04 Mar 2022
04 Mar 2022
Status: a revised version of this preprint is currently under review for the journal NHESS.

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

Ina Teutsch1, Markus Brühl2, Ralf Weisse1, and Sander Wahls2 Ina Teutsch et al.
  • 1Helmholtz-Zentrum Hereon, Max-Planck-Str. 1, 21502 Geesthacht, Germany
  • 2Delft Center for Systems and Control, Delft University of Technology, 2860 Delft, South Holland, Netherlands

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.

Ina Teutsch et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on nhess-2022-28', Anonymous Referee #1, 25 Mar 2022
    • AC1: 'Reply to RC1', Ina Teutsch, 27 May 2022
  • RC2: 'Comment on nhess-2022-28', Anonymous Referee #2, 09 Apr 2022
    • AC2: 'Reply on RC2', Ina Teutsch, 27 May 2022

Ina Teutsch et al.

Ina Teutsch et al.


Total article views: 810 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
406 387 17 810 7 8
  • HTML: 406
  • PDF: 387
  • XML: 17
  • Total: 810
  • BibTeX: 7
  • EndNote: 8
Views and downloads (calculated since 04 Mar 2022)
Cumulative views and downloads (calculated since 04 Mar 2022)

Viewed (geographical distribution)

Total article views: 753 (including HTML, PDF, and XML) Thereof 753 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 25 Oct 2022
Short summary
In the shallow waters off the coast of Norderney in the southern North Sea, more rogue waves were measured than expected. We investigate whether solitons could play a role in this enhanced occurrence. We find that at least one soliton is associated with each measured rogue wave and that time series with and without rogue waves show different characteristic soliton spectra, implying that solitons play a role for the formation of at least some shallow water rogue waves.