The Observed Joint Distribution of Periods and Heights of Sea Waves

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Abstract
Analysis is made of 89 records of surface waves for the joint distribution of the heights and periods of zero up-crossing waves. Records are classified into five groups according to the rank of the correlation coefficient between individual wave heights and periods, and the data of the joint distribution are presented for five groups separately. In comparison with the present data, the theory of Longuet- Higgins for a narrow band spectrum can describe the joint distribution in its upper portion with high waves when the spectral width parameter is fitted to the marginal distribution for wave periods, although the joint distribution in the lower portion with low waves shows deviation from the theory. Another theory by a group of C.N.E.X.O. based on the distribution of positive maxima can describe the general pattern of observed distribution better than the former theory, but the agreement remains qualitative. The present data also suggests that the joint distribution of wave periods and heights may be parameterized with the correlation coefficient between wave heights and periods.

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