Editing Rogue wave

{{short description|Unexpectedly large transient ocean surface wave}}
{{About|the natural phenomenon}}
[[File: Wea00800,1.jpg|thumb|upright=1.2|A [[merchant ship]] in heavy seas as a large wave looms ahead, [[Bay of Biscay]], {{circa|1940}}]]

'''Rogue waves''' (also known as '''freak waves''' or '''killer waves''') are large and unpredictable [[surface wave]]s that can be extremely dangerous to ships and isolated structures such as [[lighthouses]].<ref name="Econ1">{{cite news|access-date=2009-10-04 |date=September 17, 2009 |newspaper=[[The Economist]] |title=Rogue Waves – Monsters of the Deep: Huge, freak waves may not be as rare as once thought |url=http://www.economist.com/sciencetechnology/displaystory.cfm?story_id=14446734}}</ref> They are distinct from [[tsunami]]s, which are long wavelength waves, often almost unnoticeable in deep waters and are caused by the displacement of water due to other phenomena (such as [[earthquake]]s). A rogue wave at the shore is sometimes called a ''[[sneaker wave]]''.<ref>{{Cite web
| title=What Is a Sneaker Wave?
| date=3 April 2019
| url=https://www.worldatlas.com/articles/what-is-a-sneaker-wave.html
| publisher=[[WorldAtlas]]
| access-date=2020-07-29}}</ref>

In [[oceanography]], rogue waves are more precisely defined as waves whose [[wave height|height]] is more than twice the [[significant wave height]] (''H''{{sub|s}} or SWH), which is itself defined as the mean of the largest third of waves in a wave record. Rogue waves do not appear to have a single distinct cause but occur where physical factors such as high winds and strong currents cause waves to merge to create a single large wave.<ref name="Econ1"/> Research published in 2023 suggests [[sea state]] crest-trough correlation leading to linear [[Superposition principle|superposition]] may be a dominant factor in predicting the frequency of rogue waves.<ref>{{cite journal |last1=Häfner |first1=Dion |last2=Gemmrich |first2=Johannes |last3=Jochum |first3=Markus |title=Machine-guided discovery of a real-world rogue wave model |journal= Proceedings of the National Academy of Sciences|date=20 November 2023 |volume=120 |issue=48 |pages=e2306275120 |doi=10.1073/pnas.2306275120 |doi-access=free |pmid=37983488 |pmc=10691345 |arxiv=2311.12579 |bibcode=2023PNAS..12006275H }}</ref>

Among other causes, studies of [[non-linear system|nonlinear]] waves such as the [[Peregrine soliton]], and waves modeled by the [[nonlinear Schrödinger equation]] (NLS), suggest that [[modulational instability]] can create an unusual [[sea state]] where a "normal" wave begins to draw energy from other nearby waves, and briefly becomes very large. Such phenomena are not limited to water and are also studied in liquid helium, nonlinear optics, and microwave cavities. A 2012 study reported that in addition to the Peregrine soliton reaching up to about three 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 wave" (a [[breather]] around five times higher than surrounding waves) in a [[Wave tank|water-wave tank]].<ref name=super>{{cite journal |last1=Chabchoub |first1=A. |last2=Hoffmann |first2=N. |last3=Onorato |first3=M. |last4=Akhmediev |first4=N. |title=Super Rogue Waves: Observation of a Higher-Order Breather in Water Waves |url=https://www.proquest.com/openview/6e84fa9d48494ef57c4a54ad8a6c8ca6 |journal=Physical Review X |date=29 March 2012 |volume=2 |issue=1 |page=011015 |doi=10.1103/PhysRevX.2.011015|bibcode=2012PhRvX...2a1015C |hdl=1885/67997 |hdl-access=free }}</ref>

A 2012 study supported the existence of oceanic rogue holes, the inverse of rogue waves, where the depth of the hole can reach more than twice the significant wave height.<ref name="MyUser_Onlinelibrary.wiley.com_April_16_2016c"/> Although it is often claimed that rogue holes have never been observed in nature despite replication in wave tank experiments, there is a rogue hole recording from an oil platform in the North Sea, revealed in Kharif et al.<ref>{{cite book | url=https://link.springer.com/book/10.1007/978-3-540-88419-4 | doi=10.1007/978-3-540-88419-4 | title=Rogue Waves in the Ocean | series=Advances in Geophysical and Environmental Mechanics and Mathematics | date=2009 | isbn=978-3-540-88418-7 }}</ref> The same source also reveals a recording of what is known as the 'Three Sisters'.

== Background ==
[[File:Tsunami by hokusai 19th century.jpg|thumb|right|Although commonly described as a [[tsunami]], the titular wave in ''[[The Great Wave off Kanagawa]]'' by [[Hokusai]] is more likely an example of a large rogue wave.]]
Rogue waves are waves in open water that are much larger than surrounding waves. More precisely, rogue waves have a [[wave height|height]] which is more than twice the [[significant wave height]] (''H''{{sub|s}} or SWH). They can be caused when [[Current (fluid)|currents]] or [[wind]]s cause waves to travel at different speeds, and the waves [[Constructive interference|merge]] to create a single large wave; or when [[non-linearity|nonlinear effects]] cause energy to move between waves to create a single extremely large wave.

Once considered mythical and lacking hard evidence, rogue waves are now proven to exist and are known to be natural ocean phenomena. Eyewitness accounts from mariners and damage inflicted on ships have long suggested they occur. Still, the first scientific evidence of their existence came with the recording of a rogue wave by the [[Gorm Field|Gorm platform]] in the central [[North Sea]] in 1984. A stand-out wave was detected with a wave height of {{convert|11|m|abbr=on}} in a relatively low sea state.<ref name="MyUser_Soest.hawaii.edu_April_16_2016c" /> However, what caught the attention of the scientific community was the digital measurement of a rogue wave at the [[Draupner platform]] in the North Sea on January 1, 1995; called the "[[Draupner wave]]", it had a recorded maximum wave height of {{convert|25.6|m|abbr=on}} and peak elevation of {{convert|18.5|m|abbr=on}}. During that event, minor damage was inflicted on the platform far above sea level, confirming the accuracy of the wave-height reading made by a downwards pointing laser sensor.<ref name="haver2003freak">{{Cite report
 |author       = Haver, Sverre
 |date         = 2003
 |title        = Freak wave event at Draupner jacket January 1 1995
 |url          = http://www.ifremer.fr/web-com/stw2004/rogue/pres/Session_3.2/Haver_Draupner.pdf
 |publisher    = Statoil, Tech. Rep. PTT-KU-MA
 |access-date  = 2015-06-03
 |archive-date = 2015-11-07
 |archive-url  = https://web.archive.org/web/20151107183601/http://www.ifremer.fr/web-com/stw2004/rogue/pres/Session_3.2/Haver_Draupner.pdf
 |url-status   = dead
}}</ref>

