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Draft:Origin of rogue waves

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Although commonly described as a tsunami, The Great Wave off Kanagawa, by artist Hokusai, likely depicts a rogue wave off of the coast of Japan.

The exact origins deriving the mechanics of rogue waves has been a matter of active research and ongoing scientific debate.[1] Amongst scientific consensus, the development of rogue waves is likely influenced by several collective environmental factors, including wind, wave oscillations, currents, and possibly gale forces.[a] The universal cause explaining the origins of rogue waves exists in numerous hypotheses, the most prominent explanations include Diffractive focusing, nonlinear effects (modulational instability), and wind wave interactions. In human knowledge, rogue waves originated in myth, existing through anecdotal evidence given by early eyewitness accounts.[2][b] The irregular damage inflicted upon ships later suggested that large surface anomalies have long occurred; the application of modern technology and oceanographic studies confirmed the existence of unpredictable freak waves in later decades, and generated extensive research amongst the scientific community into several possible causes. The ambiguity surrounding rogue waves is deeply rooted in the unpredictability of wave propagation and the chaotic dynamics of wind waves attributing to their apparent randomness within evolving sea states.[3][4]

Rogue waves do not appear to have a single distinct cause.[5][c] The nature of a "freak" rogue wave are generally agreed to occur variably and without warning, yet can be observed to have highest predictability where a strong ocean current runs counter to the prevailing direction of the traveling waves. [removed content for cv]

Scientific studies of rogue waves can be traced to the recording of an abnormally large wave off of the Gorm Field in the central North Sea. The measurement of the Draupner wave off the Draupner platform was the first rogue wave to be detected by a measuring instrument. Early scientific research of unusual waves began in the 19th century with the discovery of wave of translation by John Scott Russell in 1834, in which the modern study of solitons was formed. The use of statistical models beginning in the 19th century helped to predict wave height while the general knowledge was that wave heights were grouped around a central value equal to the average of the largest third. Scientific works on "Freak Waves" began with Professor Laurence Draper in 20th century where he documented the efforts of the National Institute of Oceanography in the early 1960s to record wave height. The first scientific study to comprehensively prove that freak waves exist was published in 1997 and began an overall censuses amongst scientific authors that rogue waves exist with the caveat that wave models could not replicate rogue waves.[6] The 21st century saw the extensive discovery of rogue wave mechanics, with the successful replication of a wave with similar characteristics to the Draupner wave in 2019.[7][8]

Nature

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To simulate rogue waves, a Nonlinear Schrödinger's Equation (NLSE) is used, various simplifying assumptions allow different models to be built.

Rogue waves are defined as waves which are greater than twice the size of surrounding waves and contain limited predictable qualities.[9][10][11] The geometric definition of a rogue wave is given as a wave whose crest-to-trough height exceeds a threshold relative to the significant wave height . The significant wave height is defined as four times the SD of the sea surface elevation.[12][13][d] Rogue waves are ubiquitous in nature and do not appear to be effected in an ocean environment by the patterns of prevailing winds or general wave direction. A rogue wave is a natural ocean phenomenon that is not caused by land movement, only lasts briefly, occurs in a limited location, and most often happens far offshore. [deleted content].[14][15][16] A rogue wave's spontaneous formation is key feature in its lack of scientific observation. [17] Unlike tsunamis caused by earthquakes, rogue waves are appear to be unpredictable and localized in space and time.[18][19][20] As the Schrödinger equation, governing the wave function of a quantum-mechanical systems [deleted content].[21][22][23] The journal Physics Letters A, on theoretical and experimental frontier physics, describes this function by stating:

The dynamics of wind wave behavior can been directly correlated with the nature of rogue waves. When waves form as wind energy is transferred to the ocean's surface, and as conditions generate stronger winds, wave patterns become more organized and begin traveling in one direction.

