### DIRECTIONAL SPECTRA OF OCEAN SURFACE WAVES

#### Abstract

From 1971-74 seven cruises were made to measure the directional spectrum of ocean waves by using a cloverleaf buoy. Typical sets of wave data measured both in open seas and in a bay under relatively simple conditions have been analyzed to clarify the fundamental properties of the directional spectrum of ocean waves in deep water. It is shown that the directional wave spectrum can be approximated by the product of the frequency spectrum and a unimodal angular distribution with mean direction approximately equal to that of the wind. The normalized forms of the frequency spectrum show various forms lying between the Pierson-Moskowitz spectrum and the spectrum of laboratory wind wave which has a very sharp energy concentration near the spectral peak frequency. The form of the JONSWAP spectrum is very close to that of laboratory wind waves. The concentration of the spectral energy near the spectral peak frequency seems to decrease with increasing the dimensionless fetch and the spectral form finally approaches to the Pierson-Moskowitz spectrum which can be considered as the spectrum with the least concentration of the normalized spectral energy. However, the definite relation between the shape of the normalized spectrum and the dimensionless fetch has not been obtained. Concerning the angular distribution, it is shown that the shape of angular distribution of the single-peaked wave spectrum in a generating area can be approximated by the function G(6,f) = G'(s) | cos (6-6)/2 | ** proposed originally by Longuet=Higgins et al. (1963). Here G'(s) is a normalizing function, 6 is the mean direction of the spectral component, and s is a parameter which controls the concentration of the angular distribution function.

#### Keywords

directional spectra; surface waves

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