Water Wave Transformation Model for Short and Long Waves

This research presents the formulation of a governing equation for water wave propagation, developed based on the three-dimensional Laplace equation and its velocity potential solution derived through the method of separation of variables. The resulting governing equation takes the form of a parabolic differential equation. The formulation is conducted without imposing limitations on wave amplitude or seabed slope, enabling the model to accommodate maximum wave amplitudes for a given wave period and a wide range of bathymetric gradients. As such, the model is applicable to both short waves and long waves, including tsunamis and sneaker waves. The proposed model effectively simulates key wave transformation processes such as refraction-diffraction, shoaling, breaking, and run-up. Additionally, it is capable of modeling wave overtopping over breakwaters induced by short waves.