CONCLUSION

Temporal sea surface elevation data obtained at three points 3km off shore facing the Japan sea demonstrated that giant freak waves with wave heights exceeding $2H_{1/3}$ and 10m are occasionally generated by strong but normal winter-seasonal winds exceeding 10m/s blowing for a long duration over 20 hours under approximately constant speed and direction from W to NW.

The statistical characteristics of the measured waves containing freak waves can be summarized as follows.

1. The freak waves can occurr while wind wave spectra appear to be routine with usual single spectral peak and familiar equilibrium range without multi-directional effects.
2. The freak waves may cause weak nonlinearity and their corresponding PDF of surface elevations can be well described by the Gram-Chalier rahter than Gaussian distribution.
3. The freak waves can be generated from different physical processes which can be of linear or nonlinear wave systems.
4. The exceedance probabilities of the crest amplitude of the freak wave are under estimated by the Rayleigh distribution, although the wave heights are well predicted by the Rayleigh distribution.
5. The PDF of run length generally follows the Kimura theory.

These results show that the present conventional approaches of wave data analysis can detect some indications of effects of the existence of freak waves. However they are clearly unable to shed light on the practical occurrence of individual freak waves. The recently advanced approach of time-frequency wavelet transform analysis would be a potentially useful tool for further study of freak or rogue waves. Furthermore, because of the actual measurement of freak waves in the ocean is so rare, and the possible grave damage of freak waves to the mariners and offshore structures is so great, one simply can not overemphasize the pressing need for concerted efforts to make long-term, systematic measurements of freak or rogue waves.

ACKNOWLEDGEMENT

We would like to thank Mr. Shinichi Nakayama at Penta Ocean Construction Co. LTD. (former graduate student at Gifu Univeristy) for his supports. The authors to express their thanks to Dr.Yoshimoto at National Maritime Research Institute, Ministry of Land, Infrastructure and Transport, Japan for providing and allowing the use of data set.