海浪波面极大值分布的非线性影响
Effect of nonlinearity on statistical distribution of maxima Of Sea Wave surface
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摘要: 依非线性海浪模型,在二阶近似下,利用特征函数展开技术和直接求矩的方法,导出了定点波面位移及其对时间的一阶和二阶导数的联合分布。由此联合分布,导出了二阶非线性近似下的波面极大值分布。它由线性意义下的海浪频谱及所考虑的二阶级。波相互作用所确定。当忽略非线性影响时,文中给出的波面极大值分布退化为Cartwright和Longuet-Higgins所导出的分布。Abstract: Based on the nonlinear model of random sea waves which is exact to the second-order, the joint distribution of wave surface elevation and its first-and second-order derivatives with respect to time is derived by using the development of characteristic function and calculation directly each order moment. From the above joint distribution the statistical distribution of the maxima of sea wave surface is derived. The derived distribution is physically determined by both sea wave frequency spectra which is in the sense of linearity and the second-order wave-wave interaction. When nonlinear effect is neglected, the derived distribution of maxima of sea wove surface is reduced to that derived by Cartwright and Longuet-Higgins.
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Cartwright D E, Longuet-Higgins M S. The statistical distribution of the maxima of a random function. Proc. Roy. Soc.London, 1956, 237(1209):212-232 Sun Fu, Ding Pingxing, Guan Changlong. The statistical distribution of the spatial maxima of a wave surface. Chin. J.Oceanol. Limnol.,1994, 12(1):1-12 Longuet-Higgins M S. The statistical analysis of a random moving surface. Phil. Trans. Roy. Soc.,A, 1957, 249(966):321-387 孙孚,丁平兴.非线性海浪的波面高度概率分布及其物理解释.中国科学(B辑), 1994, 24(8):859-865 文圣常,余宙文.海浪理论与计算原理.北京:科学出版社,1984, 166-169 -
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