2022
DOI: 10.5194/nhess-2022-28
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Contribution of solitons to enhanced rogue wave occurrence in shallow water: a case study in the southern North Sea

Abstract: 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 wa… Show more

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Cited by 4 publications
(11 citation statements)
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“…[31,32]. A similar observation has been made recently in the analysis of rogue waves that were measured under shallow water conditions in the north sea [44].…”
Section: Discussionsupporting
confidence: 76%
“…[31,32]. A similar observation has been made recently in the analysis of rogue waves that were measured under shallow water conditions in the north sea [44].…”
Section: Discussionsupporting
confidence: 76%
“…Note that both IST and DST algorithms face rapid growth of numerical errors when increasing the number of discrete spectrum components, which can be coped with using high-precision arithmetic as recently suggested in [55,57,76]. We highlight that the complete characterization of the breather’s parameters benefits the IST analysis of experimental data on coherent structures in optics, hydrodynamics and other nonlinear waveguides described by nearly integrable models [21,32,34,77,78]. Also, our approach can be generalized to the case of vector breathers of the Manakov system [79–83] and other integrable systems with constant amplitude boundary conditions.…”
Section: Discussionmentioning
confidence: 99%
“…The conventional inverse scattering transforms procedure has its alternative called the dressing method [18,25], also known as the Darboux transformation [26,27], which is advantageous for constructing multisoliton and multi-breather solutions. With the growing interest in the IST approach for the analysis and synthesis of nonlinear wave fields [21,[28][29][30][31][32][33][34], development of numerical methods for direct and inverse scattering problems attracts more attention [35][36][37][38][39][40] with applications to the Cauchy problem [41,42], information transmission [43][44][45], fibre Bragg grating synthesis [46], etc.…”
Section: Introductionmentioning
confidence: 99%
“…The time series were recorded between 2011 and 2016. At the site WES off the coast of the island Sylt in a water depth of h = 13 m, a Waverider buoy with a measurement frequency of 1.28 Hz was installed, similarly to the site SEE off Norderney that was discussed in Teutsch et al (2023). At the site AWG in a water depth of h = 6.3 m, a down-looking radar device was mounted to a fixed platform, measuring the air gap to the sea surface at a frequency of 2 Hz in 2011 and at 4 Hz later in the measurement period.…”
Section: Measurement Region and Datamentioning
confidence: 99%
“…The NLFT reveals hidden solitons in a time series that will become visible only later when the series evolve spatially with respect to the KdV (Gardner et al, 1967;Ablowitz and Kodama, 1982). In a previous study (Teutsch et al, 2023), we applied the NLFT for the KdV equation with vanishing boundary conditions to time series measured at a specific site in the southern North Sea and analyzed the resulting soliton spectra. We pointed out that the NLFT was applied as a spectral analysis method, similar to the Fourier transform in the linear case.…”
Section: Introductionmentioning
confidence: 99%