Boussinesq-type equations of hydroelastic waves in shallow water
Accurate computation of hydroelastic waves in shallow water is critical because many hydroelastic wave applications are nearshores, such as sea-ice and floating infrastructures. In this paper, Boussinesq assumptions for shallow water are employed to derive nonlinear Boussinesq-type equations of hydr...
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crcambridgeupr:10.1017/jfm.2024.233 2024-05-19T07:48:22+00:00 Boussinesq-type equations of hydroelastic waves in shallow water Tang, Shanran Xiong, Yingfen Zhu, Liangsheng National Natural Science Foundation of China 2024 http://dx.doi.org/10.1017/jfm.2024.233 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112024002337 en eng Cambridge University Press (CUP) https://www.cambridge.org/core/terms Journal of Fluid Mechanics volume 985 ISSN 0022-1120 1469-7645 journal-article 2024 crcambridgeupr https://doi.org/10.1017/jfm.2024.233 2024-05-02T06:50:47Z Accurate computation of hydroelastic waves in shallow water is critical because many hydroelastic wave applications are nearshores, such as sea-ice and floating infrastructures. In this paper, Boussinesq assumptions for shallow water are employed to derive nonlinear Boussinesq-type equations of hydroelastic waves, in which non-uniform distribution of structural stiffness and varying water depth are considered rigorously. Application of Boussinesq assumptions enables complicated three-dimensional problems to be reduced and formulated on the two-dimensional horizontal plane, therefore the proposed Boussinesq-type models are straightforward and versatile for a wide range of hydroelastic wave applications. Two configurations, a floating plate and a submerged plate, are studied. The first-order linear governing equations are solved analytically with periodic conditions assuming constant depth and uniform stiffness, and the linear dispersion relations are subsequently derived for both configurations. For flexural-gravity waves of a floating plate, unique behaviours of flexural-gravity waves different from shallow-water waves are discussed, and a generalized solitary wave solution is investigated. A nonlinear numerical solver is developed, and nonlinear flexural-gravity waves are found to have smaller wavelength and celerity than their linear counterparts. For hydroelastic waves of a submerged plate, dual-mode analytical solutions are discovered for the first time. Numerical computation has demonstrated that a plate with decreasing submerged depth is able to transfer wave energy from the deeper water to the surface layer. Article in Journal/Newspaper Sea ice Cambridge University Press Journal of Fluid Mechanics 985 |
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Cambridge University Press |
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English |
description |
Accurate computation of hydroelastic waves in shallow water is critical because many hydroelastic wave applications are nearshores, such as sea-ice and floating infrastructures. In this paper, Boussinesq assumptions for shallow water are employed to derive nonlinear Boussinesq-type equations of hydroelastic waves, in which non-uniform distribution of structural stiffness and varying water depth are considered rigorously. Application of Boussinesq assumptions enables complicated three-dimensional problems to be reduced and formulated on the two-dimensional horizontal plane, therefore the proposed Boussinesq-type models are straightforward and versatile for a wide range of hydroelastic wave applications. Two configurations, a floating plate and a submerged plate, are studied. The first-order linear governing equations are solved analytically with periodic conditions assuming constant depth and uniform stiffness, and the linear dispersion relations are subsequently derived for both configurations. For flexural-gravity waves of a floating plate, unique behaviours of flexural-gravity waves different from shallow-water waves are discussed, and a generalized solitary wave solution is investigated. A nonlinear numerical solver is developed, and nonlinear flexural-gravity waves are found to have smaller wavelength and celerity than their linear counterparts. For hydroelastic waves of a submerged plate, dual-mode analytical solutions are discovered for the first time. Numerical computation has demonstrated that a plate with decreasing submerged depth is able to transfer wave energy from the deeper water to the surface layer. |
author2 |
National Natural Science Foundation of China |
format |
Article in Journal/Newspaper |
author |
Tang, Shanran Xiong, Yingfen Zhu, Liangsheng |
spellingShingle |
Tang, Shanran Xiong, Yingfen Zhu, Liangsheng Boussinesq-type equations of hydroelastic waves in shallow water |
author_facet |
Tang, Shanran Xiong, Yingfen Zhu, Liangsheng |
author_sort |
Tang, Shanran |
title |
Boussinesq-type equations of hydroelastic waves in shallow water |
title_short |
Boussinesq-type equations of hydroelastic waves in shallow water |
title_full |
Boussinesq-type equations of hydroelastic waves in shallow water |
title_fullStr |
Boussinesq-type equations of hydroelastic waves in shallow water |
title_full_unstemmed |
Boussinesq-type equations of hydroelastic waves in shallow water |
title_sort |
boussinesq-type equations of hydroelastic waves in shallow water |
publisher |
Cambridge University Press (CUP) |
publishDate |
2024 |
url |
http://dx.doi.org/10.1017/jfm.2024.233 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112024002337 |
genre |
Sea ice |
genre_facet |
Sea ice |
op_source |
Journal of Fluid Mechanics volume 985 ISSN 0022-1120 1469-7645 |
op_rights |
https://www.cambridge.org/core/terms |
op_doi |
https://doi.org/10.1017/jfm.2024.233 |
container_title |
Journal of Fluid Mechanics |
container_volume |
985 |
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1799466593242054656 |