A laboratory study of directional spectra with maximum likelihood mehod-Ⅱ Decaying swell

From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of swell in deep water are systematically investigated with maximum likelihood method. It is shown that the disectional spreading of swell, qualitatively similar to that of developing wind wave which is narrowest in the region of peak frequency and broadens with increasing or decreasing frequency, can be effectively described by cos^2s(θ/2) introduced by Longuet-Higgins et al.(1963, Ocean Wave Spectra.111-136).It is intriguing that bimodal distribution found in our experiments appears at the forward face instead of the rear face of a Ireyuency vpectrum in the cases of nonlinearity being very weak. Parameterized by nonlinearity, formulations which can be applied to swell as well as wind wave are proposed. It is concluded that nonlinear interaction plays a central role in controlling the development of directional angular spreading even for the swell.