Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth
The nonlinear hydroelastic waves propagating beneath an infinite ice sheet floating on an inviscid fluid of finite depth are investigated analytically. The approximate series solutions for the velocity potential and the wave surface elevation are derived, respectively, by an analytic approximation t...
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ftdoajarticles:oai:doaj.org/article:ee236b312a3040e098e381a7aebc13dc 2023-05-15T16:39:52+02:00 Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth Ping Wang Zunshui Cheng 2013-01-01T00:00:00Z https://doi.org/10.1155/2013/108026 https://doaj.org/article/ee236b312a3040e098e381a7aebc13dc EN eng Hindawi Limited http://dx.doi.org/10.1155/2013/108026 https://doaj.org/toc/1085-3375 https://doaj.org/toc/1687-0409 1085-3375 1687-0409 doi:10.1155/2013/108026 https://doaj.org/article/ee236b312a3040e098e381a7aebc13dc Abstract and Applied Analysis, Vol 2013 (2013) Mathematics QA1-939 article 2013 ftdoajarticles https://doi.org/10.1155/2013/108026 2022-12-31T00:52:28Z The nonlinear hydroelastic waves propagating beneath an infinite ice sheet floating on an inviscid fluid of finite depth are investigated analytically. The approximate series solutions for the velocity potential and the wave surface elevation are derived, respectively, by an analytic approximation technique named homotopy analysis method (HAM) and are presented for the second-order components. Also, homotopy squared residual technique is employed to guarantee the convergence of the series solutions. The present formulas, different from the perturbation solutions, are highly accurate and uniformly valid without assuming that these nonlinear partial differential equations (PDEs) have small parameters necessarily. It is noted that the effects of water depth, the ice sheet thickness, and Young’s modulus are analytically expressed in detail. We find that, in different water depths, the hydroelastic waves traveling beneath the thickest ice sheet always contain the largest wave energy. While with an increasing thickness of the sheet, the wave elevation tends to be smoothened at the crest and be sharpened at the trough. The larger Young’s modulus of the sheet also causes analogous effects. The results obtained show that the thickness and Young’s modulus of the floating ice sheet all greatly affect the wave energy and wave profile in different water depths. Article in Journal/Newspaper Ice Sheet Directory of Open Access Journals: DOAJ Articles Abstract and Applied Analysis 2013 1 13 |
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Directory of Open Access Journals: DOAJ Articles |
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English |
topic |
Mathematics QA1-939 |
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Mathematics QA1-939 Ping Wang Zunshui Cheng Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth |
topic_facet |
Mathematics QA1-939 |
description |
The nonlinear hydroelastic waves propagating beneath an infinite ice sheet floating on an inviscid fluid of finite depth are investigated analytically. The approximate series solutions for the velocity potential and the wave surface elevation are derived, respectively, by an analytic approximation technique named homotopy analysis method (HAM) and are presented for the second-order components. Also, homotopy squared residual technique is employed to guarantee the convergence of the series solutions. The present formulas, different from the perturbation solutions, are highly accurate and uniformly valid without assuming that these nonlinear partial differential equations (PDEs) have small parameters necessarily. It is noted that the effects of water depth, the ice sheet thickness, and Young’s modulus are analytically expressed in detail. We find that, in different water depths, the hydroelastic waves traveling beneath the thickest ice sheet always contain the largest wave energy. While with an increasing thickness of the sheet, the wave elevation tends to be smoothened at the crest and be sharpened at the trough. The larger Young’s modulus of the sheet also causes analogous effects. The results obtained show that the thickness and Young’s modulus of the floating ice sheet all greatly affect the wave energy and wave profile in different water depths. |
format |
Article in Journal/Newspaper |
author |
Ping Wang Zunshui Cheng |
author_facet |
Ping Wang Zunshui Cheng |
author_sort |
Ping Wang |
title |
Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth |
title_short |
Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth |
title_full |
Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth |
title_fullStr |
Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth |
title_full_unstemmed |
Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth |
title_sort |
nonlinear hydroelastic waves beneath a floating ice sheet in a fluid of finite depth |
publisher |
Hindawi Limited |
publishDate |
2013 |
url |
https://doi.org/10.1155/2013/108026 https://doaj.org/article/ee236b312a3040e098e381a7aebc13dc |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Abstract and Applied Analysis, Vol 2013 (2013) |
op_relation |
http://dx.doi.org/10.1155/2013/108026 https://doaj.org/toc/1085-3375 https://doaj.org/toc/1687-0409 1085-3375 1687-0409 doi:10.1155/2013/108026 https://doaj.org/article/ee236b312a3040e098e381a7aebc13dc |
op_doi |
https://doi.org/10.1155/2013/108026 |
container_title |
Abstract and Applied Analysis |
container_volume |
2013 |
container_start_page |
1 |
op_container_end_page |
13 |
_version_ |
1766030210450325504 |