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Rogue wave
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== Causes == Because the phenomenon of rogue waves is still a matter of active research, clearly stating what the most common causes are or whether they vary from place to place is premature. The areas of highest predictable risk appear to be where a strong [[ocean current|current]] runs counter to the primary direction of travel of the waves; the area near [[Cape Agulhas]] off the southern tip of Africa is one such area. The warm [[Agulhas Current]] runs to the southwest, while the dominant winds are [[westerlies]], but since this thesis does not explain the existence of all waves that have been detected, several different mechanisms are likely, with localized variation. Suggested mechanisms for freak waves include: ;[[Diffraction|Diffractive]] [[Focus (geometry)|focus]]ing: According to this hypothesis, coast shape or seabed shape directs several small waves to meet in phase. Their crest heights combine to create a freak wave.<ref name="OPC">{{cite web |date=April 22, 2005 |title=Rogue Waves |url=http://www.opc.ncep.noaa.gov/perfectstorm/mpc_ps_rogue.shtml |url-status=dead |archive-url=https://web.archive.org/web/20100528124448/http://www.opc.ncep.noaa.gov/perfectstorm/mpc_ps_rogue.shtml |archive-date=May 28, 2010 |access-date=May 8, 2006 |website=Ocean Prediction Center |publisher=[[National Weather Service]]}}</ref> ;Focusing by currents: Waves from one current are driven into an opposing current. This results in shortening of wavelength, causing shoaling (i.e., increase in wave height), and oncoming wave trains to compress together into a rogue wave.<ref name="OPC" /> This happens off the South African coast, where the [[Agulhas Current]] is countered by westerlies.<ref name="Iopscience.iop.org_April_17_2016c" /> ;Nonlinear effects ([[modulational instability]]):A rogue wave may occur by natural, nonlinear processes from a random background of smaller waves.<ref name="BBCFreak" /> In such a case, it is hypothesized, an unusual, unstable wave type may form, which "sucks" energy from other waves, growing to a near-vertical monster itself, before becoming too unstable and collapsing shortly thereafter. One simple model for this is a wave equation known as the [[nonlinear Schrödinger equation]] (NLS), in which a normal and perfectly accountable (by the standard linear model) wave begins to "soak" energy from the waves immediately fore and aft, reducing them to minor ripples compared to other waves. The NLS can be used in deep-water conditions. In shallow water, waves are described by the [[Korteweg–de Vries equation]] or the [[Boussinesq approximation (water waves)|Boussinesq equation]]. These equations also have nonlinear contributions and show solitary-wave solutions. The terms [[soliton]] (a type of self-reinforcing wave) and [[breather]] (a wave where energy concentrates in a localized and oscillatory fashion) are used for some of these waves, including the well-studied [[Peregrine soliton]]. Studies show that nonlinear effects could arise in bodies of water.<ref name="Iopscience.iop.org_April_17_2016c" /><ref name="MyUser_Sciencealert.com_April_15_2016c">{{cite web |date=26 August 2010 |title=Math explains water disasters – ScienceAlert |url=http://www.sciencealert.com/news/20102708-21266-2.html |url-status=dead |archive-url=https://web.archive.org/web/20160424145706/http://www.sciencealert.com/news/20102708-21266-2.html |archive-date=24 April 2016 |access-date=April 15, 2016 |newspaper=Sciencealert.com}}</ref><ref name="MyUser_Bris.ac.uk_April_15_2016c">{{cite web |date=22 August 2010 |title=Bristol University |url=http://www.bris.ac.uk/news/2010/7184.html |access-date=April 15, 2016 |newspaper=Bris.ac.uk}}</ref><ref>{{Cite journal |last1=Akhmediev |first1=N. |last2=Soto-Crespo |first2=J. M. |last3=Ankiewicz |first3=A. |date=2009 |title=How to excite a rogue wave |journal=Physical Review A |volume=80 |issue=4 |pages=043818 |bibcode=2009PhRvA..80d3818A |doi=10.1103/PhysRevA.80.043818 |hdl-access=free |hdl=10261/59738}}</ref> A small-scale rogue wave consistent with the NLS on (the Peregrine soliton) was produced in a laboratory [[Wave tank|water-wave tank]] in 2011.<ref>{{cite journal |author=Adrian Cho |date=13 May 2011 |title=Ship in Bottle, Meet Rogue Wave in Tub |url=https://www.science.org/content/article/ship-bottle-meet-rogue-wave-tub |journal=Science Now |volume=332 |issue=6031 |page=774 |bibcode=2011Sci...332R.774. |doi=10.1126/science.332.6031.774-b |access-date=2011-06-27}}</ref> ;Normal part of the wave spectrum: Some studies argue that many waves classified as rogue waves (with the sole condition that they exceed twice the SWH) are not freaks but just rare, random samples of the [[Significant wave height#Statistical distribution of the heights of individual waves|wave height distribution]], and are, as such, statistically expected to occur at a rate of about one rogue wave every 28 hours.<ref>{{Cite news |date=2013 |title=Rogue waves: rare but damaging |url=https://web.uvic.ca/~gemmrich/pdf/GBG_RogueWave_Seaways.pdf |access-date=2022-01-27 |work=Seaways Magazine}}</ref> This is commonly discussed as the question "Freak Waves: Rare Realizations of a Typical Population Or Typical Realizations of a Rare Population?"