Draft:Origin of rogue waves

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. 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.Template:Refn 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.Template:Refn 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.

Rogue waves do not appear to have a single distinct cause.Template:SfnTemplate:Refn 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. 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.

Nature

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. The geometric definition of a rogue wave is given as a wave whose crest-to-trough height $H$ exceeds a threshold relative to the significant wave height $Hs$. The significant wave height is defined as four times the SD of the sea surface elevation.Template:SfnTemplate:Refn 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]. A rogue wave's spontaneous formation is key feature in its lack of scientific observation. Unlike tsunamis caused by earthquakes, rogue waves are appear to be unpredictable and localized in space and time. As the Schrödinger equation, governing the wave function of a quantum-mechanical systems [deleted content]. 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

While there is no scientific consensus on the universal cause of rogue waves, numerous natural variables exist that most likely influence their development. 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. 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". 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. 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. 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.

Diffractive focusing

Diffractive focusing refers to the focusing of light through the division and mutual interference of a propagating electromagnetic wave. 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.

Constructive interference

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. 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

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. 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.

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See also

• Modulational instability

• Nonlinear Schrödinger's Equation
• Peregrine solitons
• Superposition principle
• Wave packet

Further reading

Books

• Kharif, Christian, Pelinovsky, Efim, Slunyaev, Alexey. Rogue Waves in the Ocean (2008) Template:ISBN
• Olagnon, Michel. Rogue Waves: Anatomy of a Monster (2017) Template:ISBN
• 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) Template:ISBN
• Torum, A., Gudmestad, O. T., Water Wave Kinematics (2012) Template:ISBN
• Maccari, Attilio. Nonlinear Physics, from Vibration Control to Rogue Waves and Beyond (2023) Template:ISBN
• Massel, Stanislaw R. Ocean Surface Waves: Their Physics and Prediction (1996) Template:ISBN
• Norse, Travis. Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (2017)
• Boccotti, Paolo. Wave Mechanics for Ocean Engineering (2000) Template:ISBN
• Hirota, Ryogo. The Direct Method in Soliton Theory (2004)

Research

• NOAA: What is a Rogue Wave?, primary causes proposed by the NOAA
• Voss, David (January 1, 2018), "Confirmation of the Existence of Rogue Waves", from the American Physical Society (APS)
• Rogue Waves Revealed Origins explained by National Geographic Education
• Trillo, Stefano, Chabchoub, Amin (December 18, 2019), "A Unifying Framework for Describing Rogue Waves" from the APS
• Kharif, Christian, Pelinovsky, Efim. (May 6, 2003), "Physical mechanisms of the rogue wave phenomenon" from the European Journal of Mechanics - B/Fluids (Volume 22, Issue 6, November–December 2003, Pages 603-634)
  • Oceanic Rogue Waves
  • Homotopy Analysis Method in Nonlinear Differential Equations (2012)
• Optical rogue waves, on the similarities with oceanic rogue waves

Rogue Wave origins

• What is a rogue wave?, origins presented by Woods Hole Oceanographic Institution
• The science and history of rogue waves, part one
• What causes rogue waves?- further explanations by the BBC (2011).
• Ocean rogue waves: a mystery unveiled?
• Primary cause for the formation of rogue waves found: by Julia Hager | Apr 18, 2024 | Antarctica, Archive, Science, Science
• Ocean Measurements Detect Conditions for Giant Waves
• Rogue waves: rare but damaging
• Rogue waves can strike without warning. These scientists found a way to predict them
• Real-world rogue wave probabilities (May 12, 2021)

Other

• Rogue Waves - BBC Horizon on YouTube- documentary on rogue wave causes, formation, and history by Sabbatical (YouTuber).

External links

• What is a rogue wave? - NOAA's National Ocean Service