波群长度的最大熵分布

Maximum entropy distribution of wave group length

将最大熵分布的概率密度函数fn(G)=αGγexp(-βGn)推广应用于海浪波群长度,该概率密度函数不仅使波群长度G的信息熵最大,符合最大熵原则,而且其形式简单且参量容易由已知观测数据确定,从而便于理论和实际应用．用实验室风浪槽中不同风速下和不同风区处实测的36组波面位移数据对其进行验证,并与至今仍被广泛应用的Longuet-Higgins推导的群长的概率密度函数作比较,结果表明,最大熵分布的概率密度函数与各组实测数据均符合良好,显著地优于Longuet-Higgins推导的概率密度函数,其中n=0．6时拟合效果最好．

The maximum entropy probability density function (PDF) fn(G) =αGγexp(-βGn)is applied to describe the group length G, whereα,βandγcan be determined by some reasonable constraints when n is given. This PDF has the following advantages: (1) This PDF maximizes the information entropy of G and accords with the maximum entropy principle, so it is competent for nonlinear sea waves whose uncertainty is large; (2) This PDF is simple and its parameters are easy to be determined from available data, so it is convenient to theoretical and practical applications. To test the validity, the derived PDF is compared with thirty-six observed wave records at different wind speeds and different fetches in a wind-wave tunnel, along with the PDF derived by Longuet-Higgins, which has been widely employed to describe the distribution of wave group lengths. The result shows that the maximum entropy probability density function gives a better fit; it has the best agreement for n = 0. 6.