A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii

Abstract

The data for the spectrums of fully developed seas obtained by Moskowitz [1964] for wind speeds from 20 to 40 knots (10.29 to 20.58 m/sec), are used to test the similarity hypothesis and the idea proposed by Kitaigorodskii [1961] that, when plotted in a certain dimensionless way, the power spectrums for all fully developed seas should be of the same shape. Over the important range of frequencies that define the total variance of the spectrum within a few per cent, the transformed plots yield a nondimensional spectral form that is nearly the same over this entire range of wind speeds within the present accuracies of the data. However, since slight variations of the wind speed have large effects on the location of this nondimensional spectral form, inaccuracies in the determination of the wind speed at sea allow for some latitude in the final choice of the form of the spectrum. Also, since the winds used to obtain the nondimensional form were measured at a height greater than 10 meters, the problem of relating the spectral form to a standard anemometer height arises. The variability introduced by this factor needs to be considered. The results, when errors in the wind speed, the sampling variability of the data, and the anemometer heights are considered, suggest a spectral form that is a compromise between the various proposed spectrums and that has features similar to many of them. A spectral form is recommended for tentative application to the problem of wave forecasting by spectral techniques. Improved wind speed measurements (taken at several elevations and averaged over longer time intervals) and better wave data (taken for longer time intervals and analyzed so as to better fit the procedures) are needed so that the form of the spectrums of fully developed wind seas and seas limited by either fetch or duration can be determined with even greater precision.