A Model in Frequency Domain for Transformation of Fully Dispersive Nonlinear Waves

Abstract

In this study, mathematical derivation and numerical verification of a wave transformation model in frequency domain is discussed. This wave model is fully dispersive and nonlinear; and is derived based on the WKB assumptions. Transforming the problem into the frequency domain and using multiple scale analysis in space and perturbation theory, the model is expanded up to second order in wave steepness. This fully dispersive nonlinear wave model is a set of evolution equations which explicitly contains quadratic near-resonant interactions. The comparison between the presented model, the existing fully dispersive model and a nearshore model with different set of laboratory and field data shows that the presented model provides significant improvements particularly at higher frequencies.