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二阶非线性随机海浪波面高度和波面垂直速度的联合分布
管长龙
青岛海洋大学物理海洋研究所物理海洋实验室 青岛 266003
摘要:
基于Longuet－Higgins提出的非线性随机海浪模型，在二阶近似下通过直接计算联合分布的各阶矩，导出了非线性海浪波面高度和波面垂直速度的联合分布。该分布为非正态，其形式为截断的级数，而非由累积矩母函数方法可能得到的渐近无穷级数。由于非线性的影响，波面高度与波面垂直速度不再相互独立。
关键词:  非线性  波面和波面垂直速度  联合分布  海浪
DOI：
分类号:
基金项目:国家自然科学基金资助项目，49676274号
JOINT DISTRIBUTION OF SURFACE ELEVATION AND ITS VERTICAL VELOCITY FOR THE SECOND ORDER NONLINEAR RANDOM SEA WAVES
Guan Changlong
Institute of Physical Oceanography and Physical Oceanography Laboratory ,Ocean University of Qingdao, Qingdao 266003
Abstract:
On the basis of the nonlinear model for random sea waves presented by Longuet-Higgins, the joint distribution of wave surface elevation η and its vertical velocity η’, accurate to second order approximation, is derived by calculating directly each moment of the joint distribution. The derived distribution is in form of the truncated series. (For the equations please see the PDF file.)

the asymptotic infinite one, which is the probable result by the cumulant-generating function method. The truncation of the series is related physically to the order of the nonlinear approximation. Owing to nonlinearity of sea waves, the distribution is non-Gaussian, and η and η’ are no longer independent of each other.
Key words:  Nonlinearity, Surface elevation and its vertical velocity, Joint distribution, Sea waves
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