Enhanced Integration of Kinematic free surface boundary condition to third order Accuracy for Wave Transformation Modeling

The relationship between wave amplitude and other wave constants is derived through the integration of the Kinematic Free Surface Boundary Condition (KFSBC) over time, yielding the wave amplitude function. This function presents the characteristics of wave breaking to determine the breaker length index—the ratio of breaking wave height to breaking wave length. Previous research achieved integration at a zero-order accuracy level, assuming small wave amplitude and long wave, resulting in a notably large critical breaker length index and wave steepness. In this research, KFSBC integration was advanced to second and third-order accuracies, yielding a wave amplitude function that significantly reduces the critical breaker length index and wave steepness compared to zero-order integration. Subsequently, utilizing the third-order wave amplitude function, a comprehensive wave transformation model incorporating shoaling, breaking, refraction, and diffraction was developed, demonstrating robust model performance.