Effects of High-Order Nonlinearities on Freak Wave Generation in Random Sea States

Document Type : Regular Article

Authors

1 Guangzhou Maritime University, Guangzhou, Guangdong, 510725, China

2 College of Harbour and Coastal Engineering, Jimei University. Xiamen, Fujian, 361021, China

10.47176/jafm.15.04.33337

Abstract

High-order nonlinearities may be an important cause of freak wave generation; however, it is still unclear how to stimulate the generation of freak waves in deep-water random waves. This study employs the modified fourth-order nonlinear Schrӧdinger equation (mNLSE) to simulate the occurrence of freak waves and analyses the influence of high-order nonlinearities on the evolution of random wave trains described initially by the JONSWAP spectrum. In the evolution of freak wave generation, variations in the linear and nonlinear terms of the mNLSE are displayed with the nonlinear growth of surface elevations. For comparison, the corresponding results from the cubic nonlinear Schrӧdinger equation (CSE) and the linear Schrӧdinger equation (LSE) are also obtained. Power spectra and spectral peakedness curves in the evolution of the wave train are also given to analyze the potential mechanism of freak wave formation. Additionally, the probabilities of freak wave appearances are estimated for different initial parameters and different governing equations. The results show that the fourth-order nonlinearity plays an important role in the generation of freak waves, but this single factor is not enough to generate freak waves, and freak wave occurrence is the contribution of multiple factors to the unstable evolution of the wave train. The higher-order nonlinearity, concentrated initial random phases, larger wave steepness, narrower initial spectral width, and smaller sideband instability parameter can increase the probability of freak wave generation.

Keywords


Chien, H., C. C. Kao and L. Z. H. Chuang (2002). On the characteristics of observed coastal freak waves. Coastal Engineering Journal 44(4), 301-319.##
Cui, C. and N. Zhang (2011). Freak wave simulation based on nonlinear model and the research on the time-frequency energy spectrum of simulation results. Marine Science Bulletin 13 (1), 25-39.##
Didenkulova, I. I., A. V. Slunyaev, E. N. Pelinovsky and C. Kharif (2006). Freak waves in 2005. Natural Hazards and Earth System Sciences 6(6), 1007–1015.##
Graham, D. M. (2000). NOAA vessel swamped by rogue wave. Oceanspace 284.##
Gramstad, O. and E. Bitner-Gregersen (2019). Predicting extreme waves from wave spectral properties using machine learning. International Conference on Ocean, Offshore and Arctic Engineering. Glasgow, Scotland, UK, 3, 1–10.##
Haver, S. (2004). A Possible Freak Wave Event Measured at the Draupner Jacket January 1 1995. Rogue waves 2004, Brest, France, 1-8.##
Haver, S. and J. O. Andersen (2000). Freak waves: rare realizations of a typical population or typical realizations of a rare population? Proceedings of the tenth international offshore and polar engineering conference, Seattle, USA, 3, 123-130.##
Hu, J. and Y. Zhang (2014). Analysis of Energy Characteristics in the Process of Freak Wave Generation, China Ocean Engineering 28(2), 193 – 205.##
Janssen P. A. E. M. (2003). Nonlinear Four-Wave Interactions and Freak Waves. Journal of Physical Oceanography 33(4), 863-884.##
Kashima, H. and N. Mori (2019). Aftereffect of high-order nonlinearity on extreme wave occurrence from deep to intermediate water, Coastal Engineering 153, 1-14.##
Kharif, C. and E. Pelinovsky (2003). Physical mechanisms of the rogue wave phenomenon. European Journal of Mechanics B/Fluids 22(6), 603-634.##
Kirezci C., A. V. Babanin and D. V. Chalikov (2021). Modelling rogue waves in 1D wave trains with the JONSWAP spectrum, by means of the High Order Spectral Method and a fully nonlinear numerical model. Ocean Engineering 231(108715), 1-14.##
Klinting, P. and S. Sand (1987). Analysis of prototype freak waves. Coastal Hydrodynamics, ASCE, 618-632.##
Lavrenov, I. V. (1998). The wave energy concentration at the Agulhas current of South Africa, Natural Hazards 17, 117-127.##
Liu, P. L. and K. R. MacHutchon (2006). Are there different kinds of rogue waves?  The 25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, 1-6.##
Lo, E. and C. C. Mei (1985). A numerical study of water-wave modulation based on a higher- order nonlinear Schroedinger equation. Journal of Fluid Mechanics 150, 395- 416.##
Mei, C. C. (1992). The applied dynamics of ocean surface waves. World Scientific Publishing Co. Pte. Ltd, Singapore.##
Mori, N. and T. Yasuda (2002). Effects of high- order nonlinear interactions on unidirectional wave trains. Ocean Engineering 29(10), 1233–1245.##
Nikolkina, I. and I. Didenkulova (2011). Rogue waves in 2006-2010. Natural Hazards and Earth System Sciences 11, 2913-2924.##
Onorato, M., A. R Osborne., M. Serio and S. Bertone (2001). Freak waves in random oceanic sea states. Physical review letters 86(25), 5831-5834.##
Shemer, L., A. Sergeeva and A. Slunyaev (2010a). Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random wave field evolution: experimental validation. Physics of Fluids 22 (016601),1-9.##
Shemer, L., A. Sergeeva and D. Liberzon (2010b). Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves. Journal of Geophysical Research 115 (C12039), 1-12.##
Tian, G. (2006). Analysis and prevention of abnormal waves along the coast of South Africa. Marine Technology 1, 21-22. (In Chinese)##
Veltcheva, A. and C. Guedes Soares (2016). Nonlinearity of abnormal waves by the Hilbert–Huang Transform method. Ocean Engineering 115, 30–38.##
Walker, D. A. G., P. H. Taylor and R. E. Taylor (2004). The shape of large surface waves on the open sea and the Draupner New Year wave. Applied Ocean Research 26 (3-4), 73-83.##
Warwick, R. W. (1996). Hurricane 'Luis', the Queen Elizabeth 2 and a Rogue Wave. Marine Observer 66, 134.##
Xia, W., Y. Ma and G. Dong (2015). Numerical simulation of freak waves in random sea state. Procedia Engineering 116, 366 – 372.##
Yu, Y. and S. Liu (2011). Random Wave and Its Applications for Engineering. Dalian University of Technology Press, Dalian, China. (In Chinese)##
Zhang, H. D., C. Guedes Soares, D. Chalikov and A. Toffoli (2016). Modeling the spatial evolutions of nonlinear unidirectional surface gravity waves with fully nonlinear numerical method. Ocean Engineering 125, 60–69.##
Volume 15, Issue 4
July and August 2022
Pages 1221-1229
  • Received: 04 September 2021
  • Revised: 22 April 2022
  • Accepted: 22 April 2022
  • First Publish Date: 15 May 2022