Ocean Dynamics

, Volume 69, Issue 1, pp 101–121 | Cite as

Impact of the four-wave quasi-resonance on freak wave shapes in the ocean

  • Wataru Fujimoto
  • Takuji WasedaEmail author
  • Adrean Webb
Part of the following topical collections:
  1. Topical Collection on the 15th International Workshop on Wave Hindcasting and Forecasting in Liverpool, UK, September 10-15, 2017


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.


Freak 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.

Funding information

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).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Frontier SciencesThe University of TokyoChibaJapan
  2. 2.Disaster Prevention Research InstituteKyoto UniversityKyotoJapan

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