PROPERTIES OF FREAK WAVES INDUCED BY TWO KINDS OF NONLINEAR MECHANISMS
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Keywords

freak waves
nonlinear mechanism
wave-wave interaction
modulation instability
wave group interaction

How to Cite

Tao, A., Zheng, J., Chen, B., Li, H., & Peng, J. (2012). PROPERTIES OF FREAK WAVES INDUCED BY TWO KINDS OF NONLINEAR MECHANISMS. Coastal Engineering Proceedings, 1(33), waves.73. https://doi.org/10.9753/icce.v33.waves.73

Abstract

We investigate the dynamic and kinematic characteristics of freak waves using a direct phase-resolved nonlinear numerical method. The focus is on the understanding of the effects of different nonlinear wave-wave interactions on freak waves development and characteristics in the evolution process of modulated Stokes wave trains. Long time simulations of modulated Stokes wave trains, with different parameters, are obtained. Based on these simulations, we find that there are different kinds of freak waves in different time scales due to two kinds of different nonlinear mechanisms. One is the modulation instability and another related to the wave group interaction. Both the dynamic and kinematic characteristics of the different kinds of freak waves are distinct. Occurrence of freak waves (especially of large height) is usually correlated with broadband wave spectra.
https://doi.org/10.9753/icce.v33.waves.73
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References

Benjamin, T. B. 1967. Instability of periodic wavetrains in nonlinear dispersive systems. Proc. R. Soc, Lond, Ser. A, 299: 59-75.

Dommermuth, D. G., and Yue, D. K. P. 1987. A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech., 184: 267-288.http://dx.doi.org/10.1017/S002211208700288X">http://dx.doi.org/10.1017/S002211208700288X

Draper L. 1965. Freak'ocean waves. Marine Observer, 35:193-195.

Dysthe, K., Krogstad, H. E., and Muller, P. 2008. Oceanic rogue waves, Annu. Rev. Fluid Mech., 40: 287-310.http://dx.doi.org/10.1146/annurev.fluid.40.111406.102203">http://dx.doi.org/10.1146/annurev.fluid.40.111406.102203

Kharif, C. and Pelinovsky, E. 2003. Physical mechanisms of the rogue wave phenomenon. European J. Mechanics/B - Fluid, 22(6):603-634.

Lake, B. M., Yuen H. C., Rungaldier, H., Ferguson, W. E. 1977. Nonlinear deep-water waves:Theory and experiment, Part 2, Evolution of a continuous wave train. J. Fluid Mech., 83: 49-74.http://dx.doi.org/10.1017/S0022112077001037">http://dx.doi.org/10.1017/S0022112077001037

Lavrenov, I.V., Porubov, A.V. 2006. Three reasons for freak wave generation in the non-uniform current. European Journal of Mechanics B/Fluids, 25: 574-585.http://dx.doi.org/10.1016/j.euromechflu.2006.02.009">http://dx.doi.org/10.1016/j.euromechflu.2006.02.009

Onorato, M., Osborne, A. R., Serio, M. 2002. Extreme wave events in directional random oceanic sea states. Phys.of Fluids, 14:L25-L28.http://dx.doi.org/10.1063/1.1453466">http://dx.doi.org/10.1063/1.1453466

Peregrine, D. H. 1976 Interaction of water waves and currents. Ad. Appl. Mech., 16:9-117.http://dx.doi.org/10.1016/S0065-2156(08)70087-5">http://dx.doi.org/10.1016/S0065-2156(08)70087-5

Tao, A. 2007. Nonlinear wave trains evolution and freak wave generation mechanisms in deep water. PhD Thesis, Hohai University, Nanjing, China (in Chinese).

Tao, A., Liu, Y. 2010. Rogue Waves Due To Nonlinear Broadband Wave Interactions, Proc. 25th International Workshop on Water Waves and Floating Bodies (IWWWFB25). Harbin, China, Paper No. iwwwfb25_41.

Tao, A., Zheng, J., Mee Mee, S., Chen, B. 2012. The Most Unstable Conditions of Modulation Instability. Journal of Applied Mathematics, 2012, Article ID:656873, 11 pages, doi:10.1155/ 2012/656873.

Tao, A., Zheng, J., Mee Mee, S., Chen, B. 2011. Re-study on recurrence period of Stokes wave train with High Order Spectral method. China Ocean Engineering, 25(4):679-686.http://dx.doi.org/10.1007/s13344-011-0054-1">http://dx.doi.org/10.1007/s13344-011-0054-1

Trulsen, K., Dysthe, K. B. 1996. A modied nonlinear Schrodinger equation for broader bandwidth gravity waves on deep water. Wave Motion, 24:281-289.http://dx.doi.org/10.1016/S0165-2125(96)00020-0">http://dx.doi.org/10.1016/S0165-2125(96)00020-0

Wu, G. 2004. Direct simulation and deterministic prediction of large scale Nonlinear ocean wave field. PhD Thesis, Massachusetts Institute of Technology, USA.

Liu, Y., Wu. G., Xiao, W., Yue, D.K.P. 2008. Nonlinear Wave Environments for Ship Motion Analysis. Proceeding of the 27th Symposium on Naval Hydrodynamics, Seoul, Korea

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