Mathematical derivation and numerical verification of a wave transformation model in the frequency domain are discussed. The model is a fully dispersive nonlinear wave model and is derived based on the boundary value problem. Transforming the problem in 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 sets of laboratory and field data shows that the presented model provides significant improvements particularly at higher frequency.

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Images of the 2004 Indian Ocean tsunami at landfall shows a leading edge marked by short waves (“fission” waves). These waves appear to be cnoidal in shape and of a temporal and spatial scale in line with the longest swell present in the region, and may interact with the longer waves in the background random wave spectrum. As part of a comprehensive series of experiments, the Large Wave Flume at Oregon State University (USA) was used to generate and measure the properties of cnoidal, random, and combined cnoidal-random wave trains. Both the nonlinear energy transfer characteristics (via bispectral analysis) and dissipation characteristics (via a proxy dissipation function) are studied for all generated wave conditions. It is generally determined that the characteristics of the cnoidal wave dominate the combined cnoidal-random wave signals if the energy of the cnoidal wave is at least equal to that of the random wave.