Editing Rogue wave (section)

=== Subsequent research ===

Following the evidence of the Draupner wave, research in the area became widespread.

The first scientific study to comprehensively prove that freak waves exist, which are clearly outside the range of Gaussian waves, was published in 1997.<ref>{{cite journal
| last1       = Skourup
| first1      = J
| last2      = Hansen
| first2     = N.-E. O.
| last3      = Andreasen
| first3     = K. K.
| date       = 1997-08-01
| title      = Non-Gaussian Extreme Waves in the Central North Sea
| journal    = Journal of Offshore Mechanics and Arctic Engineering
| volume     = 119
| issue      = 3
| page      = 146
| doi        = 10.1115/1.2829061
| quote      = The area of the Central North Sea is notorious for very high waves in certain wave trains. The short-term distribution of these wave trains includes waves far steeper than the Rayleigh distribution predicted. Such waves are often termed "extreme waves" or "freak waves". An analysis of the extreme statistical properties of these waves has been made. The analysis is based on more than 12 years of wave records from the Mærsk Olie og Gas AS operated Gorm Field, located in the Danish sector of the Central North Sea. From the wave recordings, more than 400 freak wave candidates were found. The ratio between the extreme crest height and the significant wave height (20-min value) is about 1.8, and the ratio between extreme crest height and extreme wave height is 0.69. The latter ratio is clearly outside the range of Gaussian waves, and it is higher than the maximum value for steep nonlinear long-crested waves, thus indicating that freak waves are not of a permanent form, and probably of short-crested nature. The extreme statistical distribution is represented by a Weibull distribution with an upper bound, where the upper bound is the value for a depth-limited breaking wave. Based on the measured data, a procedure for determining the freak wave crest height with a given return period is proposed. A sensitivity analysis of the extreme value of the crest height is also made. }}</ref> Some research confirms that observed wave height distribution, in general, follows well the [[Rayleigh distribution]]. Still, in shallow waters during high energy events, extremely high waves are rarer than this particular model predicts.<ref name="Laird1" /> From about 1997, most leading authors acknowledged the existence of rogue waves with the caveat that wave models could not replicate rogue waves.<ref name="Parker2012"/>

Statoil researchers presented a paper in 2000, collating evidence that freak waves were not the rare realizations of a typical or slightly non-gaussian sea surface population (''classical'' extreme waves) but were the typical realizations of a rare and strongly non-gaussian sea surface population of waves (''freak'' extreme waves).<ref name="2000_ISOPE_Conference">{{cite conference
| url          = http://www.isope.org/publications/proceedings/ISOPE/ISOPE%202000/pdffiles/papers/Vol3/020.pdf
| title        = Freak waves: rare realizations of a typical population or typical realizations of a rare population?
| author       = Haver S and Andersen O J
| year         = 2010
| conference   = Proc. 10th Conf. of Int. Society for Offshore and Polar Engineering (ISOPE)
| publisher    = ISOPE
| location     = Seattle
| pages        = 123–130
| access-date  = 18 April 2016
| archive-url  = https://web.archive.org/web/20160512192003/http://www.isope.org/publications/proceedings/ISOPE/ISOPE%202000/pdffiles/papers/Vol3/020.pdf
| archive-date = 2016-05-12
| url-status   = dead
}}</ref> A workshop of leading researchers in the world attended the first Rogue Waves 2000 workshop held in Brest in November 2000.<ref name="2000_Ifremnr_Conference">{{Cite conference
| url        = http://www.ifremer.fr/metocean/conferences/wk.htm
| title      = Rogue Waves 2000
| year       = 2000
| conference = Ifremer and IRCN organised a workshop on "Rogue waves", 29–30 November 2000, during SeaTechWeek 2000, Le Quartz, Brest, France
| publisher  = iFremer
| location   = Brest
| access-date= 18 April 2016
}}</ref>