The existence of rogue waves has since been confirmed by video and photographs, [[satellite imagery]], radar of the ocean surface,<ref>{{Cite news
 | url        = http://news.bbc.co.uk/2/hi/science/nature/3917539.stm
 | publisher  = [[BBC News]]
 | title      = Freak waves spotted from space
 | date       = July 22, 2004
 | access-date = May 22, 2010}}</ref> stereo wave imaging systems,<ref name=":0">{{Cite journal|last1=Benetazzo|first1=Alvise|last2=Barbariol|first2=Francesco|last3=Bergamasco|first3=Filippo|last4=Torsello|first4=Andrea|last5=Carniel|first5=Sandro|last6=Sclavo|first6=Mauro|date=2015-06-22|title=Observation of Extreme Sea Waves in a Space–Time Ensemble|journal=[[Journal of Physical Oceanography]]|volume=45|issue=9|pages=2261–2275|doi=10.1175/JPO-D-15-0017.1|issn=0022-3670|bibcode=2015JPO....45.2261B|hdl=10278/3661049|s2cid=128962800 |hdl-access=free}}</ref> pressure transducers on the sea-floor, and oceanographic research vessels.<ref name="MyUser_Glerl.noaa.gov_April_16_2016c"/> In February 2000, a British oceanographic research vessel, the [[RRS Discovery (1962)|RRS ''Discovery'']], sailing in the [[Rockall Trough]] west of Scotland, encountered the largest waves ever recorded by any scientific instruments in the open ocean, with an SWH of {{convert|18.5|m|ft}} and individual waves up to {{convert|29.1|m|ft}}.<ref name="Rockall">{{Cite journal|title=Were extreme waves in the Rockall Trough the largest ever recorded? |date=March 2006 |doi=10.1029/2005GL025238 |bibcode=2006GeoRL..33.5613H |volume=33 |issue = 5|pages=L05613 |journal=[[Geophysical Research Letters]] | last1 = Holliday | first1 = Naomi P.|doi-access=free }}</ref> In 2004, scientists using three weeks of radar images from [[European Space Agency]] satellites found ten rogue waves, each {{convert|25|m|ft}} or higher.<ref name="Laird1">{{Cite journal
| url     = https://apps.dtic.mil/sti/pdfs/ADA462573.pdf
| archive-url = https://web.archive.org/web/20130408131805/http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA462573
| url-status = live
| archive-date = April 8, 2013
| title   = Observed Statistics of Extreme Waves
| author  = Laird, Anne Marie
| journal = Doctoral Dissertation, Monterey, California Naval Postgraduate School
| date    = December 2006
| pages   = 2}}</ref>

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 out at sea.<ref name="Econ1" /> Rogue waves are considered rare, but potentially very dangerous, since they can involve the spontaneous formation of massive waves far beyond the usual expectations of [[ship design]]ers, and can overwhelm the usual capabilities of ocean-going vessels which are not designed for such encounters. Rogue waves are, therefore, distinct from [[tsunami]]s.<ref name="Econ1" /> Tsunamis are caused by a massive displacement of water, often resulting from [[earthquake|sudden movement]]s of the [[ocean floor]], after which they propagate at high speed over a wide area. They are nearly unnoticeable in deep water and only become dangerous as they approach the shoreline and the ocean floor becomes shallower;<ref>{{Cite web
| url         = http://wcatwc.arh.noaa.gov/?page=tsunami_science
| title       = Physics of Tsunamis
| date        = 27 January 2016
| website     = NOAA.gov
| access-date = 29 January 2016
| publisher   = [[United States Department of Commerce]]
| quote       = They cannot be felt aboard ships, nor can they be seen from the air in the open ocean.}}</ref> therefore, tsunamis do not present a threat to shipping at sea (e.g., the only ships lost in the [[2004 Indian Ocean earthquake|2004 Asian tsunami]] were in port.). These are also different from the wave known as a "[[hundred-year wave]]", which is a purely [[statistics|statistical]] description of a particularly high wave with a 1% chance to occur in any given year in a particular body of water.

Rogue waves have now been proven to cause the sudden loss of some ocean-going vessels. Well-documented instances include the freighter [[MS München|MS ''München'']], lost in 1978.<ref name="BBCFreak" /> Rogue waves have been implicated in the loss of other vessels, including the ''[[Ocean Ranger]]'', a [[semisubmersible]] mobile [[oil platform|offshore drilling unit]] that sank in Canadian waters on 15 February 1982.<ref name="(Canada)1985">{{Cite book
 | author     = Royal Commission on the Ocean Ranger Marine Disaster (Canada)
 | title      = Safety offshore Eastern Canada, summary of studies & seminars
 | url        = https://books.google.com/books?id=iv7bAAAAMAAJ
 | year       = 1985
 | publisher  = The Commission| isbn = 9780660118277
 }}</ref> In 2007, the United States' [[National Oceanic and Atmospheric Administration]] (NOAA) compiled a catalogue of more than 50 historical incidents probably associated with rogue waves.<ref name="chron">{{Cite journal
 | last       = Liu
 | first      = Paul C.
 | year       = 2007
 | title      = A Chronology of Freaque Wave Encounters
 | journal    = Geofizika
 | volume     = 24
 | issue      = 1
 | pages      = 57–70
 | url        = http://www.glerl.noaa.gov/pubs/fulltext/2007/20070019.pdf
 | access-date = October 8, 2012}}</ref>

== History of rogue wave knowledge ==

=== Early reports ===

In 1826, French scientist and naval officer [[Jules Dumont d'Urville]] reported waves as high as {{convert|33|m|ft|0|abbr=on}} in the Indian Ocean with three colleagues as witnesses, yet he was publicly ridiculed by fellow scientist [[François Arago]]. In that era, the thought was widely held that no wave could exceed {{convert|9|m|ft|0|abbr=on}}.<ref name="Parker2012">{{cite book
 | author     = Bruce Parker
 | title      = The Power of the Sea: Tsunamis, Storm Surges, Rogue Waves, and Our Quest to Predict Disasters
 | url        = https://books.google.com/books?id=zzlNJFc4vngC
 | year       = 2012
 | publisher  = [[St. Martin's Press]]
 | isbn       = 978-0-230-11224-7}}</ref><ref name="Jones2008">{{cite book
 |author1      = Ian Jones
 |author2      = Joyce Jones
 |title        = Oceanography in the Days of Sail
 |page         = 115
 |url          = http://www.sims.org.au/wp-content/uploads/2013/03/ECODS-b5-12-1-10.pdf
 |date         = 2008
 |publisher    = [[Hale & Iremonger]]
 |isbn         = 978-0-9807445-1-4
 |quote        = Dumont d'Urville, in his narrative, expressed the opinion that the waves reached a height of 'at least 80 to 100 feet'. In an era when opinions were expressed that no wave would exceed 30 feet, Dumont d'Urville's estimations were received, with some skepticism. No one was more outspoken in his rejection than François Arago, who, calling for a more scientific approach to the estimation of wave height in his instructions for the physical research on the voyage of the ''Bonité'', suggested that imagination played a part in estimations as high as '33 metres' (108 feet). Later, in his 1841 report on the results of the'' Vénus'' expedition, Arago made further reference to the 'truly prodigious waves with which the lively imagination of certain navigators delights in covering the seas'
 |access-date  = 2016-01-15
 |archive-url  = https://web.archive.org/web/20160302232557/http://www.sims.org.au/wp-content/uploads/2013/03/ECODS-b5-12-1-10.pdf
 |archive-date = 2016-03-02
 |url-status     = dead
}}</ref> Author [[Susan Casey]] wrote that much of that disbelief came [[Survivorship bias|because there were very few people who had seen a rogue wave and survived]]; until the advent of steel [[Double hull|double-hulled ships]] of the 20th century, "people who encountered {{convert|100|ft|m|adj=on|disp=sqbr}} rogue waves generally weren't coming back to tell people about it."<ref>{{cite web|url=http://www.salon.com/2010/09/26/the_wave_susan_casey_interview/|title='The Wave': The growing danger of monster waves|date=26 September 2010|work=[[salon.com]]|access-date=26 March 2018}}</ref>

=== Pre-1995 research ===

Unusual waves have been studied scientifically for many years (for example, [[John Scott Russell]]'s [[wave of translation]], an 1834 study of a [[soliton]] wave). Still, these were not linked conceptually to sailors' stories of encounters with giant rogue ocean waves, as the latter were believed to be scientifically implausible.

