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On the basis of the linear model of random sea waves presented by Longuet-Higgins,the statis-tical distribution of the horizontal velocities of water particles at wave surface maxima is derivedtheoretically.The derived distribution is similar to that of wave surface maxima,and a new spectral widthε_u,which is defined as(1-(m_3~2/m_2m_4))~(1/2),is introduced in the distribution.When ε_u tends to zero,the distribu-tion is reduced to Rayleigh distribution and it is reduced to the normal distribution when ε_u tends to unity.For a narrow spectrum,it is proved that ε is equal to 1/2ε,where ε is(1-(m_2~2/m_0m_4))~(1/2)and is the commonlyused spectral width..
On the basis of the linear model of random sea waves presented by Longuet-Higgins, the statis-tical distribution of the horizontal velocities of water particles at wave surface maxima is derived theticallytically. The derived distribution is similar to that of a wave surface maxima, and a new spectral widthε_u, which is defined as (1- (m_3 ~ 2 / m_2m_4)) ~ (1/2), is introduced in the distribution.When ε_u tends to zero, the distribu tion is reduced to Rayleigh distribution and it is reduced to the normal distribution when ε_u tends to unity. For a narrow spectrum, it is proved that ε is equal to 1 / 2ε, where ε is (1- (m_2 ~ 2 / m_0m_4)) ~ (1/2) and is the commonlyused spectral width