In 2000, British oceanographic vessel [[RRS Discovery (1962)|RRS ''Discovery'']] recorded a {{convert|29|m|adj=on|abbr=on}} wave off the coast of Scotland near [[Rockall]]. This was a scientific research vessel fitted with high-quality instruments. Subsequent analysis determined that under severe gale-force conditions with wind speeds averaging {{convert|21|m/s|kn}}, a ship-borne wave recorder measured individual waves up to {{convert|29.1|m|ft|1|abbr=on}} from crest to trough, and a maximum SWH of {{convert|18.5|m|ft|1|abbr=on}}. These were some of the largest waves recorded by scientific instruments up to that time. The authors noted that modern wave prediction models are known to significantly under-predict extreme sea states for waves with a ''significant'' height (H<sub>s</sub>) above {{convert|12|m|ft|1|abbr=on}}. The analysis of this event took a number of years and noted that "none of the state-of-the-art weather forecasts and wave models{{px2}}{{mdash}}{{hsp}}the information upon which all ships, oil rigs, fisheries, and passenger boats rely{{px2}}{{mdash}}{{hsp}}had predicted these behemoths." In simple terms, a scientific model (and also ship design method) to describe the waves encountered did not exist. This finding was widely reported in the press, which reported that "according to all of the theoretical models at the time under this particular set of weather conditions, waves of this size should not have existed".<ref name="Econ1"/><ref name="Rockall"/><ref name="TheWeek">{{cite web
| url        = http://theweek.com/articles/490823/last-word-terrors-sea
| title      = The last word: Terrors of the sea
| date       = 27 September 2010
| website    = theweek.com
| access-date= 15 January 2016
}}</ref><ref name="Casey2010">{{cite book
| author     = Susan Casey
| title      = The Wave: In the Pursuit of the Rogues, Freaks and Giants of the Ocean
| url        = https://archive.org/details/wave00susa
| url-access = registration
| year       = 2010
| publisher  = Doubleday Canada
| isbn       = 978-0-385-66667-1}}</ref><ref name="RRS Discovery">{{cite journal
| last1       = Holliday
| first1      = N.P.
| last2      = Yelland
| first2     = M.Y.
| last3      = Pascal
| first3     = R.
| last4      = Swail
| first4     = V.
| last5      = Taylor
| first5     = P.K.
| last6      = Griffiths
| first6     = C.R.
| last7      = Kent
| first7     = E.C.
| date       = 2006
| title      = Were extreme waves in the Rockall Trough the largest ever recorded?
| journal    = Geophysical Research Letters
| volume     = 33
| issue      = 5
| pages      = L05613
| bibcode    =2006GeoRL..33.5613H
| doi        = 10.1029/2005gl025238
| quote      = In February 2000 those onboard a British oceanographic research vessel near Rockall, west of Scotland experienced the largest waves ever recorded by scientific instruments in the open ocean. Under severe gale force conditions with wind speeds averaging 21 ms1 a shipborne wave recorder measured individual waves up to 29.1 m from crest to trough, and a maximum significant wave height of 18.5 m. The fully formed sea developed in unusual conditions as westerly winds blew across the North Atlantic for two days, during which time a frontal system propagated at a speed close to the group velocity of the peak waves. The measurements are compared to a wave hindcast that successfully simulated the arrival of the wave group, but underestimated the most extreme waves.| doi-access= free
}}</ref>

In 2004, the [[ESA]] MaxWave project identified more than 10 individual giant waves above {{convert|25|m|abbr=on}} in height during a short survey period of three weeks in a limited area of the South Atlantic.<ref name = 'SEASAR 2006'/><ref name = 'ESA2004'>{{cite web
| url        = http://m.esa.int/Our_Activities/Observing_the_Earth/Ship-sinking_monster_waves_revealed_by_ESA_satellites
| title      = Observing the Earth: Ship-Sinking Monster Waves revealed by ESA Satellites
| date       = 21 July 2004
| website    = www.ESA.int
| publisher  = ESA
| access-date= 14 January 2016
}}</ref> By 2007, it was further proven via satellite radar studies that waves with crest-to-trough heights of {{convert|20|to|30|m|ft|0|abbr=on}} occur far more frequently than previously thought.<ref name="SmithConference">{{cite conference
| url        = http://www.shipstructure.org/pdf/2007symp09.pdf
| title      = Extreme Waves and Ship Design
| first      = Craig
| last       = Smith
| year       = 2007
| conference = 10th International Symposium on Practical Design of Ships and Other Floating Structures
| publisher  = American Bureau of Shipping
| location   = Houston
| pages      = 8
| access-date= 13 January 2016
| quote      = Recent research has demonstrated that extreme waves, waves with crest-to-trough heights of 20 to 30 m, occur more frequently than previously thought. }}</ref> Rogue waves are now known to occur in all of the world's oceans many times each day.

