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In this part ot the paper theoretical wind-wave spectra nave been derived oy (I) expressing the spectrum in series composed of exponential terms; (2) assuming that the spectrum satisfies a high order linear ordinary differential equation; (3) introducing proper parameters in the spectrum; and (4) making use of some known charateristics of wind-wave spectrum, for instance, the law governing the equilibrium range. The spectrum obtained contains the zero order moment of the spectrum m0, the peak frequency ω0 and the ratio R =ω/ω0 (ω being the mean zero-crossing frequency) as parameters. The shape of the nondimensional spectrum S(ω) = ω0S(ω)/m0(ω=ω/ω0) changes with R and theoretically reduces to a Dirac delta function δ(ω-1) when R = 1. A spectrum of simplified form is given for practical uses, in which R is replaced by a peakness factor P=S(1).
(2) assuming that the spectrum is a high order linear ordinary differential equation; (3) introducing proper parameters in the spectrum; and (4) making use of some known charateristics of wind-wave spectrum, for instance, the law governing the equilibrium range. The spectrum obtained contains the zero order moment of the spectrum m0, the peak frequency ω0 and the ratio R = ω / ω0 (ω being the mean zero-crossing frequency) as parameters. The shape of the nondimensional spectrum S (ω) = ω0S (ω) / m0 (ω = ω / ω0) changes with R and theoretically reduces to a Dirac delta function δ (ω-1) when R = 1. A spectrum of simplified form is given for practical uses, where R is replaced by a peakness factor P = S (1).