Water wave solutions obtained by variational method

Yang Hongli; Song Jinbao; Yang Liangui

doi:10.1007/BF02842780

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Water wave solutions obtained by variational method

OriginalPaper | Updated：2023-05-16

- Water wave solutions obtained by variational method
- Water wave solutions obtained by variational method
- 海洋湖沼学报（英文） 2006年24卷第1期页码：87-91
- Affiliations：
  
  1. Institute of Oceanology Chinese Academy of Sciences
  2. Graduate School Chimese Academy of Sciences
  3. Department of Mathematics Inner Mongolia University
- Author bio：
- Funds：
  
  Supported by the High-Tech Research and Development Program of China (863 Program, No. 2001AA633070;2003AA604040), and the National Nature Science Foundation of China (No. 40376008).
- DOI：10.1007/BF02842780
  中图分类号：
- 纸质出版：2006
- Accepted：
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Water wave solutions obtained by variational method[J]. 海洋湖沼学报（英文）, 2006,24(1):87-91.

Hongli, Y., Jinbao, S. & Liangui, Y. Water wave solutions obtained by variational method., Chin. J. Ocean. Limnol. 24, 87–91 (2006). https://doi.org/10.1007/BF02842780
Water wave solutions obtained by variational method[J]. 海洋湖沼学报（英文）, 2006,24(1):87-91. DOI： 10.1007/BF02842780.

Hongli, Y., Jinbao, S. & Liangui, Y. Water wave solutions obtained by variational method., Chin. J. Ocean. Limnol. 24, 87–91 (2006). https://doi.org/10.1007/BF02842780 DOI：

摘要

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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references

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