Since the 19th century, oceanographers, meteorologists, engineers, and ship designers have used a statistical [[mathematical model|model]] known as the [[Gaussian function]] (or Gaussian Sea or standard linear model) to predict wave height, on the assumption that wave heights in any given sea are tightly grouped around a central value equal to the average of the largest third, known as the [[significant wave height]] (SWH).<ref name="SoaresSantos2014">{{cite book
 | author1    = Carlos Guedes Soares
 | author2    = T.A. Santos
 | title      = Maritime Technology and Engineering
 | url        = https://books.google.com/books?id=kg7NBQAAQBAJ
 | year       = 2014
 | publisher  = [[CRC Press]]
 | isbn       = 978-1-315-73159-9}}</ref> In a storm sea with an SWH of {{convert|12|m|ft|0|abbr=on}}, the model suggests hardly ever would a wave higher than {{convert|15|m|ft|0|abbr=on}} occur. It suggests one of {{convert|30|m|ft|0|abbr=on}} could indeed happen, but only once in 10,000 years. This basic assumption was well accepted, though acknowledged to be an approximation. Using a Gaussian form to model waves has been the sole basis of virtually every text on that topic for the past 100 years.<ref name="SoaresSantos2014"/><ref name="MyUser_Chl.erdc.usace.army.mil_April_16_2016c">{{cite web
 |url         = http://chl.erdc.usace.army.mil/library/publications/chetn/pdf/cetn-i-60.pdf
 |title       = US Army Engineer Waterways Experimental Station: Coastal Engineering Technical Note CETN I-60
 |newspaper   = Chl.erdc.usace.army.mil
 |date        = March 1995
 |access-date  = April 16, 2016
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20130221213453/http://chl.erdc.usace.army.mil/library/publications/chetn/pdf/cetn-i-60.pdf
 |archive-date = February 21, 2013
}}</ref>{{when|date=September 2020}}{{Why|date=November 2024}}

The first known scientific article on "freak waves" was written by Professor Laurence Draper in 1964. In that paper, he documented the efforts of the [[National Oceanography Centre|National Institute of Oceanography]] in the early 1960s to record wave height, and the highest wave recorded at that time, which was about {{convert|67|ft|m|0|order=flip}}. Draper also described ''freak wave holes''.<ref name="Draper1">{{cite journal |last=Draper |first=Laurence |date=July 1964 |title='Freak' Ocean Waves |url=https://archive.org/details/oceanusv1004wood/page/12/mode/2up |journal=[[Oceanus]] |volume=10 |issue=4 |pages=12–15 |via=The Internet Archive}}</ref><ref name="Proceedings">{{Cite book
 | url        = https://books.google.com/books?id=D1VWoCgPTJMC
 | title      = Rogue Waves 2004: Proceedings of a Workshop Organized by Ifremer and Held in Brest, France, 20-21-22 October 2004, Within the Brest Sea Tech Week 2004
 | author     = Michel Olagnon, Marc Prevosto
 | year  =  2004
 | pages      = viii| publisher = Editions Quae
 | isbn     = 9782844331502
 }}</ref><ref name="Draper2">{{cite journal
 | last       = Draper
 | first      = Laurence
 | date       = July 1971
 | title      = Severe Wave Conditions at Sea
 | url        = http://www.ifremer.fr/web-com/stw2004/rw/fullpapers/draper.pdf
 | journal    = [[Journal of the Institute of Navigation]]
 | volume     = 24
 | issue      = 3
 | pages      = 274–277
 | doi=10.1017/s0373463300048244| bibcode = 1971JNav...24..273D
 | s2cid = 131050298
 }}</ref>

=== Research on cross-swell waves and their contribution to rogue wave studies ===
Before the Draupner wave was recorded in 1995, early research had already made significant strides in understanding extreme wave interactions. In 1979, Dik Ludikhuize and Henk Jan Verhagen at [[Delft University of Technology|TU Delft]] successfully generated cross-swell waves in a wave basin. Although only monochromatic waves could be produced at the time, their findings, reported in 1981, showed that individual wave heights could be added together even when exceeding breaker criteria. This phenomenon provided early evidence that waves could grow significantly larger than anticipated by conventional theories of wave breaking.<ref>{{Cite journal |last1=Ludikhuize |first1=D. |last2=Verhagen |first2=H.J. |date=1981 |title=Cross-swell: A comparison of mathematical derivations with the results of laboratory tests |url=https://repository.tudelft.nl/record/uuid:525da0fd-09ba-40f2-88c6-22faf17ae4b7 |journal=TU Delft Reports |access-date=18 October 2024 |via=[[Delft University of Technology]]}}</ref>

This work highlighted that in cases of crossing waves, wave steepness could increase beyond usual limits. Although the waves studied were not as extreme as rogue waves, the research provided an understanding of how multidirectional wave interactions could lead to extreme wave heights - a key concept in the formation of rogue waves. The crossing wave phenomenon studied in the Delft Laboratory therefore had direct relevance to the unpredictable rogue waves encountered at sea.<ref>{{cite thesis | last1 = Ludikhuize | first1 = D. | last2 = Verhagen | first2 = H.J. | last3 = Bijker | first3 = E.W. | title = Bengkulu Harbour Project | date = 1978 | type = Master's thesis | department = Hydraulic Engineering (CEG) | publisher = [[TU Delft]] | url = http://resolver.tudelft.nl/uuid:b7a0999d-2c4a-42af-96d0-1070087d1452 | access-date = 18 October 2024}}</ref>

Research published in 2024 by TU Delft and other institutions has subsequently demonstrated that waves coming from multiple directions can grow up to four times steeper than previously imagined.<ref>{{Cite journal |last1=McAllister |first1=M. L. |last2=Draycott |first2=S. |last3=Calvert |first3=R. |last4=Davey |first4=T. |last5=Dias |first5=F. |last6=van den Bremer |first6=T. S. |date=2024 |title=Three-dimensional wave breaking |journal=Nature |language=en |volume=633 |issue=8030 |pages=601–607 |doi=10.1038/s41586-024-07886-z |pmid=39294351 |issn=1476-4687 |pmc=11410657 |bibcode=2024Natur.633..601M }}</ref>

=== The 1995 Draupner wave ===
{{Main|Draupner wave}}
[[File:Drauper freak wave.png|thumb|Measured amplitude graph showing the Draupner wave (spike in the middle).  Horizontal axis is seconds relative to a nominal (uncalibrated) start time of 15:20 UTC.]]
The Draupner wave was the first rogue wave to be detected by a [[measuring instrument]]. The wave was recorded in 1995 at Unit E of the [[Draupner platform]], a gas pipeline support complex located in the North Sea about {{cvt|100|miles|km|order=flip}} southwest from the southern tip of Norway.<ref name="TheWeek"/>{{efn|The location of the recording was {{Coord|58|11|19.30|N|2|28|0.00|E|display=inline}}}} 

