Theoretical wind wave frequency spectra in deep water——Ⅰ. Form of spectrum

In this part ot the paper theoretical wind-wave spectra nave been derived by (1) 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 ω₀, 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 Š(ω)=ω₀S(ω)/ω₀(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=Š(1).