均匀水底上二维随机波面的二阶谱

BISPECTRA OF TWO-DIMENSIONAL RANDOM WAVES IN WATER OF UNIFORM DEPTH

本文用摄动方法导出了均匀水底上精确至二阶的二维随机波动解。依据此解并将二阶谱定义为三阶矩函数的Fourier变换,首次给出了精确至二阶的二维随机波面二阶谱的理论表达式并简略地考虑了它的各个组成部分的物理意义。

By means of perturbation method, solutions exact to the second order are strictly deduced for two-dimensional random waves in water of arbitary uniform depth. Based on the solutions, the theoretical expression of bispectra is given for the first time, which is written as follows:It may be seen from the above that the bispectra of surface elevation are composed of three parts, which respectively describe the interaction between two free waves of the frequencies w and ω', and between one secondary forced wave of the frequency ω + ω' and the two free waves.The results presented in this paper might be an essential development for applying bispectral analysis to the study of the nonlinearity of the sea waves.