海洋表面波约化Hamilton方程的新发展:从小幅波到有限幅波的推广

王兆玲; 肖衡

doi:10.3879/j.issn.1000-0887.2015.11.002

海洋表面波约化Hamilton方程的新发展:从小幅波到有限幅波的推广

doi: 10.3879/j.issn.1000-0887.2015.11.002

王兆玲^1,2,
肖衡^2,3

¹潍坊学院数学与信息科学学院,山东潍坊 261061;²省部共建高品质特殊钢冶金与制备国家重点实验室(上海大学),上海 200444;³上海大学上海市应用数学和力学研究所,上海 200072

基金项目: 国家教委211工程科研启动基金（A.15-B002-09-032）;国家自然科学基金（11372172）

详细信息

作者简介:
王兆玲（1979—），女，山东潍坊人，博士(E-mail: wangzhaoling555@126.com);肖衡（1963—），男，湖南永州人，教授，博士，博士生导师(通讯作者. E-mail: xiaoheng@shu.edu.cn).

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出版历程
- 收稿日期: 2015-04-10
- 修回日期: 2015-09-08
- 刊出日期: 2015-11-15

A New Development of Reduced Hamiltonian Equations for Ocean Surface Waves: an Extension From Small to Finite Amplitude

WANG Zhao-ling>^1,2,
XIAO Heng^2,3

¹School of Mathematics and Information Sciences, Weifang University, Weifang, Shandong 261061, P.R.China;²The State Key Laboratory of Advanced Special Steel(Shanghai University),Shanghai 200444, P.R.China;³Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China(11372172)

摘要

摘要: 海洋表面波的3-波至5-波约化Hamilton方程由于其对称多项式简化结构以及保能量等独特优点，得到广泛应用.但是，据相关近似假设，其适用范围局限于波陡很小的弱非线性波.于是进一步探讨下述推广问题: 对一定范围内的有限幅非线性波，在足够精确意义上是否也能获得具对称多项式简化结构的约化Hamilton方程？由于涉及复杂非线性强耦合，在该重要方面至今尚未取得进展.提出基于Chebyshev(切比雪夫)多项式逼近处理精确水波方程强非线性耦合的新简化途径，导出具对称多项式简化结构的新约化Hamilton方程.新结果将波数与波陡之积为小量的弱非线性情形拓广到该积直至1.035的非线性情形.分析表明,在该范围内新结果的误差不超过5%，特别,当前述积邻近于0.9时新结果给出精确结果.
- 海洋表面波 /
- 有限波幅 /
- 新简化途径 /
- 新约化Hamilton方程
Abstract: The reduced 3-wave and 4-wave Hamiltonian equations for ocean surface waves were widely used for the simplified structure with symmetric polynomial kernels and for the conservation of energy, etc. However, according to the related assumption for approximation in derivation, the range of applicability was limited to weakly nonlinear waves of small amplitude. Here the following issue was further studied: for nonlinear waves of finite amplitude within a certain range, was it also possible to obtain reduced Hamiltonian equations with symmetric polynomial kernels in a sense of sufficient accuracy? Because of complicated strongly nonlinear coupling, few development in this significant respect had been made as yet. A new approach was proposed based on the Chebyshev polynomials to best approximate the primitive water wave equations in the exact sense of strongly nonlinear coupling and derive new reduced Hamiltonian equations with symmetric polynomial kernels. The new results exhibit an extension from a weakly nonlinear case in which the product of the wave number and the wave steepness is small to a nonlinear case in which this product goes up to about 1.035. Moreover, within this range, the approximation errors are lower than 5%, and in particular, the new results prove exact whenever the said product lies close to 0.9.
- ocean surface wave /
- finite amplitude /
- new approach for reduction /
- new reduced Hamiltonian equation

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参考文献(21)

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海洋表面波约化Hamilton方程的新发展:从小幅波到有限幅波的推广

doi: 10.3879/j.issn.1000-0887.2015.11.002

作者简介:
王兆玲（1979—），女，山东潍坊人，博士(E-mail: wangzhaoling555@126.com);肖衡（1963—），男，湖南永州人，教授，博士，博士生导师(通讯作者. E-mail: xiaoheng@shu.edu.cn).

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A New Development of Reduced Hamiltonian Equations for Ocean Surface Waves: an Extension From Small to Finite Amplitude

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目录

留言板

海洋表面波约化Hamilton方程的新发展:从小幅波到有限幅波的推广

doi: 10.3879/j.issn.1000-0887.2015.11.002

作者简介: 王兆玲（1979—），女，山东潍坊人，博士(E-mail: wangzhaoling555@126.com);肖衡（1963—），男，湖南永州人，教授，博士，博士生导师(通讯作者. E-mail: xiaoheng@shu.edu.cn).

计量

出版历程

A New Development of Reduced Hamiltonian Equations for Ocean Surface Waves: an Extension From Small to Finite Amplitude

计量

出版历程

目录

作者简介:
王兆玲（1979—），女，山东潍坊人，博士(E-mail: wangzhaoling555@126.com);肖衡（1963—），男，湖南永州人，教授，博士，博士生导师(通讯作者. E-mail: xiaoheng@shu.edu.cn).