A Parabolic Equation Model for Transformation of Irregular Waves Due to Refraction, Diffraction and Breaking

A numerical model is developed for calculating the transformation of irregular waves due to refraction, diffraction and breaking. The model is based on a parabolic equation which is derived from the mild slope equation1) with an additional term of energy dissipation.In the present model, irregular waves are treated as a superposition of component regular waves with different frequencies and directions. In order to calculate the transformation accurately for a wide range of propagation directions of component waves, a new parabolic equation is derived by taking into account the difference between directions of wave propagation and a prechosen coordinate. As a first step in modeling the breaking transformation of irregular waves, the breaking criterion and the energy dissipation coefficient are formulated as a function of a parameter corresponding to the significant wave.Results of numerical calculation are compared with available analytical solutions and show a fairy good agreement. Sample results of applications are also shown.