浅水非线性长波的数值模拟与实验研究

Experimental study and numerical simulation of long non-linear shallow-water waves

从数值与实验两方面研究了非线性长周期水波———椭圆余弦波在浅水中的传播。根据造波板作椭圆余弦波运动速度,推导出数值模拟波浪水槽时固定入射边界上的二阶入射边界条件,计算结果表明,二阶入射边界条件对波浪的预报结果比一阶入射边界条件对波浪的预报结果更为精确。对二阶入射边界条件计算结果和实验结果的波面升高时间历程进行傅里叶分析表明,各次谐波幅值沿波浪传播方向作周期性变化,只是变化程度较小;但入射边界条件为一阶时则没有这种现象。

The long non-linear waves in shallow water propagation is studied experimentally and numerically. First order and second order incident boundary condition on fixed incident boundary are derived for numerical simulations, based on the cnoidal motion of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. The Fourier analysis of measured and computed time history of water elevations with second order incident boundary condition shows that there is periodic transformation for different component of waves along wave flume, while no periodic transformation with first order incident boundary condition.