| Homotopy-based analytical approximation to nonlinear short-crested waves in a fluid of finite depth |
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| 作者姓名： | 王苹 卢东强 |
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| 作者单位： | Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University;School of Mathematics and Physics, Qingdao University of Science and Technology;Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University |
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| 基金项目： | Project Supported by the National Key Basic Research Development Program of China，the National Natural Science Foundation of China，the Natural Science Foundation of Shanghai |
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| 摘 要： | A nonlinear short-crested wave system, consisting of two progressive waves propagating at an oblique angle to each other in a fluid of finite depth, is investigated by means of an analytical approach named the homotopy analysis method(HAM). Highly convergent series solutions are explicitly derived for the velocity potential and the surface wave elevation. We find that, at every value of water depth, there is little difference between the kinetic energy and the potential energy for nonlinear waves. The nonlinear short-crested waves with a larger angle of incidence always contain the more potential wave energy. With the aid of the HAM, we obtain the dispersion relation for nonlinear short-crested waves. Furthermore, it is shown that the wave elevation tends to be smoothened at the crest and be sharpened at the trough as the water depth increases, and the wave pressure crests and troughs become steeper with increasing incident wave steepness.
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| 关 键 词： | convergent oblique propagating elevation Roberts trough explicitly embedding Highly realistic |
Homotopy-based analytical approximation to nonlinear short-crested waves in a fluid of finite depth |
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| WANG Ping
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LU Dong-qiang.Homotopy-based analytical approximation to nonlinear short-crested waves in a fluid of finite depth[J].Journal of Hydrodynamics,2015,27(3):321-331. |
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| Authors: | WANG Ping LU Dong-qiang |
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| Affiliation: | 1. Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China;School of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266061,China
2. Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China;Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai University,Shanghai 200072,China |
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| Abstract: | A nonlinear short-crested wave system, consisting of two progressive waves propagating at an oblique angle to each other in a fluid of finite depth, is investigated by means of an analytical approach named the homotopy analysis method(HAM). Highly convergent series solutions are explicitly derived for the velocity potential and the surface wave elevation. We find that, at every value of water depth, there is little difference between the kinetic energy and the potential energy for nonlinear waves. The nonlinear short-crested waves with a larger angle of incidence always contain the more potential wave energy. With the aid of the HAM, we obtain the dispersion relation for nonlinear short-crested waves. Furthermore, it is shown that the wave elevation tends to be smoothened at the crest and be sharpened at the trough as the water depth increases, and the wave pressure crests and troughs become steeper with increasing incident wave steepness. |
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| Keywords: | nonlinear short-crested waves finite water depth homotopy analysis method (HAM) wave energy wave profile |
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