Investigation of Measured Non-Rogue Wave Time Series With Large Outstanding Spectral Solitons

We consider measurement data from a surface-following wave buoy in the southern North Sea. The data were collected in a water depth that lies within the range of applicability of the Korteweg-de Vries (KdV) equation. We intend to increase the understanding of nonlinear processes that might be responsible for the increased rogue wave occurrence observed at this site (Teutsch et al., 2020). More specifically, we investigate the role of (potentially “spectral”) solitons identified by the nonlinear Fourier transform (NLFT) for the KdV equation for the occurrence of rogue waves. In a previous study, we identified a connection between the spectral solitons and rogue waves at the considered station. Teutsch et al. (2022) showed that KdV-NLFT spectra containing one exceptionally large outstanding soliton often corresponded to measured time series including a rogue wave. Some of the time series with a large outstanding soliton however did not contain rogue waves. In this study, we investigate if these outliers might correspond to rogue waves at a different location. This is motivated by the fact that the NLFT soliton spectrum does not change under the KdV equation. We therefore propagate the time series without rogue waves, but with an outstanding soliton in the KdV-NLFT spectrum, according to the KdV equation, to investigate the occurrence of rogue waves shortly upstream or downstream of the recorded time series.

References:

Teutsch, I., Weisse, R., Moeller, J., and Krueger, O. (2020): A statistical analysis of rogue waves in the southern North Sea, Natural Hazards and Earth System Sciences, 20, 2665–2680.

Teutsch, I., Brühl, M., Weisse, R., and Wahls, S (2022): Contribution of solitons to enhanced rogue wave occurrence in shallow water: a case study in the southern North Sea. Natural Hazards and Earth System Sciences Discussions, under review.