A time–dependent nonlinear mild slope equation for water waves
A time–dependent nonlinear mild slope equation for water waves
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DOI：
10.1098/rspa.1997.0018
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发表时间：
1997-02
期刊：
影响因子：
--
通讯作者：
S. Beji;K. Nadaoka
中科院分区：
文献类型：
--
作者：
S. Beji;K. Nadaoka
本文导出了一个弱非线性色散水波方程，它是Smith和Sprinks（1975）的含时缓坡方程的一个新形式。新波动方程对随机波的适用谱宽比Smith和Sprinks（1975）的谱宽更令人满意。对于非常浅的深度，该方程简化为艾里非线性非色散波动方程的组合形式;如果保留最低阶色散，则产生布西内斯克方程的组合形式。在深水极限下，方程允许二阶Stokes波作为解析解。此外，通过引入右移坐标变换，该方程被重铸成一个单向的形式，使KdV方程在一个极限，而再现的二阶斯托克斯波在其他。
A weakly nonlinear and dispersive water wave equation, which in linearized form yields a new version of the time–dependent mild–slope equation of Smith and Sprinks (1975), is derived. The applicable spectral width of the new wave equation for random waves is found to be more satisfactory than that of Smith and Sprinks (1975). For very shallow depths the equation reduces to the combined form of Airy's nonlinear non–dispersive wave equations; if the lowest–order dispersion is retained it produces the combined form of Boussinesq's equations. In the deep–water limit the equation admits the second–order Stokes waves as analytical solutions. Furthermore, by introducing a right–moving coordinate transformation, the equation is recast into a unidirectional form, rendering the KdV equation in one limit while reproducing the second–order Stokes waves in the other.