Abstract
This paper proposed an energy balance equation including the effect of wave diffraction as a multi-directional random wave transformation model. The term of wave diffraction was included explicitly in the model, which was formulated based on a parabolic wave refraction-diffraction equation. The present wave model is easy to solve numerically and is stable. The wave model was employed to estimate wave transformations through the mouth between two breakwaters, and the estimated results were compared with the predictions by the existing energy balance equation without wave diffraction effect and with the Sommerfeld solutions. The comparison between the wave heights shows that the present wave model is the good predictor. The present wave model was also applied to the experiments of wave transformation due to an elliptic shoal, and it was found that the model predictions agreed well with the experimental observations excluding the cases where the wave breaking on the shoal was severe.
