Lei Wang, Jinxuan Li^*, Shuxue Li

Show more
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, China.
Show less

Abstract: In this paper, a numerical wave tank is developed based on High Order Spectral (HOS) method considering the wave-maker boundary. The 2D irregular wave trains are simulated for a long time by using this model. The freak wave is observed in the wave train, and its generation process is analyzed via wavelet analysis. The results show that the numerical tank can accurately simulate the wave generation and propagation, even for the freak wave. From the analysis of freak wave generation, it can be found that, two wave groups with different frequency components superpose together to form a large wave group. The large wave group modulation generates the freak wave.

Keywords: Freak Wave, High Order Spectral Method, Numerical Wave Tank

Cite this paper: Wang, L. , Li, J. and Li, S. (2015) Numerical Simulation of Freak Wave Generation in Irregular Wave Train. Journal of Applied Mathematics and Physics, 3, 1044-1050. doi: 10.4236/jamp.2015.38129.

References

[1]   Kharif, C. and Pelinovsky, E. (2003) Physical Mechanisms of the Rogue Wave Phenomenon. European Journal of Mechanics—B/Fluids, 22, 603-634. http://dx.doi.org/10.1016/j.euromechflu.2003.09.002

[2]   Dysthe, K., Krogstad, H.E. and Muller, P. (2008) Oceanic Roguewaves. Annu. Rev. Fluid Mech., 40, 287-310. http://dx.doi.org/10.1146/annurev.fluid.40.111406.102203

[3]   Slunyaev, A., Didenkulova, I. and Pelinovsky, E. (2011) Roguewaters. Contemp. Phys., 52, 571-590. http://dx.doi.org/10.1080/00107514.2011.613256

[4]   Janssen, P. (2003) Nonlinear Four-Wave Interaction and Freak Waves. J Phys Oceanogr, 22, 863-884. http://dx.doi.org/10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2

[5]   Clamond, D. and Grue, J. (2002) Interaction between Envelope Solitons as a Model for Freak Wave Formations. Part I: Long Time Interaction. C R Mec, 330, 575-580. http://dx.doi.org/10.1016/S1631-0721(02)01496-1

[6]   Johannessen, T. and Swan, C. (2001) A Laboratory Study of the Focusing of Transient and Directionally Spread Surface Water Waves. Philos Trans R SocLond, Ser A, 457, 971-1006. http://dx.doi.org/10.1098/rspa.2000.0702

[7]   Liu, S. and Hong, K. (2005) Physical Investigation of Directional Wave Focusing and Breaking Waves in Wave Basin. China Ocean Eng, 19, 21-35.

[8]   Hjelmervi, K.B. and Trulsen, K. (2009) Freak Wave Statistics on Collinear Currents. Journal of Fluid Mechanics, 637, 267-284. http://dx.doi.org/10.1017/S0022112009990607

[9]   Toffoli, A., Cavaleri, L., Babanin, A.V., Benoit, M., Bitn-er-Gregersen, E.M., Monbaliu, J., Onorato, M., Osborne, A.R. and Stansberg, C.T. (2011) Occurrence of Extreme Waves in Three-Dimensional Mechanically Generated Wave Fields Propagating over an Oblique Current. Natural Hazards and Earth System Sciences, 11, 895-903. http://dx.doi.org/10.5194/nhess-11-895-2011

[10]   Kharif, C., Giovanangeli, J.P., Touboul, J., Grare, L. and Pelinovsky, E. (2008) Influence of Wind on Extreme Wave Events: Experimental and Numerical Approaches. Journal of Fluid Mechanics, 594, 209-247. http://dx.doi.org/10.1017/S0022112007009019

[11]   Benjamin, T.B. and Feir, J.E. (1967) The Disintegration of Wa-vetrains on Deep Water. Part 1: Theory. J. Fluid Mech., 27, 417-430. http://dx.doi.org/10.1017/S002211206700045X

