Nonlinear Decomposition of Transmitted Wave Trains Behind Submerged Reef Structures Using “Nonlinear Fourier Transform”: The Nonlinear Spectral Basic Components

The nonlinear Fourier transform (NLFT) is introduced as an alternative analysis method for nonlinear waves in shallow water. In physics the NLFT is the application of the inverse scattering transform (IST) for the solution of the Korteweg-deVries (KdV) equation that gouverns the evolution of waves in shallow water. In coastal and ocean engineering the NLFT can be regarded as an extension of the conventional Fourier transform (FT) as it uses nonlinear shallow water waves (cnoidal waves) as basic components for the spectral decomposition and explicitly considers the nonlinear wave-wave interactions during the analysis. A first description of the numerical implementation and its application for the analysis of soliton fission over and behind submerged reefs is given in a former paper [1]. This paper presents a closer view on the interpretation of both types of spectral basic components of the nonlinear decomposition: solitons and nonlinear oscillatory waves.