ALTERNATIVE FORM OF BOUSSINESQ EQUATIONS FOR NEARSHORE WAVE-PROPAGATION
ALTERNATIVE FORM OF BOUSSINESQ EQUATIONS FOR NEARSHORE WAVE-PROPAGATION
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DOI：
10.1061/(asce)0733-950x(1993)119:6(618
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发表时间：
1993-11-01
期刊：
影响因子：
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通讯作者：
NWOGU, O
中科院分区：
文献类型：
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作者：
NWOGU, O
Boussinesq型方程可以用来模拟浅水中由于浅水、折射、绕射和反射效应引起的表面波的非线性变换。用不同的速度变量表示方程，可以得到不同的线性色散关系。本文用距静水面任意距离处的流速代替常用的水深平均流速作为流速变量，导出了Boussinesq方程的一种新形式。这显著改善了Boussinesq方程的线性色散特性，使其适用于更广泛的水深范围。用有限差分法求解方程组。对规则波和不规则波在恒定坡度海滩上的传播进行了数值模拟和实验比较。结果表明，新形式的方程可以合理地模拟几个非线性效应，发生在浅水的表面波从深到浅，包括放大的强制低和高频率的波谐波和相关的增加的水平和垂直不对称的波。
Boussinesq-type equations can be used to model the nonlinear transformation of surface waves in shallow water due to the effects of shoaling, refraction, diffraction, and reflection. Different linear dispersion relations can be obtained by expressing the equations in different velocity variables. In this paper, a new form of the Boussinesq equations is derived using the velocity at an arbitrary distance from the still water level as the velocity variable instead of the commonly used depth-averaged velocity. This significantly improves the linear dispersion properties of the Boussinesq equations, making them applicable to a wider range of water depths. A finite difference method is used to solve the equations. Numerical and experimental results are compared for the propagation of regular and irregular waves on a constant slope beach. The results demonstrate that the new form of the equations can reasonably simulate several nonlinear effects that occur in the shoaling of surface waves from deep to shallow water including the amplification of the forced lower- and higher-frequency wave harmonics and the associated increase in the horizontal and vertical asymmetry of the waves.