At 15:24 UTC on 1 January 1995, the device recorded a rogue wave with a maximum [[wave height]] of {{cvt|25.6|m|ft}}. Peak elevation above still water level was {{cvt|18.5|m|ft}}.<ref name=PTaylor2005>{{cite web |url=http://www.icms.org.uk/archive/meetings/2005/roguewaves/presentations/Taylor.pdf |last=Taylor |first=Paul H. |title=The shape of the Draupner wave of 1st January |year=2005 |department=Department of Engineering Science |publisher=University of Oxford |access-date=20 January 2007 |url-status=unfit |archive-url=https://web.archive.org/web/20070810055739/http://www.icms.org.uk/archive/meetings/2005/roguewaves/presentations/Taylor.pdf |archive-date=2007-08-10}}</ref> The reading was confirmed by the other sensors.<ref name="Sciencenordic.com">{{cite web|author1=Bjarne Røsjø, Kjell Hauge|title=Proof: Monster Waves are real|url=http://sciencenordic.com/proof-monster-waves-are-real|publisher=ScienceNordic|date=2011-11-08|quote="Draupner E had only been operating in the North Sea for around half a year, when a huge wave struck the platform like a hammer. When we first saw the data, we were convinced it had to be a technological error," says Per Sparrevik. He is the head of the underwater technology, instrumentation, and monitoring at the Norwegian NGI&nbsp;... but the data were not wrong. When NGI looked over the measurements and calculated the effect of the wave that had hit the platform, the conclusion was clear: The wave that struck the unmanned platform Draupner E on 1 January 1995 was indeed extreme.|access-date=2016-08-23|archive-date=2018-10-18|archive-url=https://web.archive.org/web/20181018055020/http://sciencenordic.com/proof-monster-waves-are-real|url-status=dead}}</ref> In the area, the SWH at the time was about {{cvt|12|m|ft}}, so the Draupner wave was more than twice as tall and steep as its neighbors, with characteristics that fell outside any known wave model. The wave caused enormous interest in the scientific community.<ref name="TheWeek" /><ref name="Sciencenordic.com" />

=== 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>]]

==Extreme rogue wave events==
On 17 November 2020, a buoy moored in {{convert|45|m|0}} of water on [[Amphitrite Bank]] in the Pacific Ocean {{convert|7|km|mi nmi}} off [[Ucluelet]], [[Vancouver Island]], [[British Columbia]], Canada, at {{coord|48.9|N|125.6|W}} recorded a lone {{convert|17.6|m|0|adj=on}} tall wave among surrounding waves about {{convert|6|m|0}} in height.<ref name=gemmrich20220202>{{cite journal|last1=Gemmrich |first1=Johannes |last2=Cicon |first2=Leah | journal=Scientific Reports | title=Generation mechanism and prediction of an observed extreme rogue wave | date=2 February 2022 |volume=12 |issue=1 |page=1718 |doi=10.1038/s41598-022-05671-4 |pmid=35110586 |pmc=8811055 |bibcode=2022NatSR..12.1718G }}</ref> The wave exceeded the surrounding significant wave heights by a factor of 2.93. When the wave's detection was revealed to the public in February 2022, one scientific paper<ref name=gemmrich20220202/> and many news outlets christened the event as "the most extreme rogue wave event ever recorded" and a "once-in-a-millennium" event, claiming that at about three times the height of the waves around it, the Ucluelet wave set a record as the most extreme rogue wave ever recorded at the time in terms of its height in proportion to surrounding waves, and that a wave three times the height of those around it was estimated to occur on average only once every 1,300 years worldwide.<ref>{{cite news| url=https://www.newswire.ca/news-releases/record-breaking-rogue-wave-recorded-off-the-coast-of-vancouver-island-830202783.html | author=MarineLabs | work=Cision | title=Four-story high rogue wave breaks records off the coast of Vancouver Island | date=8 February 2022 | access-date=24 October 2023}}</ref><ref>{{cite news| url=https://www.cnn.com/2022/02/12/weather/rogue-wave-record-vancouver-island/index.html | last1=Kaiser |first1= Caitlin |last2=Sater |first2=Tom | work=CNN | title=Four-story high rogue wave breaks records off the coast of Vancouver Island | date=14 February 2022 | access-date=24 October 2023}}</ref><ref>{{cite news| url=https://www.sciencealert.com/extreme-rogue-wave-in-the-north-pacific-confirmed-as-most-extreme-on-record | last=Cassella |first= Carly | work=ScienceAlert | title=Extreme 'Rogue Wave' in the North Pacific Confirmed as Most Extreme on Record | date=12 January 2023 | access-date=24 October 2023}}</ref>

The Ucluelet event generated controversy. Analysis of scientific papers dealing with rogue wave events since 2005 revealed the claims for the record-setting nature and rarity of the wave to be incorrect. The paper ''Oceanic rogue waves''<ref>{{Cite web | title=(PDF) Oceanic Rogue Waves | url=https://www.researchgate.net/publication/234151195_Oceanic_Rogue_Waves | archive-url=https://web.archive.org/web/20201125042148/https://www.researchgate.net/publication/234151195_Oceanic_Rogue_Waves | access-date=2025-02-26 | archive-date=2020-11-25}}</ref> by Dysthe, Krogstad and Muller reports on an event in the [[Black Sea]] in 2004 which was far more extreme than the Ucluelet wave, where the Datawell Waverider buoy reported a wave whose height was {{convert|10.32|m|2}} higher and 3.91 times the significant wave height, as detailed in the paper. Thorough inspection of the buoy after the recording revealed no malfunction. The authors of the paper that reported the Black Sea event<ref>{{Cite web | title=(PDF) A freak wave in the Black Sea: Observations and simulation | url=https://www.researchgate.net/publication/292873547_A_freak_wave_in_the_Black_Sea_Observations_and_simulation | archive-url=https://web.archive.org/web/20230617003642/https://www.researchgate.net/publication/292873547_A_freak_wave_in_the_Black_Sea_Observations_and_simulation | access-date=2025-02-26 | archive-date=2023-06-17}}</ref> assessed the wave as "anomalous" and suggested several theories on how such an extreme wave may have arisen. The Black Sea event differs in the fact that it, unlike the Ucluelet wave, was recorded with a high-precision instrument. The ''Oceanic rogue waves'' paper also reports even more extreme waves from a different source, but these were possibly overestimated, as assessed by the data's own authors. The Black Sea wave occurred in relatively calm weather.

Furthermore, a paper<ref>{{cite journal | url=https://nhess.copernicus.org/articles/11/2913/2011/ | doi=10.5194/nhess-11-2913-2011 | title=Rogue waves in 2006–2010 | year=2011 | last1=Nikolkina | first1=I. | last2=Didenkulova | first2=I. | journal=Natural Hazards and Earth System Sciences | volume=11 | issue=11 | pages=2913–2924 | bibcode=2011NHESS..11.2913N | doi-access=free }}</ref> by I.&nbsp;Nikolkina and I.&nbsp;Didenkulova also reveals waves more extreme than the Ucluelet wave. In the paper, they infer that in 2006 a {{convert|21|m|0|adj=on}} wave appeared in the Pacific Ocean off the [[Port of Coos Bay]], Oregon, with a significant wave height of {{convert|3.9|m}}. The ratio is 5.38, almost twice that of the Ucluelet wave. The paper also reveals the {{MV|Pont-Aven}} incident as marginally more extreme than the Ucluelet event. The paper also assesses a report of an {{convert|11|m|0|adj=on}} wave in a significant wave height of {{convert|1.9|m}}, but the authors cast doubt on that claim. A paper written by Craig B. Smith in 2007 reported on an incident in the North Atlantic, in which the submarine ''Grouper'' was hit by a 30-meter wave in calm seas.<ref>{{Cite web| title=Extreme Waves and Ship Design | url=http://shipstructure.org/pdf/2007symp09.pdf | archive-url=https://web.archive.org/web/20090106160704/http://www.shipstructure.org/pdf/2007symp09.pdf | archive-date=2009-01-06}}</ref>

