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Boussinesq方程关于变水深问题的应用早已被Peresrine所推导,其作用能够描述不规则波与方向谱在浅水区的非线性作用和能量转换。其沿水深积分使三维波浪传播问题转化成二维问题进行处理。近些年来,一些工作已经扩展了Boussinesq方程在深水中的应用范围,靠促进其方程频散性来实现。Madsen仿Witting作法采用变量线性组合构成的量级小项,加入到动量方程中来拓展变水深条件下的Boussinesq频散性,使其达到了2阶频散精度。Nwogu采用水深之某一特定层的水平速度变量来推导出可随不同水深层的选取来达到改善其频散精度的Boussinesq方程。
The application of the Boussinesq equation to the problem of variable water depth has been derived by Peresrine and its role is to describe the nonlinear effects and energy transfer of irregular wave and direction spectra in shallow water. Its integration along the depth of the three-dimensional wave propagation problems into two-dimensional problems for processing. In recent years, some work has expanded the application range of the Boussinesq equation in deep water by promoting the dispersion of its equation. The Madsen imitation Witting method uses a small order of variables linear combination and adds to the momentum equation to expand the Boussinesq frequency dispersion under varying water depth to achieve the second order dispersion accuracy. Nwogu uses the horizontal velocity variances of a particular layer of water depth to derive a Boussinesq equation that can be refined with different water depths to improve its dispersion accuracy.