Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Honorary Note. Evgeny Georgievich Morozov: A Life at Sea as a Devoted Ocean Observer Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Rogue Waves in the Ocean, the Role of Modulational Instability, and Abrupt Changes of Environmental Conditions that Can Provoke Non Equilibrium Wave Dynamics

Author : Karsten Trulsen

Published in: The Ocean in Motion

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Modulational instability is an efficient mechanism for the generation of rogue waves in the limit of narrow-banded and long-crested wave fields. While such wave fields are easily achieved in laboratories, there appears to be lacking evidence that known occurrences of rogue waves in the ocean (e.g. Draupner “New Year” wave, Andrea wave) or ship accidents that could have been provoked by rogue waves (e.g. the Prestige accident) actually happened in sea states favorable for the modulational instability to have played an important role. The absence of modulational instability does not mean that nonlinear interactions are unimportant. Here we point out recent results that suggest large deviations from Gaussian statistics can happen due to nonlinearity in the absence of modulational instability, the key ingredient seems to be that the wave field is brought into a state of non-equilibrium.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
previous chapter Abyssal Mixing in the Laboratory
next chapter Simulation of Standing and Propagating Sea Waves with Three-Dimensional ARMA Model
Literature
1.
Alber, I. E. (1978). The effects of randomness on the stability of two-dimensional surface wavetrains. Proceedings of the Royal Society of London A, 363, 525–546.CrossRef
2.
Alber, I. E, Saffman, P. (1978). Stability of random nonlinear deep water waves with finite bandwidth spectra. Technical Report, 31326–6035–RU–TRW Defense and Space System Group
3.
Benjamin, T. B. (1967). Instability of periodic wavetrains in nonlinear dispersive systems. Proceedings of the Royal Society of London A, 299, 59–75.CrossRef
4.
Benjamin, T. B., & Feir, J. E. (1967). The disintegration of wave trains on deep water. Journal of Fluid Mechanics, 27, 417–430.CrossRef
5.
Benney, D. J., & Roskes, G. J. (1969). Wave instabilities. Studies in Applied Mathematics, 48, 377–385.CrossRef
6.
Bitner-Gregersen, E. M, Gramstad, O. (2016). Rogue waves—Impact on ships and offshore structures. Technical Report, 05–2015, DNV-GL
7.
Bitner-Gregersen, E. M., Fernandez, L., Lefèvre, J. M., Monbaliu, J., & Toffoli, A. (2014). The North Sea Andrea storm and numerical simulations. Natural Hazards and Earth System Science, 14, 1407–1415.CrossRef
8.
Cavaleri, L., Barbariol, F., Benetazzo, A., Bertotti, L., Bidlot, J. R., Janssen, P., et al. (2016). The Draupner wave: A fresh look and the emerging view. Journal of Geophysical Research: Oceans, 121, 6061–6075.
9.
Chabchoub, A., Hoffmann, N. P., & Akhmediev, N. (2011). Rogue wave observation in a water wave tank. Physical Review Letters, 106, 204,502.CrossRef
10.
Chabchoub, A., Akhmediev, N., & Hoffmann, N. P. (2012). Experimental study of spatiotemporally localized surface gravity water waves. Physical Review Letters, 86, 016,311.
11.
Chabchoub, A., Kibler, B., Dudley, J. M., & Akhmediev, N. (2014). Hydrodynamics of periodic breathers. Philosophical Transactions of the Royal Society of London A, 372, 20140,005.CrossRef
12.
Crawford, D. R., Saffman, P. G., & Yuen, H. C. (1980). Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves. Wave Motion, 2, 1–16.CrossRef
13.
Davey, A. (1972). The propagation of a weak nonlinear wave. Journal of Fluid Mechanics, 53, 769–781.CrossRef
14.
Dommermuth, D. (2000). The initialization of nonlinear waves using an adjustment scheme. Wave Motion, 32, 307–317.CrossRef
15.
Donelan, M. A., & Magnusson, A. K. (2017). The making of the Andrea wave and other rogues. Scientific Reports, 7, 44,124.CrossRef
16.
Draper, L. (1964). ‘Freak’ ocean waves. Oceanus, 10, 13–15.
17.
Dysthe, K., Krogstad, H. E., & Müller, P. (2008). Oceanic rogue waves. Annual Review of Fluid Mechanics, 40, 287–310.CrossRef
18.
