Shoaling-breaking Water Wave Modeling Using Velocity Potential Equation with Weighting Coefficient Extracted Analytically from The Dispersion Equation

A shoaling and breaking water wave model was developed in this study using the velocity potential of the solution of the Laplace equation. Formulation was carried out using Weighted Kinematic Free Surface Boundary Condition Equation, wave number conservation equation, and energy conservation equation. In the Weighted Kinematic Free Surface Boundary Condition equation, a weighting coefficient was used which needs to be determined. The value of the weighting coefficient was extracted from the dispersion equation. The dispersion equation was formulated using Weighted Kinematic Free Surface Boundary Condition and Weighted Momentum Equation to obtain weighting coefficient that meets the hydrodynamic equilibrium equation. By using the weighting coefficient, good shoaling and breaking results were obtained.