The influence of finite depth on the evolution of extreme wave statistics in numerical wave tanks

Abstract

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.