Hilbert变换在海浪波高与周期联合分布函数中的应用

Longuet-Higgins(1983)1]导出了波高与周期的联合分布函数,此分布函数虽然与实际数据符合良好,但存在很大的缺陷,如:由此分布函数得出的波高分布为形式较为复杂的非Rayleigh分布,很难应用于工程计算中。孙孚(1988a)2]应用射线理论导出了一种波高与周期联合分布,虽然弥补了Longuet-Higgins的一些缺陷,但推导过程过于复杂。本文在窄谱假定下通过应用Hilbert变换方法得出新的分布函数并与前两者比较,表明Hilbert变换的方法不但简便,而且完全克服Longuet-Higgins的不足,可以方便的应用于工程计算中。本文也为Hilbert变换的方法在工程中的应用提供了理论依据。

The application of Hilbert transform on joint distribution function of wave period and wave height

Based on narrow-band Gaussian process,theoretical probability density function(PDF) is derived by applying an approximate Hilbert transform.The PDF is the joint distribution of the wave period and wave height.It has the same merits as the PDF previously derived by Longuet-Higgins(1983),in being asymmetric and in depending only on the spectral width parameter,but gains an advantage that it predicts an exactly Rayleigh distribution of,and so facilitates its handling in theory and application in practice.In virtue of the advantage a relatively simple conditional PDF of assuming is derived,which may be used to predict an arbitrarily defined characteristic conditional wave period assuming the wave height from the average wave period.This paper provides theoretical basis for the applications of Hilbert Transform on engineering.