五阶双色双向海洋表面波理论

黄虎; 刘国梁

doi:10.3879/j.issn.1000-0887.2016.05.003

五阶双色双向海洋表面波理论

doi: 10.3879/j.issn.1000-0887.2016.05.003

黄虎,
刘国梁

上海大学上海市应用数学和力学研究所;上海市力学在能源工程中的应用重点实验室, 上海 200072

基金项目: 国家自然科学基金（11172157）；上海市浦江人才计划（12PJD001）；上海交通大学海洋工程国家重点实验室开放课题基金（1503）

详细信息

作者简介:
黄虎（1964—），男，教授，博士，博士生导师(通讯作者. E-mail: hhuang@shu.edu.cn).

中图分类号: O353.2
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- 被引次数: 0
出版历程
- 收稿日期: 2016-11-09
- 修回日期: 2015-12-23
- 刊出日期: 2016-05-15

A 5th-Order Theory for Bichromatic and Bidirectional Ocean Surface Waves

Shanghai Institute of Applied Mathematics and Mechanics;Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China（11172157）

摘要

摘要: 将经典的“纯波动的三阶单色单向Stokes波理论”提升至“可包含环境均匀流效应的有限水深五阶双色双向海洋表面波理论”.亦即，在已有三阶双色双波理论的基础上得到了自由表面位移、速度势和非线性振幅色散关系的第四阶、第五阶显式表达式.从中,将居于核心地位的“双色双向波的第五阶非线性振幅色散关系”又推广到“无穷多波中任意两两不同频率不同振幅相互作用波的非线性振幅色散关系”.针对双色双向短峰波的典型特性,以若干个图表详加示之.
- 五阶理论 /
- 双色双向波 /
- 海洋表面波 /
- 非线性振幅色散关系
Abstract: The classical Stokes wave theory of pure wave motion for the 3rd-order monochromatic and monodirectional waves was expanded to a 5th-order theory for bichromatic and bidirectional ocean surface waves under the ambient uniform current effect in water of finite depth, which, based on the 3rd-order theory for bichromatic and bidirectional waves, comprised the 4th- and the 5th-order explicit expressions for the free surface elevations, the velocity potential and the nonlinear amplitude dispersion relation. The 5th-order nonlinear amplitude dispersion relation playing a key role in the bichromatic and bidirectional wave theory was generalized to one relation of 2 arbitrary interacting waves with different frequencies and ampitudes in pairs out of infinite waves. The typical characteristics of bichromatic and bidirectional short-crested waves were illustrated in detail with diagrams.
- 5th-order theory /
- bichromatic and bidirectional wave /
- ocean surface wave /
- nonlinear amplitude dispersion relation

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参考文献(29)

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