Boussinesq Model for Weakly Nonlinear Fully Dispersive Water Waves
Boussinesq Model for Weakly Nonlinear Fully Dispersive Water Waves
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DOI：
10.1061/(asce)0733-950x(2009)135:5(187
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
T. Karambas;C. Memos
中科院分区：
文献类型：
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作者：
T. Karambas;C. Memos
本文提出了一种新的Boussinesq色散波传播模型。该模型是基于一个系统的方程表示的自由表面高程和深度平均水平速度。该方法是为完全色散和弱非线性不规则波传播在任何恒定的水深在两个水平维度，但它也可以应用在轻度倾斜的海滩相当的精度。该模型在其二维配方涉及在每个动量方程，包括经典的浅水项和只有一个频散项共五项。后者通过卷积积分表示，使用适当的脉冲函数估计。该公式在空间上是完全显式的，因此不需要反演数值解。该模型适用于模拟规则和不规则波的传播，使用一个简单的显式有限差分格式。还需要卷积积分的数值积分。模拟的结果与实验数据进行了比较，以及与线性和非线性波理论。结果表明，该方法能够较好地模拟弱非线性色散波在有限定常水深或缓减水深上的传播。
In the present work a new Boussinesq dispersive wave propagation model is proposed. The model is based on a system of equations expressed in terms of the free-surface elevation and the depth-averaged horizontal velocities. The approach is developed for fully dispersive and weakly nonlinear irregular waves propagating over any constant water depth in two horizontal dimensions, but it can also be applied in mildly sloping beaches with considerable accuracy. The model in its two-dimensional formulation involves in total five terms in each momentum equation, including the classical shallow water terms and only one frequency dispersion term. The latter is expressed through convolution integrals, which are estimated using appropriate impulse functions. The formulation is fully explicit in space and thus no inversion is required for the numerical solution. The model is applied to simulate the propagation of regular and irregular waves using a simple explicit scheme of finite differences. Numerical integration of a convolution integral is also required. The results of the simulations are compared with experimental data, as well as with linear and nonlinear wave theory. The comparisons show that the method is capable of simulating weakly nonlinear dispersive wave propagation over finite constant or slowly diminishing water depth in a satisfactory way.