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金红 邹志利. 具有精确色散性的非线性波浪数学模型[J]. 力学学报, 2010, 42(1): 23-34. DOI: 10.6052/0459-1879-2010-1-2008-080
引用本文: 金红 邹志利. 具有精确色散性的非线性波浪数学模型[J]. 力学学报, 2010, 42(1): 23-34. DOI: 10.6052/0459-1879-2010-1-2008-080
Hong Jin, Zhili Zou. The nonlinear water wave equations with full dispersion[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 23-34. DOI: 10.6052/0459-1879-2010-1-2008-080
Citation: Hong Jin, Zhili Zou. The nonlinear water wave equations with full dispersion[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 23-34. DOI: 10.6052/0459-1879-2010-1-2008-080

具有精确色散性的非线性波浪数学模型

The nonlinear water wave equations with full dispersion

  • 摘要: 以完全非线性的自由表面边界条件为基础,以波面升高\eta和自由表面速度势\phi _\eta为待求变量,建立了新的波浪方程.方程在色散性上是完全精确的,非线性近似至三阶.与缓坡方程相比较,两者都具有精确的色散性,但该方程属于非线性模型,可模拟波浪的非线性效应,且适用于不规则波.方程的特点是属于微分-积分方程,对如何处理方程中积分项进行了讨论,并数值模拟了不同周期的线性波和二阶Stokes波,也模拟了波群的非线性演化,以对模型进行验证.

     

    Abstract: A 2D nonlinear water wave model with full dispersion isdeveloped. The model is based on the nonlinear kinematic and dynamic freesurface boundary conditions and is expressed in terms of free surfaceelevation \eta and the velocity potential \phi _\eta at the freesurface. The derivation of the equations is accurate to third order innonlinearity and keeps exact dispersion. The mild slope assumption isadopted and the derived equations can be seen as the extention of the mildslope equation of Berkhoff (1972) to the nonlinear and irregular wave case.The corresponding numerical scheme is presented, and the special attentionis paid on the treatment of the integration terms in the equations. Thevalidation of the model is made by simulating the first and second orderStokes waves and the nonlinear evolution of wave groups, the advantage ofthe model is shown by the good prediction of amplitude dispersion andfour-wave resonant interaction for the wave group evolution.

     

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