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Derivatives and hypotheses

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While there is no scientific consensus on the universal cause of rogue waves, numerous natural variables exist that most likely influence their development.[24][25][26][27] This includes water depth, tidal forces, wind blowing across the water, physical objects such as islands that reflect waves, and interaction with other waves and ocean currents.[28][29][30] The research paper Physica D: Nonlinear Phenomena on Intricate dynamics of rogue waves governed by the Sasa–Satsuma equation describes as "large amplitude waves, localized in both space and time, thus making these events unexpected".[31][32] Hypothesized mechanisms for rogue waves include:

Nonlinear effects

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Originating in the 1990s as a possible solution to the NLS equation for the mechanisms of rogue wave formation, whether second-order or third-order nonlinearities are a dominant factor in the origins of freak waves is a subject of considerable debate.[33][34] Recent theoretical studies show that third-order quasi-resonant interactions are insignificant to the formation of large waves in realistic oceanic seas. As typical oceanic wind seas contain short-crested, or multidirectional wave field features, nonlinear focusing due to modulational effects is diminished since energy can spread directionally.[35] Therefore, the process of modulation instabilities may have an insignificant effect in the development of wave patterns, especially in finite water depth where they are further reduced.[36][37][38]

Diffractive focusing

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Diffractive focusing refers to the focusing of light through the division and mutual interference of a propagating electromagnetic wave.[39] In the context of ocean waves, the effects of diffractive focusing on smaller wind and current-driven waves by underwater and coastal topology is often attributed to the development of rogue waves. During this process, coast shape or seabed shape directs several small waves to converge, therefore combining their crests to create a larger wave.[40][41]

Constructive interference

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According to this hypothesis, as these swells travel at different speeds and directions and pass through one another, their crests, troughs, and lengths coincide and reinforce each other.[42] This process can form abnormally large waves, and may last for several minutes before subsiding as swells travel in the same direction.

Wave train interaction

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Amongst another theory describing the origin of rogue waves includes the focusing of wave energy due to the interaction of opposing wave patterns. As an opposing water current is formed by the development of storm surges, the interaction between the opposite current and the normal wave direction results in a shortening of the wave frequency.[43][44] This can result in the dynamic convergence of waves, subsequently forming a single larger wave. This effect can reportedly be seen around areas the Gulf Stream and where Agulhas current is countered by the westerlies.[45][46]

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See also

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Notes

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  1. ^ The nature behind what causes rogue waves remains unresolved.[2]
  2. ^ Before science could prove the existence of rogue waves, they were regarded as folklore.[2]
  3. ^ The nature behind what causes rogue waves remains unresolved.[2]
  4. ^ Häfner uses a rogue wave criterion with a threshold of 2.0:.

