Comparative analysis of bore propagation over long distances using conventional linear and KdV-based nonlinear Fourier transform

In this paper, we study the propagation of bores over a long distance. We employ experimental data as input for numerical simulations using COULWAVE. The experimental flume is extended numerically to an effective relative length of x/h=3000, which allows all far-field solitons to emerge from the undular bore in the simulation data. We apply the periodic KdV-based nonlinear Fourier transform (KdV-NFT) to the time series taken at different numerical gauges and compare the results with those of the conventional Fourier transform. We find that the periodic KdV-NFT reliably predicts the number and the amplitudes of all far-field solitons from the near-field data long before the solitons start to emerge from the bore, even though the propagation is only approximated by the KdV. It is the first time that the predictions of the KdV-NFT are demonstrated over such long distances in a realistic set-up. In contrast, the conventional linear FT is unable to reveal the hidden solitons in the bore. We repeat our analyses using space instead of time series to investigate whether the space or time version of the KdV provides better predictions. Finally, we show how stepwise superposition of the determined solitons, including the nonlinear interactions between individual solitons, returns the analysed initial bore data.