A laboratory study of directional spectra with maximum likelihood method-Ⅰ Developing wind wave

measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likelihood method The investigations reveal that the angular spreading of the wave energy is consistent with cos^2s(θ/2) proposed by Longuet-Higgins et al.(1963, Ocean Wave Spectra, 111-136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole resalts. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al.(1975, Journal of Physical Oceanography, 5, 750-760) and Hasselmann et al.(1980, Journal of Physical Oceanography, 10, 1264-1280) in the field, and the relationship between the four nondimensional parameters s_m, f_o, b₁ and b₂, determining the directional width, and ū₁₀ (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al.(1985, Philosophical Transaction of Royal Society of London, A315, 509-562) when applied to field waves.