Alternative forms of the higher-order Boussinesq equations: Derivations and validations
Alternative forms of the higher-order Boussinesq equations: Derivations and validations
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DOI：
10.1016/j.coastaleng.2008.02.001
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发表时间：
2008-06
影响因子：
4.4
通讯作者：
Z. Zou;K. Fang
中科院分区：
文献类型：
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作者：
Z. Zou;K. Fang
发展了Boussinesq方程的另一种形式，创建了一个模型，该模型在O（μ4）（μ是水深与波长的比值）下是完全非线性的，并且具有精确到Padé [4，4]近似的色散。对底坡没有限制;自由表面和海底之间的可变距离由σ变换来解释。本文还提出了两种简化形式，它们采用ε=O（μ2/3）（ε为波高水深比）的假设，简化了O（μ4）项。这些可以看作是塞尔方程的扩展，由Padé [2，2]和Padé [4，4]近似给出色散。三阶非线性特性的这三个模型进行了讨论，使用傅立叶分析，并与其他高阶配方的Boussinesq方程。模型验证了对实验测量波传播的潜堤。最后，波群沿水平水槽沿着的非线性演化进行了模拟，并与实验数据进行了比较，以研究振幅色散和四波共振相互作用的影响。
An alternative form of the Boussinesq equations is developed, creating a model which is fully nonlinear up to O(μ4) (μ is the ratio of water depth to wavelength) and has dispersion accurate to the Padé [4,4] approximation. No limitation is imposed on the bottom slope; the variable distance between free surface and sea bottom is accounted for by a σ-transformation. Two reduced forms of the model are also presented, which simplify O(μ4) terms using the assumption ε=O(μ2/3) (ε is the ratio of wave height to water depth). These can be seen as extensions of Serre's equations, with dispersions given by the Padé [2,2] and Padé [4,4] approximations. The third-order nonlinear characteristics of these three models are discussed using Fourier analysis, and compared to other high-order formulations of the Boussinesq equations. The models are validated against experimental measurements of wave propagation over a submerged breakwater. Finally, the nonlinear evolution of wave groups along a horizontal flume is simulated and compared to experimental data in order to investigate the effects of the amplitude dispersion and the four-wave resonant interaction.