Nobuhito Mori, Hajime Mase, Tomohiro Yasuda


The kurtosis of the surface elevation, Benjamin-Feir Index (BFI) and directional spread are measures of nonlinear four-wave interactions and freak waves. The dependence of kurtosis, BFI and directional spread under typhoon conditions are examined by numerical simulations. The BFI is significantly large in the fourth quadrant of the typhoon while the directional spread is small in the fourth quadrant. It was found that the potentially possible area of freak wave occurrence is the fourth quadrant of the typhoon rather than the other quadrants.


freak wave; extreme wave; typhoon; BFI; directional spread

Full Text:



Booij, N., R. Ris, and L. Holthuijsen. 1999. A third-generation wave model for coastal regions. I-Model description and validation, Journal of Geophysical Research, 104 (C4), 7649, 7666.

Dean, R. 1990. Freak waves: a possible explanation, A. Torum and O. Gudmestad (Eds.), Water wave kinematics, 609 612. Kluwer Academic Pub.

Dysthe, K., H. Krogstand, and P. Muller. 2008. Oceanic Rogue Waves, Annual Review of Fluid Mechanics, 40, in print.

Fujii, t. and Y. Mitsuta. 1986. Simulation of winds in typhoons by a stochastic model, J. Wind Eng. 28, 1 12.

Gramstad, O. and K. Trulsen. 2007. Influence of crest and group length on the occurrence of freak waves, Journal of Fluid Mechanics, 582, 463 472.

Guedes Soares, G., Z. Cherneva, and E. Antao. 2003. Characteristics of abnormal waves in North Sea storm sea steas, Applied Ocean Research, 25, 337, 344

Guedes Soares, G., Z. Cherneva, and E. Antao. 2004. Abnormal waves during hurricane Camille, Journal of Geophysical Research, 109, C08008.

Janssen, P. A. 2003. Nonlinear four-wave interactions and freak waves, Journal of Physical Oceanography, 33(4), 863 884.<863:NFIAFW>2.0.CO;2

Lavrenov, I.. 1908. The wave energy concentration at the Agulhas current off South Africa, Natural Hazard, 17, 117, 127.

Longuet-Higgins, M. 1963. The effect of non-linearities on statistical distirbuations in the theory of sea waves, Journal of Fluid Mechanics, 17, 459 480.

Mori, N. and P. Janssen. 2006. On kurtosis and occurrence probability of freak waves, Journal of Physical Oceanography, 36(7), 1471 1483.

Mori, N., P. Liu, and T. Yasuda. 2002. Analysis of freak wave measurements in the Sea of Japan, Ocean Engineering, 29(11), 1399 1414.

Mori, N., M. Onorato, and P. A. Janssen. 2010. On the estimation of the kurtosis in directional sea states for freak wave forecasting, Journal of Physical Oceanography, submitted.

Mori, N., M. Onorato, P. A. Janssen, A. R. Osborne, and M. Serio. 2007. Exceedance probability for strongly nonlinear long crested waves, Journal of Geophysical Research,, doi:10.1029/2006JC004024

Onorato, M., L. Cavaleri, s. Fouques, O. Gramstad, and P. A. E. M. Janssen. 2009. Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a 3d wave basin, Journal of Fluid Mechanics, in press.

Onorato, M., A. Osborne, and M. Serio. 2005. On deviations from Guassian statistics for surface gravity waves, Proceedings Rogue Waves, Hawaiian Winter Workshop, 79 83.

Onorato, M., A. Osborne, M. Serio, and S. Bertone. 2001. Freak waves in random oceanic sea states, Physical Review Leters, 86(25), 5831 5834. PMid:11415369

Onorato, M., T. Waseda, A. Toffoli, L. Cavaleri, O. Gramstad, P. Janssen, T. Kinoshita, J. Monbaliu, N. Mori, A. Osboren, et al. 2009. Staistical properties of directional ocean waves: The role of the modulational instability in the formation of extreme events, Physical Review Letters, 102(11), 114502.

Osborne, A., M. Onorato, M. Serio, and S. Bertone. 2000. The nonlinear dynamics of rogue waves and holes in deep water gravity wave trains, Physical Letter A, 275(5-6), 386 393.

Petrova, P. and C. Guedes Soares. 2008. Maximum wave crest and height statistics of irrefular and abnormal waves in an offshore basin, Applied Ocean Research, 30(2), 144 152.

Stansell, P., J. Wolfram, and S. Zachary. 2003. Horizontal asymmetry and steepness distributions for wind-driven ocean waves, Applied Ocean Research, 25, 137 155.

Trulsen, K. and K. Dysthe. 1997. Freak waves - A three-dimensional wave simulation, Proceedings of the 21st Symposium on Naval Hydrodynamics, 550 558. (National Academy Press. Waseda, T. 2006. Impact of directionality on the extreme wave occurrence in a discrete random wave system, The 9th Wave Workshop, 10p.

Yasuda, T. and N. Mori. 1994. High order nonlinear effects on deep-water random wave trains, INternational Symposium: Waves-Physical and Numerical Modelling, Volume 2, Vancouver, 823 332.

Yasuda, T. and N. Mori. 1997. Occurrence properties of giant freak waves the sea area around Japan, 123(4), 209 213.

Yasuda, T., N. Mori, and K. Ito. 1991. Freak waves in a unidirectional wave train and their kinematics, Proc. of the 23th Int. Conf. on Coastal Eng., Volume 1, Venice, ASCE, 751 764.

Yasuda, T., N. Mori, and S. Nakayama. 1997. Characteristics of giant freak waves observed in the Sea of Japan, Waves97, Virginia, VA, 482 495.

Young, I. 2006. Directional spectra of hurricane wind waves, Journal of Geohphysical Research, 111(C8), C08020.