摘要
A probability density function (PDF) is derived of beta distribution with both lambda (3) skewness) and lambda (4) (kurtosis) as parameters for weakly nonlinear wave surface elevation by use of a method recently proposed by Srokosz. This PDF not only has a simpler form than the well-known Gram-Charlier Series PDF derived by Longuet-Higgins, but also overcomes an obvious shortcoming of the latter that when the series is unsuitably truncated, the resulting PDF is locally negative. To test the derived beta PDF, laboratorial experiments of wind waves are conducted. The experimental data indi cate that the theoretical requirements of the parameters in the beta PDF are fulfilled. The experimental results show that the present PDF is in better agreement with the measured data than the beta PDF only including parameter lambda (3), and also than the Gram-Charlier Series PDF truncated up to the term of H-6.
A probability density function (PDF) is derived of beta distribution with both lambda (3) skewness) and lambda (4) (kurtosis) as parameters for weakly nonlinear wave surface elevation by use of a method recently proposed by Srokosz. This PDF not only has a simpler form than the well-known Gram-Charlier Series PDF derived by Longuet-Higgins, but also overcomes an obvious shortcoming of the latter that when the series is unsuitably truncated, the resulting PDF is locally negative. To test the derived beta PDF, laboratorial experiments of wind waves are conducted. The experimental data indi cate that the theoretical requirements of the parameters in the beta PDF are fulfilled. The experimental results show that the present PDF is in better agreement with the measured data than the beta PDF only including parameter lambda (3), and also than the Gram-Charlier Series PDF truncated up to the term of H-6.
基金
This work was financially supported by the National Natural Science Foundation of China (No. 59676277)
the 863-818 Project (05-02)