Rogue waves are now accepted as a common phenomenon. Professor Akhmediev of the [[Australian National University]] has stated that 10 rogue waves exist in the world's oceans at any moment.<ref name="MyUser_Anu.edu.au_April_16_2016c">{{cite news
| url        = http://www.anu.edu.au/news/all-news/rogue-wave-theory-to-save-ships
| title      = Rogue wave theory to save ships |newspaper=Anu.edu.au
| date       = 29 July 2015
| access-date=  April 16, 2016}}</ref> Some researchers have speculated that roughly three of every 10,000 waves on the oceans achieve rogue status, yet in certain spots{{px2}}{{mdash}}{{hsp}}such as coastal inlets and river mouths{{px2}}{{mdash}}{{hsp}}these extreme waves can make up three of every 1,000 waves, because wave energy can be focused.<ref>{{Cite journal|last1=Janssen|first1=T. T.|last2=Herbers|first2=T. H. C.|date=2009|title=Nonlinear Wave Statistics in a Focal Zone|journal=Journal of Physical Oceanography|language=en|volume=39|issue=8|pages=1948–1964|doi=10.1175/2009jpo4124.1|issn=0022-3670|bibcode=2009JPO....39.1948J|doi-access=free}}</ref>

Rogue waves may also occur in [[lake]]s. A phenomenon known as the "Three Sisters" is said to occur in [[Lake Superior]] when a series of three large waves forms. The second wave hits the ship's deck before the first wave clears. The third incoming wave adds to the two accumulated backwashes and suddenly overloads the ship deck with large amounts of water. The phenomenon is one of various theorized causes of the sinking of the {{SS|Edmund Fitzgerald}} on Lake Superior in November 1975.<ref name="Wolff">Wolff, Julius F. (1979). "Lake Superior Shipwrecks", p. 28. Lake Superior Marine Museum Association, Inc., Duluth, Minnesota. {{Listed Invalid ISBN|0-932212-18-8}}.</ref>

A 2012 study reported that in addition to the Peregrine soliton reaching up to about 3 times the height of the surrounding sea, a hierarchy of higher order wave solutions could also exist having progressively larger sizes, and demonstrated the creation of a "super rogue {{nowrap|wave"{{mdash}}}}{{hsp}}a [[breather]] around 5 times higher than surrounding waves{{px2}}{{mdash}}{{hsp}}in a [[water tank]].<ref name=super/> Also in 2012, researchers at the Australian National University proved the existence of "rogue wave holes", an inverted profile of a rogue wave. Their research created rogue wave holes on the water surface in a water-wave tank.<ref name="MyUser_Onlinelibrary.wiley.com_April_16_2016c">{{cite journal
| last1       = Chabchoub
| first1      = A.
| last2      = Hoffmann
| first2     = N. P.
| last3      = Akhmediev
| first3     = N.
| date       = 1 February 2012
| title      = Observation of rogue wave holes in a water wave tank
| journal    = Journal of Geophysical Research: Oceans
| volume     = 117
| issue      = C11
| pages      = C00J02
| doi=10.1029/2011JC007636| bibcode= 2012JGRC..117.0J02C
 | doi-access= 
}}</ref> In maritime [[folklore]], stories of rogue holes are as common as stories of rogue waves. They had followed from theoretical analysis but had never been proven experimentally.

