A study on the spectral models for waves in finite water depth

From an extension of the Wallops Spectrum (Huang et al., 1981) for the deep water waves, spectral models for waves in finite water depths are developed. Stokes wave expansions are found to offer a good approximation for intermediate water depth. The spectral function in this case is controlled by three parameters: the significant slope, the nondimensional depth, and the peak frequency. It is pointed out that solitary and cnoidal wave models must be used for the shallow water waves. The controlling parameters now reduce to the Urell number and the peak frequency. Even though the resulting spectral models place special emphasis on the energy-containing range of the spectrum, they are not limited to this range and they are not limited to any particular sea state. They are seen as offering a possible explanation of the variations in the special slope observed by previous investigators.