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

• Applicant: Professor Dr.-Ing. Hocine Oumeraci
• Subject Area: Geotechnics, Hydraulic Engineering
• Term: from 2007 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 40649693

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.

• DFG Programme: Research Grants