| Water wave solutions obtained by variational method |
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| 作者姓名： | 杨红丽 宋金宝 杨联贵 |
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| 作者单位： | Institute of Oceanology，Institute of Oceanology，Department of Mathematics Chinese Academv of Sciences，Qingdao 266071，China Graduate School，Chinese Academy of Sciences，Beijing 100039，China，Chinese Academy of Sciences，Qingdao 266071，China，Inner Mongolia University，Hohhot 010021，China |
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| 基金项目： | Supported by the High-Tech Research and Development Program of China (863 Program, No. 2001AA633070 2003AA604040) the National Nature Science Foundation of China (No.40376008). |
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| 摘 要： | Abstract Variational problem for irrotational, incompressible inviscid fluid in finite water depth is considered. Based on the variational principle, a special solution of the problem is presented under the assumption that the dispersion /u and the nonlinearity ?satisfied e = O(fj2) as the Lagrange function is expanded up to O(//). It is shown that the elevation of the free surface should be expanded to // order to ensure the Lagrange function is in fj* order. Comparison the nonlinear free surface profiles obtained from the solution with the corresponding ones obtained from linear solutions showed that the wave crest of the nonlinear wave is steepened but the trough is flattened compared to the linear wave as expected.
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| 关 键 词： | 海洋动力学 波浪 水波 变化性 |
| 收稿时间： | 2005-05-28 |
| 修稿时间： | 2005-06-06 |
Water wave solutions obtained by variational method |
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| Yang Hongli,Song Jinbao,Yang Liangui.Water wave solutions obtained by variational method[J].Chinese Journal of Oceanology and Limnology,2006,24(1):87-91. |
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| Authors: | Yang Hongli Song Jinbao Yang Liangui |
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| Institution: | (1) Institute of Oceanology, Chinese Academy of Sciences, 266071 Qingdao, China;(2) Department of Mathematics, Inner Mongolia University, 010021 Hohhot, China;(3) Graduate School, Chimese Academy of Sciences, 100039 Beijing, China |
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| Abstract: | Variational problem for irrotational, incompressible inviseid fluid in finite water depth is considered. Based on the variational principle, a special solution of the problem is presented under the assumption that the dispersion μ and the nonlinearity ε satisfied ε=O(μ2) as the Lagrange function is expanded up toO(μ8). It is shown that the elevation of the free surface should be expanded to μ4 order to ensure the Lagrange function is in μ8 order. Comparison the nonlinear free surface profiles obtained from the solution with the corresponding ones obtained from linear solutions showed that the wave crest of the nonlinear wave is steepened but the trough is flattened compared to the linear wave as expected. |
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| Keywords: | nonlinear water waves variational principle |
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