"Rogue wave" has become a near-universal term used by scientists to describe isolated, large-amplitude waves that occur more frequently than expected for normal, Gaussian-distributed, statistical events. Rogue waves appear ubiquitous and are not limited to the oceans. They appear in other contexts and have recently been reported in liquid helium, nonlinear optics, and microwave cavities. Marine researchers universally now accept that these waves belong to a specific kind of sea wave, not considered by conventional models for sea wind waves.<ref name="2008AnnualReview">{{cite journal
| last1      = Dysthe
| first1     = K.
| last2      = Krogstad
| first2     = H.
| last3      = Müller
| first3     = P.
| date       = 2008
| title      = Oceanic Rogue Waves
| journal = Annual Review of Fluid Mechanics
| volume = 40
| issue = 1
| pages      = 287–310
|doi=10.1146/annurev.fluid.40.111406.102203 
 | bibcode = 2008AnRFM..40..287D
}}</ref><ref name="2003Physical">{{cite journal
| last1      = Kharif
| first1     = C.
| last2      = Pelinovsky
| first2     = E.
| date       = 2003
| title      = Physical mechanisms of the rogue wave phenomenon
| journal    = European Journal of Mechanics B
| volume     = 22
| issue      = 6
| pages      = 603–634
| doi        = 10.1016/j.euromechflu.2003.09.002
| bibcode= 2003EuJMB..22..603K| citeseerx      = 10.1.1.538.58
 | s2cid = 45789714
}}</ref><ref name="2013Generating">{{cite journal
| last1      = Onorato
| first1     = M.
| last2      = Residori
| first2     = S.|author2-link=Stefania Residori
| last3      = Bortolozzo
| first3     = U.
| last4      = Montina
| first4     = A.
| last5      = Arecchi
| first5     = F.
| date       = 10 July 2013
| title      = Rogue waves and their generating mechanisms in different physical contexts
| journal    = Physics Reports
| volume     = 528
| issue      = 2
| pages      = 47–89
| doi=10.1016/j.physrep.2013.03.001
| bibcode= 2013PhR...528...47O}}</ref><ref name="Rogue_waters">{{cite journal
| last1      = Slunyaev
| first1     = A.
| last2      = Didenkulova
| first2     = I.
| last3      = Pelinovsky
| first3     = E.
| date       = November 2011
| title      = Rogue waters
| url        = https://www.scopus.com/record/display.uri?eid=2-s2.0-84856290502&origin=inward&txGid=0
| journal    = Contemporary Physics
| volume     = 52
| issue      = 6
| pages      = 571–590
| doi        = 10.1080/00107514.2011.613256
| access-date=16 April 2016| arxiv= 1107.5818| bibcode= 2011ConPh..52..571S| s2cid = 118626912
}}</ref> A 2015 paper studied the wave behavior around a rogue wave, including optical and the Draupner wave, and concluded, "rogue events do not necessarily appear without warning but are often preceded by a short phase of relative order".<ref>[http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.213901 Predictability of Rogue Events], Simon Birkholz, Carsten Brée, Ayhan Demircan, and Günter Steinmeyer, ''Physical Review Letters'' 114, 213901, 28 May 2015</ref>

In 2019, researchers succeeded in producing a wave with similar characteristics to the Draupner wave (steepness and breaking), and proportionately greater height, using multiple [[Wave packet|wavetrain]]s meeting at an angle of 120°. Previous research had strongly suggested that the wave resulted from an interaction between waves from different directions ("crossing seas"). Their research also highlighted that wave-breaking behavior was not necessarily as expected. If waves met at an angle less than about 60°, then the top of the wave "broke" sideways and downwards (a "plunging breaker"). Still, from about 60° and greater, the wave began to break vertically upwards, creating a peak that did not reduce the wave height as usual but instead increased it (a "vertical jet"). They also showed that the steepness of rogue waves could be reproduced in this manner. Lastly, they observed that optical instruments such as the laser used for the Draupner wave might be somewhat confused by the spray at the top of the wave if it broke, and this could lead to uncertainties of around {{convert|1.0|to|1.5|m|ft|0|abbr=on}} in the wave height. They concluded, "... the onset and type of wave breaking play a significant role and differ significantly for crossing and noncrossing waves. Crucially, breaking becomes less crest-amplitude limiting for sufficiently large crossing angles and involves the formation of near-vertical jets".<ref name="McAllister 2019">[https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/laboratory-recreation-of-the-draupner-wave-and-the-role-of-breaking-in-crossing-seas/65EA3294DAFD97A50C8046140B45F759 Laboratory recreation of the Draupner wave and the role of breaking in crossing seas – McAllister ''et al'' – ''Journal of Fluid Mechanics'', 2019, vol. 860, pp. 767–786, pub. Cambridge University Press], {{doi|10.1017/jfm.2018.886}}</ref><ref name="McAllister 2019 media report">{{Cite web|url=https://arstechnica.com/science/2019/01/oxford-scientists-successfully-recreated-a-famous-rogue-wave-in-the-lab|title=Oxford scientists successfully recreated a famous rogue wave in the lab|date=24 January 2019}}</ref>

[[File:Rogue waves breaking behavior at different crossing angles, McAllister 2019.png|thumb|600px|centre|Images from the 2019 simulation of the Draupner wave show how the steepness of the wave forms, and how the crest of a rogue wave breaks when waves cross at different angles. ''(Click image for full resolution)''
<ul><li>In the first row (0°), the crest breaks horizontally and plunges, limiting the wave size.</li>
<li>In the middle row (60°), somewhat upward-lifted breaking behavior occurs.</li>
<li>In the third row (120°), described as the most accurate simulation achieved of the Draupner wave, the wave breaks ''upward'', as a vertical jet, and the wave crest height is not limited by breaking.</li></ul>]]