[12]   Dysthe, K.B. and Trulsen, K. (1999) Note on Breather Type Solutions of the NLS as a Model for Freak Waves. Physica Scripta, T82, 48-52. http://dx.doi.org/10.1238/Physica.Topical.082a00048

[13]   Osborne, A.R., Onorato, M. and Serio, M. (2000) The Nonlinear Dynamics of Rogue Waves and Holes in Deep-Water Gravity Wave Train. Phys. Letters A, 275, 386-393. http://dx.doi.org/10.1016/S0375-9601(00)00575-2

[14]   Onorato, M., Osborne, A.R., Serio, M. and Cavaleri, L. (2005) Modulational Instability and Non-Gaussian Statistics in Experimental Random Water-Wave Trains. Physics of Fluids, 17, Article ID: 078101. http://dx.doi.org/10.1063/1.1946769

[15]   Onorato, M., Osborne, A.R., Serio, M., Cavaleri, L., Brandini, C. and Stansberg, C.T. (2004) Observation of Strongly Non-Gaussian Statistics for Random Sea Surface Gravity Waves in Wave Flume Experiments. Phys Rev E, 70, Article ID: 067302. http://dx.doi.org/10.1103/physreve.70.067302

[16]   Li, J., Yang, J., Liu, S. and Ji, X. (2015) Wave Groupiness Analysis of the Process of 2D Freak Wave Generation in Random Wave Trains. Ocean Engineering, 104, 480-488. http://dx.doi.org/10.1016/j.oceaneng.2015.05.034

[17]   Baldock, T., Swan, C. and Taylor, P. (1996) A Laboratory Study of Nonlinear Surface Waves on Water. Philos. Roy. Soc. London, 452A, 649-676. http://dx.doi.org/10.1098/rsta.1996.0022

[18]   Chin, H. and Yao, A. (2004) Laboratory Measurement of Limiting Freak Waves on Currents. Journal of Geophysical Research, 109, Article ID: C12002.

[19]   Onorato, M., Osborne, A.R., Serio, M. and Bertone, S. (2001) Freak Waves in Random Oceanic Sea States. Phys Rev Lett, 86, 5831-5834. http://dx.doi.org/10.1103/PhysRevLett.86.5831

[20]   Zhao, X.Z., Hu, C.H. and Sun, Z.C. (2010) Numerical Simulation of Extreme Wave Generation Using VOF Method. Journal of Hydrodynamics, 22, 466-477. http://dx.doi.org/10.1016/S1001-6058(09)60078-0

[21]   Yan, S. and Ma, Q.W. (2010) Numerical Simulation of Interaction between Wind 2D Freak Waves. European Journal of Mechanics, B/Fluids, 29, 18-31. http://dx.doi.org/10.1016/j.euromechflu.2009.08.001

[22]   Dommermuth, D.G. and Yue, D.K.P. (1987) A High-Order Spectral Method for the Study of Nonlinear Gravity Waves. Journal Fluid Mechanics, 184, 267-288. http://dx.doi.org/10.1017/S002211208700288X

[23]   Zakharov, V.E. (1968) Stability of Periodic Waves of Finite Am-plitude on the Surface of a Deep Fluid. J. Appl. Mech. Tech. Phys, 9, 190-194 (English Transl.). http://dx.doi.org/10.1007/BF00913182

[24]   Agnon, Y. and Bingham, H. (1999) A Non-Periodic Spectral Method with Application to Nonlinear Water Waves. European Journal Mech. B/Fluids, 18, 527-534. http://dx.doi.org/10.1016/S0997-7546(99)80047-8

[25]   Bonnefoy, F., Touzé, D. and Le Ferrant, P. (2004) Generation of Fully-Nonlinear Prescribed Wave Fields Using a High-Order Spectral Model. Proc. 14th International Offshore and Polar Engineering Conference, Toulon.

[26]   Li, J. and Liu, S. (2015) Foused Wave Properties Based on a High Order Spectral Method with a Non-Periodic Boundary. China Ocean Engineering, 29, 1-16. http://dx.doi.org/10.1007/s13344-015-0001-7