Time Series Water Wave Model Based on Energy Conservation

The time series water wave model comprises two equations: the water surface elevation equation and the water particle velocity equation. The elevation equation, derived from the continuity equation, captures changes in potential energy but lacks an energy source. The velocity equation describes changes in kinetic energy but does not include potential energy contributions. In this research, the energy deficiency in the elevation equation is addressed by combining it with the conservation of kinetic energy, while the velocity equation incorporates a driving force derived from the continuity equation. Both equations use a weighted Taylor series expansion to produce realistic wavelengths consistent with natural waves. The model is executed using a periodic solitary wave input, defined as a profile in which the trough and crest lie above the still water level. This input satisfies the initial conditions at the entry point, where the water surface elevation and its time derivative are zero. Shoaling and breaking analysis with the developed model yielded breaking parameters that agree with previous research.