A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.
Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolu-tion equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of en-ergy from high to low frequencies without introducing the concept of nonlinear wave-wave interac-tions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spa-tial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.
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 mote 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.
It is well known that energy spectrum bandwidth should be able to reflect the degree of energy concentration. However, the commonly used bandwidth factors defined by Longuet-Higgins could not fit the concept satisfactorily. A new kind of spectrum bandwidth scale factor with a clear physical meaning is given in the present paper and a constant is obtained which reveals the intrinsic characteristics of sea waves. Thereby a universal relationship between significant wave height of sea waves and spectrum bandwidth is established.
By virtue of neural network, a series of signals is extended forward and backward, as a result, two additional maxima and two additional minima are obtained at both ends of the original data set, with which the EMD decomposition can be exactly achieved with cubic spline interpolation. Meanwhile, by using of neural network every IMF component can also be extended forward and backward, which effectively restrains the end effect, thus the veracious Hilbert spectra are achieved. Verifications of the sample signals and the actual surface elevation of sea waves show that the present extension method is relatively accurate.
DENG Yongjun, WANG Wei, QIAN Chengchun, WANG Zhong & DAI DejunNetwork Center, Ocean University of Qingdao. Qingdao 266003, China
