On the Role of Spectral Width and Shape Parameters in Control of Individual Wave Height Distribution

Abstract

Distributions of individual wave heights approximately follow the Rayleigh distribution regardless of the bandwidth of frequency spectra, even though Longuet-Higgins derived the theory on the condition of narrow-band spectrum in 1952. The spectral width parameter does not affect the wave height distribution, but it merely provides a measure of the minuteness of data sampling interval relative to mean wave period for waves in the sea. A spectral shape parameter introduced by Rice in 1945 for wave envelope amplitude is a better measure to describe a slight departure of wave height distribution from the Rayleigh. Several sets of linearly simulated wave profiles and field measurement records have been re-analyzed to verify the above findings. The spectral shape parameter also governs the spread of wave period distribution for single peaked spectral waves.