Time-frequency analysis of water waves with special regard to their non-stationary and nonlinear properties - Nonlinear Fourier transform

该项目的主要目标之一--开发和实现非线性傅立叶变换(NLFT)--已在该项目的第一阶段成功实现。在已完成的准备工作和工作进展的基础上，得出了应用期间的以下目标：第一，将进行逆散射变换(IST)，识别非线性波相互作用项；第二，利用所实现的非线性傅立叶变换，一致地识别潜礁波-结构相互作用中的非线性过程；第三，利用非线性傅立叶变换，正确地识别有限长度暗礁后传输的波列中的孤立波数。第四，利用非线性傅立叶变换，识别有限长的暗礁后的波-结构相互作用的非线性过程。最后，利用非线性傅立叶变换，对有限长的暗礁后传播的波列中的孤立波个数进行识别评价了希尔伯特-黄变换(HHT)和小波变换(WT)对波浪-结构相互作用中的非线性过程的描述能力，并对HHT和NLFT的联合应用提出了建议。最后，根据NLFT的“非线性”傅里叶谱的能量平衡分析，确定了暗礁的水力效率。

One of the main objectives within this project, the development and the implementation ofthe nonlinear Fourier transform (NLFT), has been successfully realised in the first phase ofthe project. Based on the completed preparatory work and the work progress, the followingobjectives for the application period are derived.First, the inverse scattering transform (IST) will be implemented and the nonlinear wavewaveinteraction terms identified.Second, the nonlinear processes involved in the wave-structure interaction at submerged reefswill be consistently identified using the implemented NLFT.Third, the number of solitary waves in the transmitted wave trains behind submerged reefswith finite length will be identified properly using nonlinear Fourier transform.Forth, the capability of Hilbert-Huang transform (HHT) and wavelet transform (WT) forthe description of the nonlinear processes involved in the wave-structure interaction will beevaluated and recommendations will be given for a combined application of HHT and NLFTwill be given.Finally, the hydraulic efficiency of submerged reefs will be determined on the basis of aenergy balance analysis of the “nolinear” Fourier spectra of NLFT.