Comparison of Distributions of Wave Heights From Nonlinear Schröedinger Equation Simulations and Laboratory Experiments

Numerical simulations of the nonlinear Schrödinger (NLS) equation are performed by imposing randomly synthesized free surface displacement at the wave maker characterized by the Joint North Sea Wave Project (JONSWAP) spectrum and compared with four different sea states generated in the deepwater wave basin of Marintek. The comparisons show that the numerical simulations have a high degree of agreement with the laboratory experiments although a little overestimation can be observed, especially in the severe sea state. Thus, the simulations still catch the main characteristics of extreme waves and provide an important physical insight into their generation. The coefficient of kurtosis $λ40$ presents a similar spatial evolution trend with the abnormal wave density, and the nonlinear Gram–Charlier (GC) model is used to predict the wave height distribution. It is demonstrated again that the theoretical approximation based on the GC expansion can describe large wave heights reasonably well in most cases. However, if the sea state is severe, wave breaking can significantly decrease the actual tail of wave height distribution, and discrepancy occurs when comparing with the numerical simulation. Moreover, the number of waves also plays an important role on the prediction of extreme wave height.