approach to steady periodic waves which propagate with constant velocity and without change of form on the surface of a three-dimensional expanse of fluid which is at rest at infinite depth and moving irrotationally under gravity, bounded above by a frictionless el...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society Publishing
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6107614/ https://www.ncbi.nlm.nih.gov/pubmed/30126914 http://dx.doi.org/10.1098/rsta.2017.0343 |
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author | Plotnikov, P. I. Toland, J. F. |
author_facet | Plotnikov, P. I. Toland, J. F. |
author_sort | Plotnikov, P. I. |
collection | PubMed |
description | This paper outlines a mathematical approach to steady periodic waves which propagate with constant velocity and without change of form on the surface of a three-dimensional expanse of fluid which is at rest at infinite depth and moving irrotationally under gravity, bounded above by a frictionless elastic sheet. The elastic sheet is supposed to have gravitational potential energy, bending energy proportional to the square integral of its mean curvature (its Willmore functional), and stretching energy determined by the position of its particles relative to a reference configuration. The equations and boundary conditions governing the wave shape are derived by formulating the problem, in the language of geometry of surfaces, as one for critical points of a natural Lagrangian, and a proof of the existence of solutions is sketched. This article is part of the theme issue ‘Modelling of sea-ice phenomena’. |
format | Online Article Text |
id | pubmed-6107614 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-61076142018-08-24 Variational problems in the theory of hydroelastic waves Plotnikov, P. I. Toland, J. F. Philos Trans A Math Phys Eng Sci Articles This paper outlines a mathematical approach to steady periodic waves which propagate with constant velocity and without change of form on the surface of a three-dimensional expanse of fluid which is at rest at infinite depth and moving irrotationally under gravity, bounded above by a frictionless elastic sheet. The elastic sheet is supposed to have gravitational potential energy, bending energy proportional to the square integral of its mean curvature (its Willmore functional), and stretching energy determined by the position of its particles relative to a reference configuration. The equations and boundary conditions governing the wave shape are derived by formulating the problem, in the language of geometry of surfaces, as one for critical points of a natural Lagrangian, and a proof of the existence of solutions is sketched. This article is part of the theme issue ‘Modelling of sea-ice phenomena’. The Royal Society Publishing 2018-09-28 2018-08-20 /pmc/articles/PMC6107614/ /pubmed/30126914 http://dx.doi.org/10.1098/rsta.2017.0343 Text en © 2018 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Articles Plotnikov, P. I. Toland, J. F. Variational problems in the theory of hydroelastic waves |
title | Variational problems in the theory of hydroelastic waves |
title_full | Variational problems in the theory of hydroelastic waves |
title_fullStr | Variational problems in the theory of hydroelastic waves |
title_full_unstemmed | Variational problems in the theory of hydroelastic waves |
title_short | Variational problems in the theory of hydroelastic waves |
title_sort | variational problems in the theory of hydroelastic waves |
topic | Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6107614/ https://www.ncbi.nlm.nih.gov/pubmed/30126914 http://dx.doi.org/10.1098/rsta.2017.0343 |
work_keys_str_mv | AT plotnikovpi variationalproblemsinthetheoryofhydroelasticwaves AT tolandjf variationalproblemsinthetheoryofhydroelasticwaves |