Characterisation of Ship-Induced Long-Period Primary Waves Using Nonlinear Fourier Transform (KdV-NFT)

Abstract

Large vessels propagating in narrow, shallow maritime waterways generate a system of ship-induced waves consisting of long-period primary waves and short-period secondary waves. Progressive long-period free-surface wave systems are governed by the Korteweg–de Vries (KdV) equation, and are known to possibly disperse into a train of solitons and trailing oscillatory waves in the far field. By application of the nonlinear Fourier transform based on the KdV equation (KdV-NFT), these far-field solitons can already be revealed in the nonlinear spectra of the near-field data. In this paper, we apply the KdV-NFT to measured ship-wave time series from experiments in order to investigate the solitonic structures of these strongly nonlinear waves. Furthermore, we present qualitative and quantitative relations between the spectral solitons from frequency-domain KdV-NFT and channel, geometry, ship dynamics and primary-wave height as obtained by time-domain analysis of the time series.