In the coastal engineering field, breaking waves cause the destruction of coastal structures due to impulsive breaking wave pressure. Although the phenomenon of wave breaking is very important in terms of engineering, the occurrence condition of breaking waves is not sufficiently understood yet. In this research, to clarify the occurrence condition to the breaking of waves, the theoretical analyses of progressive waves in constant water depth are carried out. Further, the numerical simulation of wave run-up on a uniform gradient water depth is also performed. In the theoretical analysis, the characteristic phenomenon of the kinetic energy of the water surface exceeding the potential energy as the wave height depth ratio increases on the Hyperbolic wave and the solitary wave are shown. To show the validity of the theoretical analysis, the numerical simulation of wave run-up on the periodic wave and the solitary wave are conducted, and the simulation result confirms the same results as the theoretical analysis. As a conclusion of this study according to the results of the theoretical analysis and the numerical calculation, the kinetic energy of water particles on the water surface increases divergently as the wave height to depth ratio increases which leads to wave breaking; because it occurs the wave height depth ratio is the same order as the breaking wave height depth ratio in the case of constant water depth and just before the wave collapses in the case of uniform gradient water depth.
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