Water Wave Velocity Potential on Sloping Bottom in Water Wave Transformation Modeling

In this research, we formulated the equation for water wave velocity potential on sloping bottoms. The resulting velocity potential equation for sloping bottoms closely mirrors that of flat bottoms, simplifying its application in sloping terrain scenarios. By exploring velocity potential on sloping bottoms, we derived conservation equations governing wave constant changes as waves transition from deep to shallow waters. These equations encompass the wave number conservation and energy conservation principles. Utilizing these conservation equations, we developed a comprehensive wave transformation model. The one-dimensional model focused on shoaling and breaking phenomena, while the two-dimensional model delved into refraction-diffraction, shoaling, and breaking. The model's framework allows for straightforward extensions, facilitating future advancements in the field.