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

水波的时频分析，特别是其非平稳和非线性特性 - 非线性傅里叶变换

• 批准号: 40649693
• 负责人: Professor Dr.-Ing. Hocine Oumeraci
• 金额: --
• 依托单位: Leichtweiß-Institut für Wasserbau
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2011-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/40649693?language=en
• 关键词: Time; frequency; analysis; water; waves

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.

该项目的主要目标之一，非线性傅立叶变换（NLFT）的发展和实施，已在项目的第一阶段成功实现。根据已完成的准备工作和工作进展，得出申请期的目标如下：首先，实现逆散射变换，识别非线性波-波相互作用项；其次，使用所实现的NLFT将一致地识别暗礁波结构相互作用中涉及的非线性过程。第三，利用非线性傅立叶变换正确识别有限长度暗礁后透射波列中的孤立波数。第四，将评估Hilbert-Huang变换（HHT）和小波变换（WT）描述波-结构相互作用中涉及的非线性过程的能力，并给出HHT和nlft联合应用的建议。最后，通过对NLFT的“非线性”傅立叶谱进行能量平衡分析，确定暗礁的水力效率。