== 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&nbsp;– although not on the causes of rogue waves&nbsp;– 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>

== Research efforts ==
{{Expand section|Some universities' names are only listed. No information about their research is provided|date=November 2024}}
A number of research programmes are currently underway or have concluded whose focus is/was on rogue waves, including:
* In the course of Project MaxWave, researchers from the GKSS Research Centre, using data collected by [[ESA]] [[satellite]]s, identified a large number of radar signatures that have been portrayed as evidence for rogue waves. Further research is underway to develop better methods of translating the radar echoes into sea surface elevation, but at present this technique is not proven.<ref name="SEASAR 2006">{{cite web
 | date       = April 2006
 | url        = http://earth.esa.int/workshops/seasar2006/proceedings/papers/s1_5_jan.pdf
 | title      = Critical review on potential use of satellite date to find rogue waves
 | website    = European Space Agency SEASAR 2006 proceedings
 | access-date = February 23, 2008}}</ref><ref>{{cite news
 | date       = 22 July 2004
 | url        = http://news.bbc.co.uk/2/hi/science/nature/3917539.stm
 | title      = Freak waves spotted from space
 | work       = [[BBC News Online]]
 | access-date = May 8, 2006}}</ref>
* The Australian National University, working in collaboration with [[Hamburg University of Technology]] and the [[University of Turin]], have been conducting experiments in nonlinear dynamics to try to explain rogue or killer waves. The "Lego Pirate" video has been widely used and quoted to describe what they call "super rogue waves", which their research suggests can be up to five times bigger than the other waves around them.<ref name="MyUser_Phys.org_April_15_2016c">{{cite web
 | url        = http://phys.org/news/2012-04-lego-pirate-survives-super-rogue.html
 | title      = Lego pirate proves, survives, super rogue wave
 | newspaper  = Phys.org
 | access-date = April 15, 2016}}</ref><ref name="MyUser_Homelandsecuritynewswire.com_April_15_2016c">{{cite press release
 | url        = http://www.homelandsecuritynewswire.com/dr20120406-lego-pirate-proves-survives-super-rogue-wave
 | title      = Maritime security |newspaper=Homelandsecuritynewswire.com
 | access-date = April 15, 2016}}</ref>
* The [[European Space Agency]] continues to do research into rogue waves by radar satellite.<ref name="MyUser_The_New_York_Times_April_15_2016c">{{Cite news|url=https://www.nytimes.com/2006/07/11/science/11wave.html?ei=5090&en=d5cdc1cbc2182342&ex=1310270400&partner=rssuserland&emc=rss&pagewanted=print&_r=0|title=Rogue Giants at Sea|newspaper=[[The New York Times]]|date=July 11, 2006|access-date=April 15, 2016|last1=Broad|first1=William J.}}</ref>
* [[United States Naval Research Laboratory]], the science arm of the Navy and Marine Corps published results of their modelling work in 2015.<ref name="MyUser_The_New_York_Times_April_15_2016c" /><ref name="MyUser_Maritime-executive.com_April_15_2016c">{{cite web
 | url        = http://www.maritime-executive.com/article/deadliest-catch
 | title      = Scientists Model Rogue Waves |newspaper=Maritime-executive.com
 | access-date = April 15, 2016}}</ref><ref name="MyUser_Thenewstribune.com_April_15_2016c">{{cite web
 |url         = http://www.thenewstribune.com/news/business/article69818917.html
 |title       = Mapping a strategy for rogue monsters of the seas
 |newspaper   = [[The News Tribune]]
 |publisher   = Thenewstribune.com
 |access-date  = April 15, 2016
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20160424005636/http://www.thenewstribune.com/news/business/article69818917.html
 |archive-date = April 24, 2016
}}</ref>
* [[Massachusetts Institute of Technology|Massachusetts Institute of Technology(MIT)]]'s research in this field is ongoing. Two researchers there partially supported by the Naval Engineering Education Consortium (NEEC) considered the problem of short-term prediction of rare, extreme water waves and developed and published their research on a predictive tool of about 25 wave periods. This tool can give ships and their crews a two to three-minute warning of a potentially catastrophic impact allowing crew some time to shut down essential operations on a ship (or offshore platform). The authors cite landing on an aircraft carrier as a prime example.<ref name="MyUser_Thenewstribune.com_April_15_2016c" /><ref name="MyUser_Cio.com_April_8_2016c">{{cite web
 |url          = http://www.cio.com/article/3038356/a-new-algorithm-from-mit-could-protect-ships-from-rogue-waves-at-sea.html
 |title        = A new algorithm from MIT could protect ships from 'rogue waves' at sea
 |newspaper    = Cio.com
 |date         = 25 February 2016
 |author       = Katherine Noyes
 |access-date  = April 8, 2016
 |archive-date = 1 April 2016
 |archive-url  = https://web.archive.org/web/20160401121238/http://www.cio.com/article/3038356/a-new-algorithm-from-mit-could-protect-ships-from-rogue-waves-at-sea.html
 |url-status   = dead
}}</ref><ref name="MyUser_Sandlab.mit.edu_April_8_2016c">{{Cite journal
 | url        = http://sandlab.mit.edu/Papers/16_JFM.pdf
 | title      = Reduced-order precursors of rare events in unidirectional nonlinear water waves
 | journal    = Journal of Fluid Mechanics
 | volume     = 790
 | pages      = 368–388
 | date       = 5 January 2016
 | author     = Will Cousins and Themistoklis P. Sapsis
 | access-date = April 8, 2016| doi      = 10.1017/jfm.2016.13
 | bibcode      = 2016JFM...790..368C
 | hdl = 1721.1/101436
 | s2cid = 14763838
 | hdl-access= free
 }}</ref>
* The [[University of Colorado]] and the [[University of Stellenbosch]]<ref name="MyUser_The_New_York_Times_April_15_2016c" /><ref name="MyUser_Education.nationalgeographic.org_April_16_2016c">{{cite web
 |url          = http://education.nationalgeographic.org/news/rogue-waves/
 |title        = Rogue Waves – National Geographic Society
 |newspaper    = Education.nationalgeographic.org
 |date         = 3 December 2012
 |author       = Stuart Thornton
 |access-date  = April 16, 2016
 |archive-date = 13 April 2016
 |archive-url  = https://web.archive.org/web/20160413064546/http://education.nationalgeographic.org/news/rogue-waves/
 |url-status   = dead
}}</ref>
* [[Kyoto University]]<ref name="MyUser_Oceanwave.jp_April_15_2016c">{{cite web
 | url        = http://www.oceanwave.jp/index.php?Introduction
 | title      = Introduction – Nobuhito Mori
 | newspaper  = Oceanwave.jp
 | access-date = April 15, 2016}}</ref>
* [[Swinburne University of Technology]] in Australia recently published work on the probabilities of rogue waves.<ref name="MyUser_Abc.net_April_15_2016c">{{cite web  | url       = http://www.abc.net.au/science/articles/2011/10/06/3332878.htm
 | title      = Freak wave probability higher than thought ' News in Science (ABC Science)
 | newspaper  = Abc.net
 | date       =2011-10-05
 | access-date = April 15, 2016}}</ref>
* The [[University of Oxford]] Department of Engineering Science published a comprehensive review of the science of rogue waves in 2014.<ref name="MyUser_Https:_April_15_2016c">{{cite web
 | url        = https://www.sciencedaily.com/releases/2015/12/151216082200.htm
 | title      = 'Freak' ocean waves hit without warning, new research shows |newspaper=Science Daily
 | access-date = April 15, 2016}}</ref><ref name="Iopscience.iop.org_April_17_2016c">{{Cite journal
 | title      = The physics of anomalous ('rogue') ocean waves
 |journal = Reports on Progress in Physics|volume = 77|issue = 10|pages = 105901| date       = 14 October 2014
 | author     = Thomas A A Adcock and Paul H Taylor
 |doi = 10.1088/0034-4885/77/10/105901|pmid = 25313170|bibcode = 2014RPPh...77j5901A|s2cid = 12737418}}</ref> In 2019, A team from the Universities of Oxford and Edinburgh recreated the Draupner wave in a lab.<ref>{{cite web
 | url        = https://www.sciencealert.com/lab-experiments-recreate-a-devastating-freak-wave-for-the-first-time-and-it-s-beautiful
 | title      = Scientists Recreated a Devastating 'Freak Wave' in The Lab, And It's Weirdly Familiar
 | date       = January 23, 2019
 | author     = Mike McRae
 | access-date= January 25, 2019}}</ref>
* [[University of Western Australia]]<ref name="MyUser_Https:_April_15_2016c" />
* [[Tallinn University of Technology]] in Estonia<ref name="MyUser_Smh.com_April_16_2016c">{{cite web
 | url        = http://www.smh.com.au/national/monster-waves-blamed-for-shipping-disasters-20140811-3dhwk.html
 | title      = Monster waves blamed for shipping disasters
 | newspaper  = Smh.com
 | date       = 11 Aug 2014 
 | author     = Stephen Ornes
 | access-date = April 16, 2016}}</ref>
* ''Extreme Seas Project'' funded by the EU.<ref name="MyUser_Smh.com_April_16_2016c" /><ref name="MyUser_Cordis.europa.eu_April_16_2016c">{{cite web
 | url        = http://cordis.europa.eu/result/rcn/55382_en.html
 | title      = European Commission : CORDIS : Projects & Results Service : Periodic Report Summary – EXTREME SEAS (Design for ship safety in extreme seas)
 | newspaper  = Cordis.europa.eu
 | access-date = April 16, 2016}}</ref>
* At [[Umeå University]] in Sweden, a research group in August 2006 showed that normal [[stochastic]] wind-driven waves can suddenly give rise to monster waves. The nonlinear evolution of the instabilities was investigated by means of direct simulations of the time-dependent system of nonlinear equations.<ref>P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund and L. Stenflo: "Instability and Evolution of Nonlinearly Interacting Water Waves" [https://arxiv.org/abs/nlin.CD/0608012 nlin.CD/0608012], ''Physical Review Letters'' (2006)</ref>
* The [[Great Lakes Environmental Research Laboratory]] did research in 2002, which dispelled the long-held contentions that rogue waves were of rare occurrence.<ref name="MyUser_Glerl.noaa.gov_April_16_2016c">{{cite web
 | url        = http://www.glerl.noaa.gov/res/Task_rpts/2002/ppliu02-3.html
 | title        = Task Report – NOAA Great Lakes Environmental Research Laboratory – Ann Arbor, MI, USA
 | newspaper        = Glerl.noaa.gov
 | access-date        = April 16, 2016
 | archive-date        = October 21, 2018
 | archive-url        = https://web.archive.org/web/20181021104139/https://www.glerl.noaa.gov/res/Task_rpts/2002/ppliu02-3.html
 | url-status        = dead
 }}</ref>
* The [[University of Oslo]] has conducted research into crossing sea state and rogue wave probability during the [[Prestige oil spill|Prestige accident]]; nonlinear wind-waves, their modification by tidal currents, and application to Norwegian coastal waters; general analysis of realistic ocean waves; modelling of currents and waves for sea structures and extreme wave events; rapid computations of steep surface waves in three dimensions, and comparison with experiments; and very large internal waves in the ocean.<ref name="MyUser_Mn.uio.no_April_17_2016c">{{cite web
 | url        = http://www.mn.uio.no/math/english/research/groups/mechanics/
 | title      = Mechanics – Department of Mathematics
 | publisher  = University of Oslo, The Faculty of Mathematics and Natural Sciences
 | date       = 27 January 2016
 | access-date = April 17, 2016}}</ref>
* The [[National Oceanography Centre]] in the United Kingdom<ref>{{Cite journal |last1=Alex |first1=Cattrell |title=Can Rogue Waves Be Predicted Using Characteristic Wave Parameters? |journal=Journal of Geophysical Research: Oceans |volume=123 |issue=8 |pages=5624–5636 |doi=10.1029/2018JC013958 |year=2018 |bibcode=2018JGRC..123.5624C |s2cid=135333238 |url=http://nora.nerc.ac.uk/id/eprint/520662/1/Paper2018JC013958_acceptall_final.pdf }}</ref>
* [[Scripps Institute of Oceanography]] in the United States<ref>{{Cite journal|last1=Barnett|first1=T. P.|last2=Kenyon|first2=K. E.|date=1975|title=Recent advances in the study of wind waves|journal=Reports on Progress in Physics|language=en|volume=38|issue=6|pages=667|doi=10.1088/0034-4885/38/6/001|issn=0034-4885|bibcode=1975RPPh...38..667B|s2cid=250870380 |doi-access=free}}</ref>
* [[Ritmare]] project in Italy.<ref name="Ritmare Project">{{cite web
 | url        =http://www.ritmare.it/en/
 | title      =The RITMARE flagship project
 | access-date = October 11, 2017}}</ref>
* [[University of Copenhagen]] and [[University of Victoria]]<ref>{{Cite web |last=Communication |first=SCIENCE |date=2023-11-20 |title=AI finds formula on how to predict monster waves |url=https://science.ku.dk/english/press/news/2023/ai-finds-formula-on-how-to-predict-monster-waves |access-date=2023-11-27 |website=science.ku.dk |language=en}}</ref>
[[File:Super Rogue Wave.ogv|thumb|alt=Experimental demonstration of rogue wave generation through nonlinear processes (on a small scale) in a wave tank|Experimental demonstration of rogue wave generation through [[nonlinear]] processes (on a small scale) in a [[wave tank]]]]
[[File:Linear evolution of a Gaussian wave envelop.webm|thumb|The linear part solution of the nonlinear [[Schrödinger equation]] describing the evolution of a complex wave envelope in deep water]]

