计入浅水变形的非线性波浪分离方法对不规则波的验证

摘要

在开展物理模型试验时，把实测信号分离为入射信号与反射信号十分重要。可用于信号分离的方法很多，但关注斜坡床面影响的研究十分有限。本文以一种简化的途径，通过计入波浪在斜坡床面上的浅水变形与相位变化，把一种非线性分离方法拓展到斜坡床面。以线性合成信号所作的验证表明：在中等水深条件下，波高的误差有限；但在浅水条件下误差增大，最大可达 4%。此外，若在分离中不考虑斜坡床面，则第一支波高仪处的波高在浅水中被高估、在深水中被低估。数值模拟结果表明，以水深比的 1 次幂给出的束缚波浅水变形系数对次谐波尚属合理，但对更高次的谐波并不成立。同时建议在更大范围的试验工况下检验束缚波的浅水变形。在物理模型试验中分别应用计入与不计入斜坡床面影响的两种方法时，波高的平均相对差为 1%，最大可达 4%。

Abstract

Decomposing the measured signals into incident and reflected signals is important when performing physical model experiments. Many methods exist to decompose a signal but limited studies focus on the effect of a sloping bed. In this paper, a nonlinear decomposition method is extended for a sloping bed by accounting for shoaling and phase transformation over a sloping bed with a simplified approach. Verification with linear synthetic signals shows that the error for the wave height is limited for intermediate water depth, but increases for shallow water depth with an error of up to 4%. Moreover, if the sloping bed is not considered in the decomposition, the wave height at the first wave gauge is overestimated in shallow water and underestimated in deep water. The numerical simulations show that a shoaling coefficient for the bound waves based on the water depth ratio with a power 1 is reasonably accurate for the sub-harmonics but not valid for higher harmonics. In addition, it is recommended to verify the shoaling of bound waves for a large range of test conditions. When applying the method both with and without the effects of a sloping bed in physical model experiments, the average relative differences for the wave height are 1 % with a maximum up to 4 %.