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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| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/108026 |
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| author | Ping Wang Zunshui Cheng |
| author_facet | Ping Wang Zunshui Cheng |
| author_sort | Ping Wang |
| collection | DOAJ |
| 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 |
| id | doaj-art-ee236b312a3040e098e381a7aebc13dc |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ee236b312a3040e098e381a7aebc13dc2025-02-03T00:59:09ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/108026108026Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite DepthPing Wang0Zunshui Cheng1School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaSchool of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaThe 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.http://dx.doi.org/10.1155/2013/108026 |
| spellingShingle | Ping Wang Zunshui Cheng Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth Abstract and Applied Analysis |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2013/108026 |
| work_keys_str_mv | AT pingwang nonlinearhydroelasticwavesbeneathafloatingicesheetinafluidoffinitedepth AT zunshuicheng nonlinearhydroelasticwavesbeneathafloatingicesheetinafluidoffinitedepth |