==Other media==
{{See also|Optical rogue waves}}
Researchers at [[UCLA]] observed rogue-wave phenomena in microstructured [[optical fiber]]s near the threshold of soliton [[supercontinuum]] generation and characterized the initial conditions for generating rogue waves in any medium.<ref>{{cite journal
 | author     = R. Colin Johnson
 | title      = EEs Working With Optical Fibers Demystify 'Rogue Wave' Phenomenon
 | journal    = Electronic Engineering Times
 | date       = December 24, 2007|issue=1507
 | pages      = 14, 16
 | url        = http://www.nxtbook.com/nxtbooks/cmp/eetimes122407/index.php?startid=14}}</ref> Research in [[optics]] has pointed out the role played by a Peregrine soliton that may explain those waves that appear and disappear without leaving a trace.<ref>{{cite journal
 | last1      = Kibler|first1=B.
 | last2      = Fatome
 | first2     = J.
 | last3      = Finot
 | first3     = C.
 | last4      = Millot
 | first4     = G.
 | last5      = Dias
 | first5     = F.
 | last6      = Genty
 | first6     = G.
 | last7      = Akhmediev
 | first7     = N.
 | last8      = Dudley |first8= J.M.
 | year       = 2010
 | title      = The Peregrine soliton in nonlinear fibre optics
 | journal    = Nature Physics
 | doi        = 10.1038/nphys1740
 | volume     = 6
 | issue      = 10
 | bibcode    = 2010NatPh...6..790K
 | pages=790–795|citeseerx=10.1.1.222.8599
 |s2cid=16176134
 }}</ref><ref>{{cite web
 | title      = Peregrine's 'Soliton' observed at last
 | publisher  = bris.ac.uk
 | url        = http://www.bris.ac.uk/news/2010/7184.html
 | access-date = 2010-08-24 }}</ref>

