On the universal third order Stokes wave solution

查看全文 作　　者：SONG [1,2]ZhiYao;ZHAO [2]HongJun;LI [3]Ling;Lü [1]GuoNian

机构地区：[1]Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University;[2]College of Harbor, Coastal and Offshore Engineering, State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University;[3]School of Civil Engineering, The University of Queensland

出　　处：《Science China Earth Sciences》索引2013年第56卷第1期,共13页

基　　金：supported by Fundamental Research Funds for the Central Universities (Grant No. 2010B02614);Natural Science Foundation of Hohai University (Grant No. 2009423511);National Natural Science Foundation of China (Grant No. 4176008);Priority Academic Program Development of Jiangsu Higher Education Institutions 摘　　要：This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function. 关键词：STOKES波三阶非线性代数方程自由表面傅立叶级数傅里叶系数自相互作用静水位

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On the universal third order Stokes wave solution

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