ON THE PROBABILITY DISTRIBUTION OF FREAK WAVES IN FINITE WATER DEPTH

Kyungmo Ahn, Sun-Kyung Kim, Se-Hyun Cheon

Abstract


This paper presents the occurrence probability of freak waves based on the analysis of extensive wave data collected during ARSLOE project. It is suggested to use the probability distribution of extreme waves heights as a possible means of defining the freak wave criteria instead of conventional definition which is the wave height greater than the twice of the significant wave height. Analysis of wave data provided such finding as 1) threshold tolerance of 0.2 m is recommended for the discrimination of the false wave height due to noise, 2) no supportive evidence on the linear relationship between the occurrence probability of freak waves and the kurtosis of surface elevation 3) nonlinear wave-wave interactions is not thh primary cause of the generation of freak waves 4) the occurrence of freak waves does not depend on the wave period 5) probability density function of extreme waves can be used to predict the occurrence probability of freak waves. Three different distribution functions of extreme wave height by Rayleigh, Ahn, and Mori were compared for the analysis of freak waves.

Keywords


freak wave; occurrence probability; extreme wave; significant wave height

References


Ahn, K. 2002. Probability distribution of extreme wave heights in finite water depth, Proceedings of 29 th International Conference on Coastal Engineering, ASCE, 614-625.

Henderson, K.L, D.H. Peregrine and J.W. Dold. 1999. Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear Schrödinger equation. Wave Motion 29, 241-361.http://dx.doi.org/10.1016/S0165-2125(98)00045-6

Janssen, P.A.E.M. 2003. Nonlinear four-wave interactions and freak waves, Journal of Physical Oceanography 33, 863-884.http://dx.doi.org/10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2

Kharif, C. and E. Pelinovsky 2003. Physical mechanisms of the rogue wave phenomenon. European Journal of Mechanics – B/Fluids 22 (6), 603-634.http://dx.doi.org/10.1016/j.euromechflu.2003.09.002

Liu, P.C., H.S. Chen, H.J. Doong, C.C. Kao and Y.J. Hsu 2009. Freque waves during Typhoon Krosa, Annales Geophysicae, 27, 2633-2642.http://dx.doi.org/10.5194/angeo-27-2633-2009

Mori, N. 2004. Occurrence probability of a freak wave in a nonlinear wave field, Ocean Engineering, 31, 165-175.http://dx.doi.org/10.1016/S0029-8018(03)00119-7

Mori, N. and P.A.E.M Janssen 2006. On kurtosis and occurrence probability of freak waves. Journal of Physical Oceanography 36, 1471-1483http://dx.doi.org/10.1175/JPO2922.1

Mori, N., P. Liu, and Y. Yasuda 2002. Analysis of freak wave measurements in the Sea of Japan, Ocean Engineering, 29 (11), 1399-1414.http://dx.doi.org/10.1016/S0029-8018(01)00073-7

Olagnon, M. and Athanassoulis, G. (Eds.) 2000. Rogue waves. IFRMER, France.

Ochi, M. 1998. Ocean waves: The stochastic approach, Cambridge University Presshttp://dx.doi.org/10.1017/CBO9780511529559

Stansell, P. 2005. Distributions of extreme wave crest and trough heights measured in the North Sea. Ocean Engineering 32, 1015-1036.http://dx.doi.org/10.1016/j.oceaneng.2004.10.016

Yasuda, T. and N. Mori 1997. Occurrence properties of giant freak waves in sea area around Japan.


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.