Rogue waves in other media appear to be ubiquitous and have also been reported in liquid [[helium]], in quantum mechanics,<ref>{{cite journal |last1=Bayındır |first1=Cihan |year=2020 |title=Rogue quantum harmonic oscillations |url=https://www.sciencedirect.com/science/article/pii/S0378437120301965 |journal=Physica A: Statistical Mechanics and Its Applications |volume=547 |page=124462 |arxiv=1902.08823 |bibcode=2020PhyA..54724462B |doi=10.1016/j.physa.2020.124462 |s2cid=118829011}}</ref> in [[Optical rogue waves|nonlinear optics]], in microwave cavities,<ref name="Kuhl 2010">{{cite journal |last=Höhmann |first=R. |display-authors=etal |date=2010 |title=Freak Waves in the Linear Regime: A Microwave Study |journal=Phys. Rev. Lett. |volume=104 |issue=9 |page=093901 |arxiv=0909.0847 |bibcode=2010PhRvL.104i3901H |doi=10.1103/physrevlett.104.093901 |issn=0031-9007 |pmid=20366984 |s2cid=33924953}}</ref> in [[Bose–Einstein condensate]],<ref>{{cite journal |last1=Zhao |first1=Li-Chen |year=2013 |title=Dynamics of nonautonomous rogue waves in Bose–Einstein condensate |url=https://www.sciencedirect.com/science/article/pii/S0003491612001716 |journal=Annals of Physics |volume=329 |pages=73–79 |bibcode=2013AnPhy.329...73Z |doi=10.1016/j.aop.2012.10.010}}</ref> in heat and diffusion,<ref>{{cite journal |last1=Bayindir |first1=Cihan |year=2020 |title=Rogue heat and diffusion waves |url=https://www.sciencedirect.com/science/article/pii/S0960077920304446 |journal=Chaos, Solitons & Fractals |volume=139 |page=110047 |arxiv=1907.09989 |bibcode=2020CSF...13910047B |doi=10.1016/j.chaos.2020.110047 |s2cid=198179703}}</ref> and in finance.<ref>{{cite journal |last1=Yan |first1=Zhen-Ya |year=2010 |title=Financial Rogue Waves |url=https://iopscience.iop.org/article/10.1088/0253-6102/54/5/31 |journal=Communications in Theoretical Physics |volume=54 |issue=5 |pages=947–949 |arxiv=0911.4259 |bibcode=2010CoTPh..54..947Y |doi=10.1088/0253-6102/54/5/31 |s2cid=118728813}}</ref><ref name="Onorato 2013">{{cite journal |last=Onorato |first=M. |display-authors=etal |year=2013 |title=Rogue waves and their generating mechanisms in different physical contexts |journal=Physics Reports |volume=528 |issue=2 |pages=47–89 |bibcode=2013PhR...528...47O |doi=10.1016/j.physrep.2013.03.001 |issn=0370-1573}}</ref>

== Reported encounters ==
{{Main|List of rogue waves}}
Many of these encounters are reported only in the media, and are not examples of open-ocean rogue waves. Often, in popular culture, an endangering huge wave is loosely denoted as a "rogue wave", while the case has not been established that the reported event is a rogue wave in the scientific sense&nbsp;– ''i.e.'' of a very different nature in characteristics as the surrounding waves in that sea state] and with a very low probability of occurrence.

This section lists a limited selection of notable incidents.

===19th century===
* [[Eagle Island lighthouse]] (1861)&nbsp;– Water broke the glass of the structure's east tower and flooded it, implying a wave that surmounted the {{convert|40|m|ft|abbr=on}} cliff and overwhelmed the {{convert|26|m|ft|abbr=on}} tower.<ref>{{cite web
 | url        = http://www.commissionersofirishlights.com/cil/aids-to-navigation/lighthouses/eagle-island.aspx
 | title      = Eagle Island Lighthouse
 | publisher  = Commissioners of Irish Lights
 | access-date = 28 October 2010 }}</ref>
* [[Flannan Isles Lighthouse]] (1900)&nbsp;– Three lighthouse keepers vanished after a storm that resulted in wave-damaged equipment being found {{Convert|34|m|ft|abbr=on}} above sea level.<ref name=Smith>{{Haswell-Smith| 329–31}}</ref><ref>Munro, R.W. (1979) ''Scottish Lighthouses''. Stornoway. Thule Press. {{ISBN|0-906191-32-7}}. Munro (1979) pages 170–1</ref>

