A numerical investigation on nonlinear transformation of obliquely incident random waves on plane sloping bottoms

The statistical properties of obliquely incident irregular waves over a planar sloping bottom were investigated numerically by the well-known numerical wave model FUNWAVE 2.0. Irregular waves based on the averaged JONSWAP spectra with various wave heights and peak periods were simulated to propagate over planar bottoms. A wide range of incident angles from 0° though 75° were considered to study the influence of incident angles. It was found that incident angles have a significant influence on the wave nonlinearity. The wavelet-based bicoherence revealed that the degree of triad wave interactions of primary waves and the higher harmonics was apparently weakened by increasing wave incident angles. Importantly, using the simulated data, the Klopman wave height distribution was improved by incorporating the influence of obliquely incident angles. It was found that the improved Klopman distribution shows better performance for describing wave height distributions in shallow water depth. Moreover, two empirical formulae are recommended to reflect the relationship between the skewness and the asymmetry of waves and the Ursell number for obliquely incident waves on plane sloping bottoms.