Spatial Evolution of Skewness and Kurtosis of Unidirectional Extreme Waves Propagating over a Sloping Beach

Abstract

The understanding of the occurrence of extreme waves is crucial to simulate the growth of waves in coastal regions. Laboratory experiments were performed to study the spatial evolution of the statistics of group-focused waves that have a relatively broad-banded spectra propagating from intermediate water depth to shallow regions. Breaking waves with different spectral types, i.e., spectral bandwidths and wave nonlinearities, were generated in a wave flume using the dispersive focusing technique. The non-Gaussian behavior of the considered wave trains was demonstrated by the means of the skewness and kurtosis parameters estimated from a time series and was compared with the second-order theory. The skewness and kurtosis parameters were found to have an increasing trend during the focusing process. During both the downstream wave breaking and defocusing process, the wave train dispersed again and became less steep. As a result, both skewness and kurtosis almost returned to their initial values. This behavior is clearer for narrower wave train spectra. Additionally, the learning algorithm multilayer perceptron (MLP) was used to predict the spatial evolution of kurtosis. The predicted results are in satisfactory agreement with experimental findings.