Conclusion

Freak wave occurrence probability was formulated under the assumptions of a narrow banded and weakly non-Gaussian condition. The sensitivity on the value of kurtosis was examined. For the case of $N$=100, the occurrence probability of a freak wave is 3.3% by the Rayleigh distribution, while 13% by the present study under the extreme wave condition ($\mu _4$=3.5). Furthermore, for the case of a small number of waves $N=250$, the nonlinear effects of freak wave occurrence probability linearly depend on $\mu_{4}$. In comparison with the field data, freak waves sometimes appear more frequently than expected by the Rayleigh theory but were well predicted by the proposed theory.

In order to sufficiently check the dependency of number of waves and kurtosis on freak wave occurrence presented in this paper, further systematic and continuous field measurement of freak waves would be critically needed.