Model tests with unidirectional random wave fields are common for coastal engineering purposes. In this paper, we investigate the finite water depth effect on both the probability of extreme events and the averaged shape of them in such experimental conditions. We simulate some typical model test conditions with a numerical tool, which solves the fully non-linear wave equations. We find the analytical solution based on Nonlinear Schrödinger equation (NLS) to be accurate for low steepness and relatively deep water cases. However, the analytical solution underestimates the kurtosis at the steady state for high steepness cases in shallow water, and also gives zero value of kurtosis at critical water depth, whereas a small but non-zero value of kurtosis is observed in the numerical tank. We also investigate the averaged shape of the extreme events, which are modified by nonlinear physics over the distance. The horizontal asymmetry is significant initially but is greatly reduced to a steady state, and the contraction of the wave groups grows monotonically until the steady state is reached along the wave tank. Finite water depth has limited effects on the averaged shape of large events, especially for the extremely steep waves.

单向随机波场的模型测试通常用于沿海工程目的。在本文中，我们研究了在这种实验条件下，有限的水深对极端事件的概率及其平均形状的影响。我们使用数值工具模拟一些典型的模型测试条件，从而解决了完全非线性的波动方程。我们发现基于非线性薛定ding方程（NLS）的解析解决方案对于低陡度和相对深水的情况是准确的。但是，对于在浅水中的高陡度情况，分析解决方案低估了稳态下的峰度，并且在临界水深处也给出了零值，但在数字储罐中观察到的峰度很小但非零。我们还研究了极端事件的平均形状，非线性物理学会在远处对其进行修改。水平不对称性最初很明显，但会大大降低至稳态，并且波群的收缩会单调增长，直到沿着波箱达到稳态为止。有限的水深对大型事件的平均形状影响有限，尤其是对于极其陡峭的波浪。