无穷多海洋表面波共振的Zakharov方程

黄虎

doi:10.3879/j.issn.1000-0887.2014.10.009

无穷多海洋表面波共振的Zakharov方程

doi: 10.3879/j.issn.1000-0887.2014.10.009

黄虎

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）；上海高校创新团队建设资助项目

详细信息

作者简介:
黄虎（1964—），男，新疆石河子人，教授，博士，博士生导师(Tel: +86-21-56332947;E-mail: hhuang@shu.edu.cn).

中图分类号: O353.2
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- 文章访问数: 1122
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出版历程
- 收稿日期: 2014-03-24
- 修回日期: 2014-04-14
- 刊出日期: 2014-10-15

Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves

HUANG Hu

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: 从基本的波之“能量、动量、作用量”守恒定律出发，遵照普适的“对称性决定相互作用”法则和“Hamilton”结构，运用Hamilton海洋表面波复正则方程、正则变换及其Poisson括号条件，并结合经典的3-4-5-波共振条件,推导出两大类“无穷多海洋表面波相互作用的共振条件”；相应地就建立了两大类“无穷多海洋表面波共振的Zakharov方程”.以此，就为最具根本性、普遍性的海洋波湍流搭建了一个必备、先行和完备的理论框架.
- Zakharov方程 /
- 共振条件 /
- 无穷多海洋表面波 /
- 能量、动量和作用量守恒
Abstract: Based on the fundamental wave conservation laws of energy, momentum and action, together with the law of symmetry deciding interactions and the Hamilton structure, 2 main categories of resonance conditions for an infinite number of wave interactions and the corresponding 2 major Zakharov-type equations for an infinite number of wave resonances were derived by means of the complex Hamiltonian canonical equation for ocean surface waves, the canonical transformation and the Poisson bracket conditions. The presented Zakharov-type equations, in connection with the classical conditions for the 3,4 and 5-wave resonances, therefore build an indispensable, advanced and complete theoretical framework for the most fundamental and universal ocean wave turbulence.
- Zakharov equation /
- resonance condition /
- an infinite number of ocean surface waves /
- conservation of energy, momentum and action

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参考文献(19)

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无穷多海洋表面波共振的Zakharov方程

doi: 10.3879/j.issn.1000-0887.2014.10.009

作者简介:
黄虎（1964—），男，新疆石河子人，教授，博士，博士生导师(Tel: +86-21-56332947;E-mail: hhuang@shu.edu.cn).

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Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves

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留言板

无穷多海洋表面波共振的Zakharov方程

doi: 10.3879/j.issn.1000-0887.2014.10.009

作者简介: 黄虎（1964—），男，新疆石河子人，教授，博士，博士生导师(Tel: +86-21-56332947;E-mail: hhuang@shu.edu.cn).

计量

出版历程

Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves

计量

出版历程

目录

作者简介:
黄虎（1964—），男，新疆石河子人，教授，博士，博士生导师(Tel: +86-21-56332947;E-mail: hhuang@shu.edu.cn).