References

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  1. ^ Onorato, M.; Residori, S.; Bortolozzo, U.; Montina, A.; Arecchi, F. T. (2013-07-10). "Rogue waves and their generating mechanisms in different physical contexts". Physics Reports. 528 (2): 47–89. Bibcode:2013PhR...528...47O. doi:10.1016/j.physrep.2013.03.001. ISSN 0370-1573.
  2. ^ a b c d US Department of Commerce, National Oceanic and Atmospheric Administration. "What is a rogue wave?". oceanservice.noaa.gov. Retrieved 2024-09-19.
  3. ^ "Wave Dynamics | Fluid Mechanis Lab". fluids.umn.edu. Retrieved 2024-09-19.
  4. ^ "Behaviour of waves". Science Learning Hub. Retrieved 2024-09-19.
  5. ^ NOAA 2024, p. 23.
  6. ^ J. Skourup, Hansen, Andreasen, J. , N.-E. O., K. K. (August 1, 1997). "Non-Gaussian Extreme Waves in the Central North Sea". asmedigitalcollection.asme.org. Retrieved 2024-09-19.{{cite web}}: CS1 maint: multiple names: authors list (link)
  7. ^ "Famous freak wave recreated in lab mirrors Hokusai's 'Great Wave' | University of Oxford". www.ox.ac.uk. 2019-01-23. Retrieved 2024-10-09.
  8. ^ McAllister, M. L.; Draycott, S.; Adcock, T. a. A.; Taylor, P. H.; Bremer, T. S. van den (February 2019). "Laboratory recreation of the Draupner wave and the role of breaking in crossing seas". Journal of Fluid Mechanics. 860: 767–786. Bibcode:2019JFM...860..767M. doi:10.1017/jfm.2018.886. ISSN 0022-1120.
  9. ^ "Monsters of the deep". The Economist. ISSN 0013-0613. Retrieved 2024-09-20.
  10. ^ "Weird Science: Rogue Waves | manoa.hawaii.edu/ExploringOurFluidEarth". manoa.hawaii.edu. Retrieved 2024-09-19.
  11. ^ "Rogue Waves". education.nationalgeographic.org. Retrieved 2024-09-19.
  12. ^ Olagnon, Michel (2017-06-15). Rogue Waves: Anatomy of a Monster. Bloomsbury Publishing. ISBN 978-1-4729-4441-2.
  13. ^ Häfner 2023, p. 23.
  14. ^ Jenks, D. Tyler; Coates, Tyler D.; Wald, Leah (2020-02-29). Hyperwave Theory: The Rogue Waves of Financial Markets. Archway Publishing. ISBN 978-1-4808-8877-7.
  15. ^ Mori, Nobuhito; Waseda, Takuji; Chabchoub, Amin (2023-10-31). Science and Engineering of Freak Waves. Elsevier. ISBN 978-0-323-97215-4.
  16. ^ Kharif, Pelinovsky, Slunyaev, Christian, Efim, Alexey (December 11, 2008). Rogue Waves in the Ocean (in 639-2). Springer Berlin Heidelberg (published 2008). pp. 2–29. ISBN 9783540884194.{{cite book}}: CS1 maint: date and year (link) CS1 maint: multiple names: authors list (link) CS1 maint: unrecognized language (link)
  17. ^ "Enormous 'rogue waves' can appear out of nowhere. Math is revealing their secrets". Premium. 2024-09-20. Retrieved 2024-09-20.
  18. ^ #author.fullName}. "Huge rogue waves rise from nowhere to sink ships. Can we predict them?". New Scientist. Retrieved 2024-09-23. {{cite web}}: |last= has generic name (help)
  19. ^ Service, National Weather. "National Weather Service - Tsunami Hazards". www.tsunami.gov. Retrieved 2024-09-23.
  20. ^ Trillo, Stefano; Chabchoub, Amin (2019-12-18). "A Unifying Framework for Describing Rogue Waves". Physics. 12: 146. doi:10.1103/PhysRevX.9.041057.
  21. ^ Gemmrich, Johannes; Cicon, Leah (2022-02-02). "Generation mechanism and prediction of an observed extreme rogue wave". Scientific Reports. 12 (1): 1718. doi:10.1038/s41598-022-05671-4. ISSN 2045-2322. PMC 8811055. PMID 35110586.
  22. ^ Bludov, Yu. V.; Konotop, V. V.; Akhmediev, N. (2009-09-15). "Matter rogue waves". Physical Review A. 80 (3): 033610. doi:10.1103/PhysRevA.80.033610.
  23. ^ Akhmediev, N.; Ankiewicz, A.; Taki, M. (2009-02-02). "Waves that appear from nowhere and disappear without a trace". Physics Letters A. 373 (6): 675–678. doi:10.1016/j.physleta.2008.12.036. ISSN 0375-9601.
  24. ^ Spitz, Olivier (2021-05-15). Mid-infrared Quantum Cascade Lasers for Chaos Secure Communications. Springer Nature. ISBN 978-3-030-74307-9.
  25. ^ "Are rogue waves predictable?". ScienceDaily. Retrieved 2024-09-23.
  26. ^ Newkey-Burden, Chas; published, The Week UK (2024-05-23). "What are rogue waves and what causes them?". theweek. Retrieved 2024-09-21.
  27. ^ Olagnon, Michel (June 15, 2017). Rogue Waves: Anatomy of a Monster (in 639-2). Bloomsbury Publishing (published 2017). p. 19. ISBN 9781472944429.{{cite book}}: CS1 maint: unrecognized language (link)