Dysthe, K. B. (1979). Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proceedings of the Royal Society of London A, 369, 105–114.CrossRef
19.
Dysthe, K. B., & Trulsen, K. (1999). Note on breather type solutions of the NLS as models for freak-waves. Physica Scripta, T82, 48–52.CrossRef
20.
Fedele, F., Brennan, J., Ponce de León, S., Dudley, J., & Dias, F. (2016). Real world ocean rogue waves explained without the modulational instability. Scientific Reports, 6, 27,715.CrossRef
21.
Gramstad, O., & Trulsen, K. (2007). Influence of crest and group length on the occurrence of freak waves. Journal of Fluid Mechanics, 582, 463–472.CrossRef
22.
Gramstad, O., Zeng, H., Trulsen, K., & Pedersen, G. K. (2013). Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water. Physics of Fluid, 25, 122103.CrossRef
23.
Hasimoto, H., & Ono, H. (1972). Nonlinear modulation of gravity waves. Journal of the Physical Society of Japan, 33, 805–811.CrossRef
24.
Haver, S. (2000). Evidences of the existence of freak waves. In: 2000 Rogue Waves (pp. 129–140). Ifremer.
25.
Haver, S. (2004). A possible freak wave event measured at the Draupner jacket Januar 1 1995. Rogue Waves, 2004, 1–8.
26.
Janssen, P. A. E. M. (2003). Nonlinear four-wave interactions and freak waves. Journal of Physical Oceanography, 33, 863–884.CrossRef
27.
Kharif, C., Pelinovsky, E., Slunyaev, A. (2009). Rogue waves in the ocean. Springer
28.
Kuznetsov, E. A. (1977). Solitons in a parametrically unstable plasma. Soviet physics, Doklady, 22, 507–508.
29.
Longuet-Higgins, M. S. (1963). The effect of non-linearities on statistical distributions in the theory of sea waves. Journal of Fluid Mechanics, 17, 459–480.CrossRef
30.
Ma, Y. C. (1979). The perturbed plane-wave solutions of the cubic Schrödinger equation. Studies in Applied Mathematics, 60, 43–58.CrossRef
31.
Magnusson, A. K., & Donelan, M. A. (2013). The Andrea wave characteristics of a measured North Sea rogue wave. Journal of Offshore Mechanics and Arctic Engineering, 135, 031,108.CrossRef
32.
Mallory, J. K. (1974). Abnormal waves on the south east coast of South Africa. The International Hydrographic Review, 51, 99–129.
33.
Masuda, A., Kuo, Y. Y., & Mitsuyasu, H. (1979). On the dispersion relation of random gravity waves. Part 1. Theoretical framework. Journal of Fluid Mechanics, 92, 717–730.CrossRef
34.
Molin, B., Remy, F., Kimmoun, O., & Jamois, E. (2005). The role of tertiary wave interactions in wave-body problems. Journal of Fluid Mechanics, 528, 323–354.CrossRef
35.
Molin, B., Kimmoun, O., Remy, F., & Chatjigeorgiou, I. K. (2014). Third-order effects in wave-body interaction. European Journal of Mechanics-B/Fluids, 47, 132–144.CrossRef
36.
Onorato, M., & Suret, P. (2016). Twenty years of progresses in oceanic rogue waves: the role played by weakly nonlinear models. Natural Hazards, 84, 541–548.CrossRef
37.
Onorato, M., Osborne, A. R., Serio, M., & Bertone, S. (2001). Freak waves in random oceanic sea states. Physical Review Letters, 86, 5831–5834.CrossRef
38.
Onorato, M., Osborne, A. R., & Serio, M. (2002a). Extreme wave events in directional, random oceanic sea states. Physics of Fluids, 14, L25–L28.CrossRef
39.
Onorato, M., Osborne, A. R., Serio, M., Resio, D., Pushkarev, A., Zakharov, V. E., et al. (2002b). Freely decaying weak turbulence for sea surface gravity waves. Physical Review Letters, 89(14), 144,501.CrossRef
40.
Onorato, M., Osborne, A. R., Serio, M., Cavaleri, L., Brandini, C., & Stansberg, C. T. (2004). Observation of strongly non-Gaussian statistics for random sea surface gravity waves in wave flume experiments. Physical Review Letters, 70, 1–4.
41.
Onorato, M., Osborne, A. R., Serio, M., Cavaleri, L., Brandini, C., & Stansberg, C. T. (2006). Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves. European Journal of Mechanics - B/Fluids, 25, 586–601.CrossRef
42.
Onorato, M., Cavaleri, L., Fouques, S., Gramstad, O., Janssen, P. A. E. M., Monbaliu, J., et al. (2009a). a) Statistical properties of mechanically generated surface gravity waves: A laboratory experiment in a three dimensional wave basin. Journal of Fluid Mechanics, 627, 235–257.CrossRef
43.
