Impact of the four-wave quasi-resonance on freak wave shapes in the ocean
Two freak waves were observed a day apart in October 2009 at a 5000-m deep moored station in the northwest Pacific Ocean. As the typhoon passed by, the wave system transitioned within a day from a narrow and unimodal spectrum to the broad and bi-modal spectrum. The occurrence probability of a freak wave is known to increase due to a modulational instability; however, whether the modulational instability survives under a realistic directional sea state has not been conclusively determined yet. In this study, a phase-resolving wave model was used to obtain ensembles of realizations based on observed and simulated directional spectra. Unlike previous studies that focused only on the probability of freak wave occurrence, this study focuses on wave shape. It reveals that the front-to-rear asymmetry and crescent shape deformation of the crest are more pronounced for narrower spectrum and longer-lifetime freak waves; this distortion of wave shape and extended lifetime are both characteristics of nonlinear wave groups. This study also shows that the distribution of the lifetime of a freak wave depends on the sea state and that the number of nonlinear wave groups increases for a narrower spectrum. We therefore conjecture that both the four-wave quasi-resonance and dispersive focusing are responsible for freak wave generation, but their relative significance depends on the spectral broadness. Investigating the total kurtosis or occurrence probability alone is insufficient to unravel the underlying mechanisms of individual freak-wave generation.
KeywordsFreak wave Nonlinear wave interaction Third-generation wave model Higher-order spectral method
Alessandro Toffoli (University of Melbourne) and Miguel Onorato (University of Torino) provided the original HOSM model code that was modified and used. Peter Janssen (ECMWF) and Miguel Onorato gave us valuable comments with regard to the canonical transformation of the Zakharov equation and the relationship between the HOSM and the Zakharov equation. We are also grateful to the reviewers for their suggestions.
W.F. acknowledges the support from the Fundamental Research Developing Association for Shipbuilding and Offshore (REDAS) in Japan. This research was funded by the Japan Society for the Promotion of Science (JSPS) and Grants-in-Aid for Scientific Research (KAKENHI).
- Bitner-Gregersen EM, Gramstad O (2018) Impact of sampling variability on sea surface characteristics of nonlinear waves. In: ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. Madrid, SpainGoogle Scholar
- ECMWF (2006) IFS documentation CY36r4. Part VII: ECMWF wave model. ECMWF model documentation, technical reportGoogle Scholar
- Flanagan JD, Dias F, Terray E, et al (2016) Extreme water waves off the west coast of Ireland: analysis of ADCP measurements. In: The 26th International Ocean and Polar Engineering Conference, 26 June–2 July, Rhodes, Greece. International Society of Offshore and Polar Engineers, p 589Google Scholar
- Fujimoto W, Waseda T (2016) The relationship between the shape of freak waves and nonlinear wave interactions. In: ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. ASME, Busan, South Korea, p V003T02A003Google Scholar
- Guedes Soares C, Fonseca N, Pascoal R (2008) Abnormal wave-induced load effects in ship structures. J Ship Res 52:30–44Google Scholar
- Hashimoto N (1997) Analysis of the directional wave spectrum from field data. In: Advances in Coastal and Ocean Engineering. Vol. 3. World Scientific, pp 103–143Google Scholar
- Haver S (2004) A possible freak wave event measured at the Draupner jacket January 1 1995. Rogue waves, Proc. Rogue Waves 20–22 October. Brest: IFREMERGoogle Scholar
- Houtani H, Tanizawa K, Waseda T, Sawada H (2016) An experimental investigation on the influence of the temporal variation of freak wave geometry on the elastic response of a container ship. In: Proceedings of 3rd International Conference on Violent Flows. Osaka, pp 9–11Google Scholar
- Janssen PAEM (2003) Nonlinear four-wave interactions and freak waves. J Phys Oceanogr 33:863–884. https://doi.org/10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2 CrossRefGoogle Scholar
- Janssen PAEM (2004) The interaction of ocean waves and wind. Cambridge University PressGoogle Scholar
- Kitamoto A (NII) (2016) Digital typhoon: typhoon images and information. http://agora.ex.nii.ac.jp/digital-typhoon/index.html.en. Accessed 31 Aug 2016
- Osborne AR, Ponce de León S (2017) Properties of rogue waves and the shape of the ocean wave power spectrum. In: ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. ASME, Trondheim, Norway, p V03AT02A013Google Scholar
- Ponce de León S, Osborne AR, Guedes Soares C (2018) On the importance of the exact nonlinear interactions in the spectral characterization of rogue waves. In: ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. Madrid, SpainGoogle Scholar
- Tobisch E (2014) What can go wrong when applying wave turbulence theory. arXivGoogle Scholar
- Tolman HL, Chalikov D (1996) Source terms in a third-generation wind wave model. J Phys Oceanogr 26:2497–2518. https://doi.org/10.1175/1520-0485(1996)026<2497:STIATG>2.0.CO;2 CrossRefGoogle Scholar
- Waseda T, Shinchi M, Nishida T, Tamura H, Miyazawa Y, Kawai Y, … & Taniguchi K (2011) GPS-based wave observation using a moored oceanographic buoy in the deep ocean. In: Proc. Twenty-first Int. Offshore Polar Eng. Conf.Google Scholar
- Waseda T, Webb A, Kiyomatsu K et al (2016) Marine energy resource assessment at reconnaissance to feasibility study stages; wave power, ocean and tidal current power, and ocean temperature power. J Japan Soc Nav Archit Ocean Eng 23:189–198Google Scholar
- Webb A, Waseda T, Fujimoto W, et al (2016) A high-resolution, wave and current resource assessment of Japan: the Web GIS dataset. In: Proceedings of Asian Wave and Tidal Energy ConferenceGoogle Scholar
- Yuen HC, Lake BM (1982) Nonlinear dynamics of deep-water gravity waves. In: Advances in applied mechanics. ElsevierGoogle Scholar