  28. ^ Didenkulova, Ekaterina (2020-04-15). "Catalogue of rogue waves occurred in the World Ocean from 2011 to 2018 reported by mass media sources". Ocean & Coastal Management. 188: 105076. doi:10.1016/j.ocecoaman.2019.105076. ISSN 0964-5691.
  29. ^ "How Rogue Waves Work". HowStuffWorks. 1970-01-01. Retrieved 2024-09-20.
  30. ^ Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric (2016-06-21). "Real world ocean rogue waves explained without the modulational instability". Scientific Reports. 6 (1): 27715. Bibcode:2016NatSR...627715F. doi:10.1038/srep27715. ISSN 2045-2322. PMC 4914928. PMID 27323897.
  31. ^ Mu, Gui; Qin, Zhenyun; Grimshaw, Roger; Akhmediev, Nail (2020-01-15). "Intricate dynamics of rogue waves governed by the Sasa–Satsuma equation". Physica D: Nonlinear Phenomena. 402: 132252. doi:10.1016/j.physd.2019.132252. ISSN 0167-2789.
  32. ^ Trillo, Stefano; Chabchoub, Amin (2019-12-18). "A Unifying Framework for Describing Rogue Waves". Physics. 12: 146. doi:10.1103/PhysRevX.9.041057.
  33. ^ Tayfun, M. Aziz (2008-12-01). "Distributions of Envelope and Phase in Wind Waves". Journal of Physical Oceanography. 38 (12): 2784–2800. doi:10.1175/2008JPO4008.1. ISSN 0022-3670.
  34. ^ Fedele, Francesco (2008-08-15). "Rogue waves in oceanic turbulence". Physica D: Nonlinear Phenomena. Euler Equations: 250 Years On. 237 (14): 2127–2131. doi:10.1016/j.physd.2008.01.022. ISSN 0167-2789.
  35. ^ Onorato, M.; Cavaleri, L.; Fouques, S.; Gramstad, O.; Janssen, P. a. E. M.; Monbaliu, J.; Osborne, A. R.; Pakozdi, C.; Serio, M.; Stansberg, C. T.; Toffoli, A.; Trulsen, K. (May 2009). "Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin". Journal of Fluid Mechanics. 627: 235–257. doi:10.1017/S002211200900603X. hdl:2318/45746. ISSN 1469-7645.
  36. ^ "BBC - Science & Nature - Horizon - Freak Wave". www.bbc.co.uk. Retrieved 2024-09-26.
  37. ^ "Math explains water disasters - ScienceAlert". 2016-04-24. Archived from the original on 2016-04-24. Retrieved 2024-09-26.
  38. ^ Toffoli, A.; Benoit, M.; Onorato, M.; Bitner-Gregersen, E. M. (2009-02-24). "The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth". Nonlinear Processes in Geophysics. 16 (1): 131–139. doi:10.5194/npg-16-131-2009. ISSN 1023-5809.
  39. ^ "Diffractive Optics - an overview | ScienceDirect Topics". www.sciencedirect.com. Retrieved 2024-09-23.
  40. ^ "Diffraction and Current Focusing". ffden-2.phys.uaf.edu. Retrieved 2024-09-23.
  41. ^ "Ocean Prediction Center--Rogue Waves". 2010-05-28. Archived from the original on 2010-05-28. Retrieved 2024-09-23.
  42. ^ "Physics Tutorial: Interference of Waves". www.physicsclassroom.com. Retrieved 2024-09-23.
  43. ^ "Wave-Wave Interaction - an overview | ScienceDirect Topics". www.sciencedirect.com. Retrieved 2024-10-09.
  44. ^ "10.4: Breakers and Wave Trains". Geosciences LibreTexts. 2020-03-23. Retrieved 2024-10-09.
  45. ^ Korde, Umesh A.; Ertekin, R. Cengiz (2014-02-01). "On wave energy focusing and conversion in open water". Renewable Energy. 62: 84–99. doi:10.1016/j.renene.2013.06.033. ISSN 0960-1481.
  46. ^ "A short history of wave energy". Retrieved 2024-09-26.

Further reading

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Books

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  • Kharif, Christian, Pelinovsky, Efim, Slunyaev, Alexey. Rogue Waves in the Ocean (2008) ISBN 978-3-5408-8419-4
  • Olagnon, Michel. Rogue Waves: Anatomy of a Monster (2017) ISBN 9781472944429, 1472944429
  • Guo, Boling, Tian, Lixin, Yan, Zhenya, Ling, Liming, Wang, Yu-Feng, Zhejiang Science and Technology Press. Rogue Waves: Mathematical Theory and Applications in Physics (2017) ISBN 9783110470574
  • Torum, A., Gudmestad, O. T., Water Wave Kinematics (2012) ISBN 9789400905313
  • Maccari, Attilio. Nonlinear Physics, from Vibration Control to Rogue Waves and Beyond (2023) ISBN 9781527588189
  • Massel, Stanislaw R. Ocean Surface Waves: Their Physics and Prediction (1996) ISBN 9789810221096
  • Norse, Travis. Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (2017)
  • Boccotti, Paolo. Wave Mechanics for Ocean Engineering (2000) ISBN 9780080543727
  • Hirota, Ryogo. The Direct Method in Soliton Theory (2004)

Research

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Rogue Wave origins

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Other

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