海浪局部振幅和局部周期的统计分布

STATISTICAL DISTRIBUTIONS OF LOCAL WAVE AMPLITUDES AND PERIODS

根据平稳正态随机过程及其Hilbert变换的性质,在不受窄谱限制的条件下,严格导出海浪局部振幅A局部周期T的分布函和联合分布函数,并以在实验室水槽中产生的三种不同谱宽度的波浪作了验证,结果比较满意。

With an assumption that the sea surface elevation ζ(t), as a stochastic process, is stationary and normal and can be represented bythe distributions of the local amplitude A(t) and the local period and the joint distribution of A(t) and T(t), are strictly derived, by using the theory of Hilbert transform, to bewhereis the ith order moment of the wave spectrum S(ω), andEquivalently, the above three distributions can be expressed in terms of dimen-sionless variables where are the introduced dimensionless quantities andis a measure of spectral width defined by Longuet-Higgins.Three trains of random waves with respectively a narrow spectrum (v= 0.052), a JONSWAP spectrum (v = 0.308), and a P-M spectrum (v= 0.417) generated by a program-controlled wave generator are used to test the distributions. It is found that in all of the three cases the theoretical distributions given above are consistant well with the actual ones, not affected by the spectral width, while those derived by Longuet-Higgins with the narrow band assumption deviate to a certain extent from the actual ones and the larger the spectral width the more serious the deviation.