Energy Loss Coefficient Equation in the Modified Euler Momentum Conservation Equation for A Time-Series Water Wave Model

The modified Euler momentum conservation equation proposed by the author contains a term that represents wave energy dissipation. This term includes an energy loss coefficient that governs the magnitude of energy release. The coefficient is not a constant but a function of hydrodynamic parameters; therefore, an explicit formulation of this coefficient is required. In this study, the energy loss coefficient is derived using the Kinematic Free Surface Boundary Condition, incorporating wave energy, wavelength, and wave period as governing parameters. The resulting formulation enables effective representation of energy dissipation within the modified Euler momentum conservation equation. Consequently, a time-series water wave model is obtained that is capable of realistically passing through the breaking phase and propagating into shallower waters.