<ref>{{Cite journal |last1=Hayer |first1=Sverre |last2=Andersen |first2=Odd Jan |date=2000-05-28 |title=Freak Waves: Rare Realizations of a Typical Population Or Typical Realizations of a Rare Population? |url=https://onepetro.org/ISOPEIOPEC/proceedings/ISOPE00/All-ISOPE00/ISOPE-I-00-233/7014 |language=en |publisher=OnePetro}}</ref> According to this hypothesis, most real-world encounters with huge waves can be explained by linear wave theory (or weakly nonlinear modifications thereof), without the need for special mechanisms like the [[modulational instability]].<ref>{{Cite journal |last1=Gemmrich |first1=J. |last2=Garrett |first2=C. |date=2011-05-18 |title=Dynamical and statistical explanations of observed occurrence rates of rogue waves |url=https://nhess.copernicus.org/articles/11/1437/2011/ |journal=Natural Hazards and Earth System Sciences |language=English |volume=11 |issue=5 |pages=1437–1446 |bibcode=2011NHESS..11.1437G |doi=10.5194/nhess-11-1437-2011 |issn=1561-8633 |doi-access=free}}</ref><ref>{{Cite journal |last1=Fedele |first1=Francesco |last2=Brennan |first2=Joseph |last3=Ponce de León |first3=Sonia |last4=Dudley |first4=John |last5=Dias |first5=Frédéric |date=2016-06-21 |title=Real world ocean rogue waves explained without the modulational instability |journal=Scientific Reports |language=en |volume=6 |issue=1 |pages=27715 |bibcode=2016NatSR...627715F |doi=10.1038/srep27715 |issn=2045-2322 |pmc=4914928 |pmid=27323897}}</ref> Recent studies analyzing billions of wave measurements by [[Weather buoy|wave buoys]] demonstrate that rogue wave occurrence rates in the ocean can be explained with linear theory when the finite [[spectral bandwidth]] of the wave spectrum is taken into account.<ref name=":1">{{Cite journal |last1=Häfner |first1=Dion |last2=Gemmrich |first2=Johannes |last3=Jochum |first3=Markus |date=2021-05-12 |title=Real-world rogue wave probabilities |journal=Scientific Reports |language=en |volume=11 |issue=1 |pages=10084 |bibcode=2021NatSR..1110084H |doi=10.1038/s41598-021-89359-1 |issn=2045-2322 |pmc=8115049 |pmid=33980900}}</ref><ref>{{Cite journal |last1=Cattrell |first1=A. D. |last2=Srokosz |first2=M. |last3=Moat |first3=B. I. |last4=Marsh |first4=R. |date=2018 |title=Can Rogue Waves Be Predicted Using Characteristic Wave Parameters? |journal=Journal of Geophysical Research: Oceans |language=en |volume=123 |issue=8 |pages=5624–5636 |bibcode=2018JGRC..123.5624C |doi=10.1029/2018JC013958 |issn=2169-9291 |s2cid=135333238 |doi-access=free}}</ref> However, whether weakly nonlinear dynamics can explain even the largest rogue waves (such as those exceeding three times the significant wave height, which would be exceedingly rare in linear theory) is not yet known. This has also led to criticism questioning whether defining rogue waves using only their relative height is meaningful in practice.<ref name=":1" />: ;Constructive interference of elementary waves: Rogue waves can result from the constructive interference (dispersive and directional focusing) of elementary three-dimensional waves enhanced by nonlinear effects.<ref name=":0" /><ref>{{cite journal |last1=Fedele |first1=Francesco |last2=Brennan |first2=Joseph |last3=Ponce de León |first3=Sonia |last4=Dudley |first4=John |last5=Dias |first5=Frédéric |date=2016-06-21 |title=Real world ocean rogue waves explained without the modulational instability |journal=Scientific Reports |language=en |volume=6 |pages=27715 |bibcode=2016NatSR...627715F |doi=10.1038/srep27715 |issn=2045-2322 |pmc=4914928 |pmid=27323897}}</ref>: ;[[Wind wave]] interactions: While wind alone is unlikely to generate a rogue wave, its effect combined with other mechanisms may provide a fuller explanation of freak wave phenomena. As the wind blows over the ocean, energy is transferred to the sea surface. When strong winds from a storm blow in the ocean current's opposing direction, the forces might be strong enough to generate rogue waves randomly. Theories of instability mechanisms for the generation and growth of wind waves – although not on the causes of rogue waves – are provided by Phillips<ref name="JFM">Phillips 1957, ''[[Journal of Fluid Mechanics]]''</ref> and Miles.<ref name="Iopscience.iop.org_April_17_2016c" /><ref name="JFM2">Miles, 1957, ''[[Journal of Fluid Mechanics]]''</ref> The [[spatiotemporal]] focusing seen in the [[NLS equation]] can also occur when the non-linearity is removed. In this case, focusing is primarily due to different waves coming into phase rather than any energy-transfer processes. Further analysis of rogue waves using a fully nonlinear model by R. H. Gibbs (2005) brings this mode into question, as it is shown that a typical wave group focuses in such a way as to produce a significant wall of water at the cost of a reduced height. A rogue wave, and the deep trough commonly seen before and after it, may last only for some minutes before either breaking or reducing in size again. Apart from a single one, the rogue wave may be part of a wave packet consisting of a few rogue waves. Such rogue [[wave group]]s have been observed in nature.<ref>[http://www.ifremer.fr/web-com/stw2004/rw Frederic-Moreau. The Glorious Three], translated by M. Olagnon and G.A. Chase / Rogue Waves-2004, Brest, France</ref>
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