Histograms, Cumulants, and Spectra of Mechanical and Wind Waves in a Wind-Wave Channel

Abstract—For the purpose of studying the interrelation between the statistical characteristics of waves on the water surface and the laws of their variability the histograms are constructed and the cumulants and spectra are calculated for mechanical and wind waves in a wind-wave channel. The diversity of the histograms for the waves of different nature and their variability with variation in the wave type, parameters, and fetch are analyzed. The regularity in the deviations from the Gaussian wave amplitude distribution presented by their cumulants in the numerical form is noted. With account for the laws of evolution of the frequency spectrum of the waves established along the channel it is asserted that the variability of the wave statistics is uniquely determined by the variability of the shape of their spectrum rather than individual characteristics of the system (wave fetch, steepness, or age). This assertion is theoretically substantiated.