抄録
The properties of the maximum wave height and harmonic components of Stokes and trochoidal wave which are in the state of the heighest value are analysed. Wave profile and the ratio of the heighest amplitude to r.m.s. are as follows: 1) Stokes wave ζe^<1-ζ>=cosθ; Maxζ÷r.m.s.ζ=2.705. 2) trochoidal waves ζ=cosφ, θ=φ-sinφ; Maxζ÷r.m.s.ζ=3.000. Extending these results analogically, the fact is found that the above-mentioned maximum value corresponds to the ordihate of the centre of the minimum radius of curvature of probability density curve. The distribution function and the numerical value is: 1) Gauss-Laplace distribution p(x)=1/√<2π>e^<-(x^2)/2>, Maxx=2.618. 2) Rayleigh distribution p(x)=xe^<-(x^2)/2>, Maxx=3.170. Stokes wave has drift current, but trochoidal wave is quite stational. The former occurs in the center of storm and the latter in calm weather. so that the distribution of the height of Stokes wave becomes Gauss-Laplace type, and trochoidal wave shows Rayleigh type, namely the former corresponds to seas and the latter to swells respectively. These oceanographical phenomena are in good accordance with the above relations. The maximum values of oceanographical data by day, by month or by year form usually Gauss-Laplace distribution, so the estimation of the critical value is to be done by the following formula.: MaxX=MeanX+3.281|MeanX-MeanX| Wfere Xs denote every data. The validity is proved by various observed records.
