A combined refraction and diffraction water wave model using phase-averaged approach

It is important in practical engineering to study the propagation of waterwaves in coastal waters using mathematical modeling methods. The research ofwater waves has progressed very much in the recent decades. Water wave models, suchas mild-slope equation, Boussinesq equation and so on, have been put intopractical engineering applications. But different water wave models havedifferent effectiveness. The respective theoretical basis of the water wave modelsdetermines the features of these models. As mathematical models,based on the conversation law of wave energy or wave action, spectral wavemodels are used to determine wave conditions in coastal regions, which canaccount for all relevant processes of generation, dissipation andpropagation. But the conventional spectral wave models can not simulate thewave diffraction. With diffraction being incorporated, the spectralwave models can be more widely used to simulate waves in the coastalregions. In this paper, a new phase averaged wave model is developed, inwhich the conservation of wave energy or wave action is used to formulatethe wave propagation and a combined refraction and diffraction contributionis coupled through introducing a diffraction factor based on analysis of themild slope equation. Computational results in extreme diffraction casesagree reasonably well with observations. It is shown that the new model canbe used to simulate refraction and diffraction of water waves in coastalregions.