The Relationship Between Wave Period, Deep Water Wave and Breaking Wave Heights, Formulated Using the Wave Amplitude Function

The wave amplitude function is a relational equation that links wave amplitude with various water wave parameters, such as wave number, wave angular frequency, and wave constant. This function is derived by integrating the Kinematic Free Surface Boundary Condition over time. The wave amplitude function incorporates breaking characteristics, allowing for the extraction of breaking parameters, including breaking wave height, breaking wave length, and breaking water depth, as functions of the wave period. By combining the Euler momentum conservation equation with the wave amplitude function, a dispersion equation is obtained. This dispersion equation elucidates the relationships between deep water wave height, deep water wave length, and deep water depth in relation to the wave period. The results obtained for both deep water wave height and breaking wave height are consistent with previous research.