Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribution. Results show that the agreement between the Gram-Charlier series and the observed distribution becomes better and better as the truncated order of the series increases in a certain range, which is contrary to the phenomenon observed by Huang and Long (1980). It is also shown that the Gram-Charlier series is sensitive to the anomalies in the data set which will make the agreement worse if they are not preprocessed appropriately. Negative values of the probability distribution expressed by the Gram-Charlier series in some ranges of surface elevations are discussed, but the absolute values of the negative values as well as the ranges of their occurrence become smaller gradually as more and more terms are included. Therefore the negative values will have no evident effect on the form of the whole surface elevation distribution when the series is truncated at higher orders. Furthermore, a simple recurrence formula is obtained to calculate the coefficients of the Gram-Charlier series in order to extend the Gram-Charlier series to high orders conveniently.
A genuine geostrophic small amplitude wave solution is deduced for the first time from the general form of linear fluid dynamic equations with the f-plane approximation, where the horizontal component of angular velocity of the earth rotation is taken into account. The Coriolis- induced stress obtained from this solution consists of lateral and reverse component, while its first order approximation is reduced to the result of Hasselmann or Xu Zhigang. Accordingly, combining the Coriolis-induced wave stress with the virtual wave stress proposed by Longuet-Higgins, the ratio of total wave-induced stress to wind stress on the sea surface is es- timated, through which the importance of the wave-induced stress is emphasized in the study of the currents in the seas around China, especially in the Bohai Sea and the Yellow Sea.
A probability density function of surface elevation is obtained through improvement of the method introduced byCieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The densityfunction can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basicbehavior of the probability. Moreover because the distribution is derived without any assumption about sea waves, it isfound from comparison with several accepted distributions that the new form of distribution can be applied in a widerrange of wave conditions. In addition, the density function can be used to fit some observed distributions of surface verti-cal acceleration although something remains unsolved.
