Contribution of solitons to enhanced rogue wave occurrence in shallow water: a case study in the southern North Sea

Abstract. The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected according to second-order theory. The role of nonlinear processes for the generation of rogue waves at this location is currently unclear. Within the framework of the Korteweg–de Vries (KdV) equation, we investigated the discrete soliton spectra of measured time series at Norderney to determine differences between time series with and without rogue waves. For this purpose, we applied a nonlinear Fourier transform for the Korteweg–de Vries equation with vanishing boundary conditions (vKdV-NLFT). For each time series containing a rogue wave, we were able to identify at least one soliton in the discrete nonlinear vKdV-NLFT spectrum that contributed to the occurrence of the rogue wave in that time series. The amplitudes of these solitons were generally found to be smaller than the crest height of the corresponding rogue wave and interaction with the continuous wave spectrum is needed to fully explain the observed rogue wave. Time series with and without rogue waves showed different characteristic soliton spectra. In most of the spectra calculated from rogue wave time series, most of the solitons clustered around similar heights, while the largest soliton was outstanding with an amplitude significantly larger than all other solitons. The presence of a clearly outstanding soliton in the spectrum was found to be an indicator pointing towards enhanced probability for detecting a rogue wave in the time series. Similarly, when the discrete spectrum appears as a cluster of solitons without the presence of a clearly outstanding soliton, the presence of a rogue wave in the observed time series is unlikely. Under the hypothesis that the KdV describes the evolution of the sea state around the measurement site well, these results suggest that solitons and nonlinear processes substantially contribute to the enhanced occurrence of rogue waves off Norderney.