Onorato, M., Waseda, T., Toffoli, A., Cavaleri, L., Gramstad, O., Janssen, P. A. E. M., et al. (2009b). (b) Statistical properties of directional ocean waves: The role of the modulational instability in the formation of extreme events. Physical Review Letters, 102, 114,502.CrossRef
44.
Osborne, A. R., Onorato, M., & Serio, M. (2000). The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains. Physics Letters A, 275, 386–393.CrossRef
45.
Peregrine, D. H. (1983). Water-waves, non-linear Schrödinger-equations and their solutions. Journal of the Australian Mathematical Society B, 25, 16–43.CrossRef
46.
Pierson, W. J. (1955). Wind generated gravity waves. Advances in Geophysics, 2, 93–178.CrossRef
47.
Raustøl, A. (2014). Freake bølger over variabelt dyp. Master’s thesis, University of Oslo
48.
Sand, S. E., Ottesen Hansen, N. E., Klinting, P., Gudmestad, O. T., & Sterndorff, M. J. (1990). Freak wave kinematics. In O. T. Gudmestad, A. Tørum (Ed.), Water Wave Kinematics (pp. 535–549). Kluwer.
49.
Sergeeva, A., Pelinovsky, E., & Talipova, T. (2011). Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework. Natural Hazards and Earth System Sciences, 11, 323–330.CrossRef
50.
Stokes, G. G. (1847). On the theory of oscillatory waves. Transactions of the Cambridge Philosophical Society, 8, 441–455.
51.
Tamura, H., Waseda, T., & Miyazawa, Y. (2009). Freakish sea state and swell-windsea coupling: Numerical study of the Suwa-Maru incident. Geophysical Research Letters, 36, L01,607.CrossRef
52.
Tayfun, M. A. (1980). Narrow-band nonlinear sea waves. Journal of Geophysical Research, 85, 1548–1552.CrossRef
53.
Tick, L. J. (1959). A non-linear random model of gravity waves I. Journal of Mathematics and Mechanics, 8, 643–651.
54.
Toffoli, A., & Bitner-Gregersen, E. M. (2011). Extreme and rogue waves in directional wave fields. Open Ocean Engineering Journal, 4, 24–33.CrossRef
55.
Trulsen, K., & Dysthe, K. B. (1996). A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion, 24, 281–289.CrossRef
56.
Trulsen, K., & Dysthe, K. B. (1997). Freak waves—a three-dimensional wave simulation. In: Proceedings of the 21st Symposium on Naval Hydrodynamics, National Academy Press (pp 550–560).
57.
Trulsen, K., Kliakhandler, I., Dysthe, K. B., & Velarde, M. G. (2000). On weakly nonlinear modulation of waves on deep water. Physics of Fluids, 12, 2432–2437.CrossRef
58.
Trulsen, K., Zeng, H., & Gramstad, O. (2012). Laboratory evidence of freak waves provoked by non-uniform bathymetry. Physics of Fluids, 24, 097,101.CrossRef
59.
Trulsen, K., Nieto Borge, J. C., Gramstad, O., Aouf, L., & Lefèvre, J. M. (2015). Crossing sea state and rogue wave probability during the Prestige accident. Journal of Geophysical Research: Oceans, 120, 7113–7136.
60.
Viotti, C., & Dias, F. (2014). Extreme waves induced by strong depth transitions: Fully nonlinear results. Physics of Fluids, 26, 051,705.CrossRef
61.
Viste-Ollestad I, Andersen TL, Oma N, Zachariassen S (2016) Granskingsrapport etter hendelse med fatalt utfall på COSL Innovator 30. desember 2015. Tech. rep., Petroleumstilsynet
62.
Waseda, T., Tamura, H., & Kinoshita, T. (2012). Freakish sea index and sea states during ship accidents. Journal of Marine Science and Technology, 17, 305–314.CrossRef
63.
Waseda, T., In, K., Kiyomatsu, K., Tamura, H., Miyazawa, Y., & Iyama, K. (2014). Predicting freakish sea state with an operational third-generation wave model. Natural Hazards and Earth System Science, 14, 945–957.CrossRef
64.
Zakharov, V. E. (1968). Stability of periodic waves of finite amplitude on the surface of a deep fluid. Journal of Applied Mechanics and Technical Physics, 9, 190–194.CrossRef
65.
Zeng, H., & Trulsen, K. (2012). Evolution of skewness and kurtosis of weakly nonlinear unidirectional waves over a sloping bottom. Natural Hazards and Earth System Science, 12, 631–638.CrossRef
Metadata
Title
Rogue Waves in the Ocean, the Role of Modulational Instability, and Abrupt Changes of Environmental Conditions that Can Provoke Non Equilibrium Wave Dynamics
Author
Karsten Trulsen
Copyright Year
2018
Book
The Ocean in Motion

Print ISBN: 978-3-319-71933-7

Electronic ISBN: 978-3-319-71934-4

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-71934-4_17