===20th century===
* [[SS Kronprinz Wilhelm|SS ''Kronprinz Wilhelm'']], September 18, 1901&nbsp;– The most modern German ocean liner of its time (winner of the [[Blue Riband]]) was damaged on its maiden voyage from Cherbourg to New York by a huge wave. The wave struck the ship head-on.<ref>''[[The New York Times]]'', September 26, 1901, p. 16</ref>
* [[RMS Lusitania|RMS ''Lusitania'']] (1910)&nbsp;– On the night of 10 January 1910, a {{convert|75|ft|m|adj=on|order=flip|abbr=on}} wave struck the ship over the bow, damaging the forecastle deck and smashing the bridge windows.<ref>{{cite web|url=http://freaquewaves.blogspot.com/2009/12/encounter-of-rms-lusitania.html|title=Freaque Waves: The encounter of RMS Lusitania|last=Freaquewaves|date=17 December 2009|website=freaquewaves.blogspot.com|access-date=26 March 2018}}</ref>
* [[Voyage of the James Caird|Voyage of the ''James Caird'']] (1916)&nbsp;– [[Sir Ernest Shackleton]] encountered a wave he termed "gigantic" while piloting a lifeboat from [[Elephant Island]] to [[South Georgia]].<ref name="Müller, et al.">{{Cite web| url=http://www.tos.org/oceanography/issues/issue_archive/issue_pdfs/18_3/18.3_muller_et_al.pdf | title=Rogue Waves - The fourteenth ‘aha huliko’a Hawaiian winter workshop | access-date=2010-01-10 | url-status=dead | archive-url=https://web.archive.org/web/20090106002536/http://www.tos.org/oceanography/issues/issue_archive/issue_pdfs/18_3/18.3_muller_et_al.pdf | archive-date=2009-01-06}}, Müller, et al., "Rogue Waves," 2005</ref>
* [[USS Tennessee (ACR-10)|USS ''Memphis'']], August 29, 1916&nbsp;– An [[armored cruiser]], formerly known as the USS ''Tennessee'', wrecked while stationed in the harbor of [[Santo Domingo]], with 43 men killed or lost, by a succession of three waves, the largest estimated at 70 feet.<ref>Smith, Craig B., ''Extreme Waves'', pp.67-70 (Washington, D.C.: [[Joseph Henry Press]], 2006) {{ISBN|0-309-10062-3}}.</ref>
* [[RMS Homeric (1913)|RMS ''Homeric'']] (1924)&nbsp;– Hit by a {{convert|80|ft|adj=on|order=flip|abbr=on}} wave while sailing through a hurricane off the East Coast of the United States, injuring seven people, smashing numerous windows and portholes, carrying away one of the lifeboats, and snapping chairs and other fittings from their fastenings.<ref name="Kerbrech">{{cite book|last1=Kerbrech|first1=Richard De|title=Ships of the White Star Line|date=2009|publisher=Ian Allan Publishing|page=190|isbn=978-0-7110-3366-5}}</ref>
* [[USS Ramapo (AO-12)|USS ''Ramapo'']] (1933) – Triangulated at {{convert|112|ft|m|order=flip|abbr=on}}.<ref name="broad">[https://www.nytimes.com/2006/07/11/science/11wave.html?8dpc Rogue Giants at Sea], Broad, William J, ''[[New York Times]]'', July 11, 2006</ref>
* {{RMS|Queen Mary}} (1942) – [[wikt:broadside|Broadsided]] by a {{convert|92|ft|m|adj=on|order=flip|abbr=on}} wave and listed briefly about 52° before slowly righting.<ref name="Parker2012"/>
* [[Michelangelo (ship)|SS ''Michelangelo'']] (1966) – Hole torn in superstructure, heavy glass was smashed by the wave {{convert|80|ft|m|order=flip|abbr=on}} above the waterline, and three deaths.<ref name="broad"/>
* {{SS|Edmund Fitzgerald}} (1975) – Lost on [[Lake Superior]], a Coast Guard report blamed water entry to the hatches, which gradually filled the hold, or errors in navigation or charting causing damage from running onto [[shoal]]s. However, another nearby ship, the {{SS|Arthur M. Anderson}}, was hit at a similar time by two rogue waves and possibly a third, and this appeared to coincide with the sinking around 10 minutes later.<ref name="Wolff"/>
* {{MS|München}} (1978) – Lost at sea, leaving only scattered wreckage and signs of sudden damage including extreme forces {{convert|66|ft|m|order=flip|abbr=on}} above the water line. Although more than one wave was probably involved, this remains the most likely sinking due to a freak wave.<ref name="BBCFreak"/>
* [[Esso Languedoc]] (1980) – A {{convert|25|to|30|m|ft|adj=on|-1|abbr=on}} wave washed across the deck from the stern of the French [[supertanker]] near [[Durban]], South Africa.<ref>{{Cite web |title=Ship-sinking monster waves revealed by ESA satellites |url=https://www.esa.int/Applications/Observing_the_Earth/Ship-sinking_monster_waves_revealed_by_ESA_satellites |access-date=2024-11-12 |website=www.esa.int |language=en}}</ref><ref>{{cite magazine|last1=Kastner|first1=Jeffrey|title=Sea Monsters|url=http://www.cabinetmagazine.org/issues/16/kastner.php|magazine=Cabinet Magazine|access-date=10 October 2017}}</ref>
* [[Fastnet Lighthouse]] – Struck by a {{convert|48|m|ft|adj=on|}} wave in 1985<ref>{{Cite news |title=Light on a lonely rock |url=https://www.economist.com/christmas-specials/2008/12/18/light-on-a-lonely-rock |access-date=2024-11-12 |newspaper=The Economist |issn=0013-0613}}</ref>
* Draupner wave ([[North Sea]], 1995) – The first rogue wave confirmed with scientific evidence, it had a maximum height of {{convert|26|m|ft|}}.<ref name="esa.int">{{cite web |url=http://www.esa.int/esaCP/SEMOKQL26WD_index_0.html|title=Ship-sinking monster waves revealed by ESA satellites|last=esa|website=esa.int|access-date=26 March 2018}}</ref>
* ''[[Queen Elizabeth 2]]'' (1995) – Encountered a {{Convert|29|m|ft|adj = on|abbr=on}} wave in the North Atlantic, during [[Hurricane Luis]]. The master said it "came out of the darkness" and "looked like the [[White Cliffs of Dover]]."<ref name="skuld">{{cite web|url=http://www.skuld.com/upload/News%20and%20Publications/Publications/Beacon/Beacon%202005%20185/Freak%20waves.pdf |title=Freak waves |url-status=dead |archive-url=https://web.archive.org/web/20080414151343/http://www.skuld.com/upload/News%20and%20Publications/Publications/Beacon/Beacon%202005%20185/Freak%20waves.pdf |archive-date=2008-04-14 }}&nbsp;{{small|(1.07&nbsp;[[Mebibyte|MiB]])}}, ''Beacon'' #185, [[Assuranceforeningen Skuld|Skuld]], June 2005</ref> Newspaper reports at the time described the cruise liner as attempting to "[[surfing|surf]]" the near-vertical wave in order not to be sunk.

===21st century===
* U.S. [[Naval Research Laboratory]] ocean-floor [[pressure sensor]]s detected a freak wave caused by [[Hurricane Ivan]] in the [[Gulf of Mexico]], 2004. The wave was around {{Convert|27.7|m|ft|abbr=on}} high from peak to trough, and around {{Convert|200|m|ft|abbr=on}} long.<ref name="ElReg">{{cite web|url=https://www.theregister.co.uk/2005/08/05/hurricane_prompts_wave_rethink/|title=Hurricane Ivan prompts rogue wave rethink|author=Lucy Sherriff|publisher=[[The Register]]|date=August 5, 2005|accessdate=September 6, 2021}}</ref> Their computer models also indicated that waves may have exceeded {{convert|40|m|ft|}} in the eyewall.<ref name="ivan">{{cite web|url=https://www.nrl.navy.mil/media/news-releases/2005/nrl-measures-record-wave-during-hurricane-ivan|title=NRL Measures Record Wave During Hurricane Ivan – U.S. Naval Research Laboratory|date=February 17, 2005|website=www.nrl.navy.mil|access-date=March 26, 2018|archive-date=November 1, 2017|archive-url=https://web.archive.org/web/20171101025311/https://www.nrl.navy.mil/media/news-releases/2005/nrl-measures-record-wave-during-hurricane-ivan|url-status=dead}}</ref>
* ''Aleutian Ballad'', ([[Bering Sea]], 2005) footage of what is identified as an {{convert|60|ft|m|adj=on|order=flip|abbr=on}} wave appears in an episode of ''[[Deadliest Catch]]''. The wave strikes the ship at night and cripples the vessel, causing the boat to tip for a short period onto its side. This is one of the few video recordings of what might be a rogue wave.<ref>[[Deadliest Catch]] Season 2, Episode 4 "Finish Line" Original airdate: April 28, 2006; approximate time into episode: 0:40:00–0:42:00. Edited footage viewable online at [http://dsc.discovery.com/videos/deadliest-catch-tragedy-at-sea.html Discovery.com] {{webarchive|url=https://web.archive.org/web/20090806051946/http://dsc.discovery.com/videos/deadliest-catch-tragedy-at-sea.html |date=2009-08-06 }}</ref>
* In 2006, researchers from [[U.S. Naval Institute]] theorized rogue waves may be responsible for the unexplained loss of low-flying aircraft, such as U.S. Coast Guard helicopters during [[search-and-rescue]] missions.<ref>{{cite web|url= http://www.check-six.com/Coast_Guard/Monster_Waves_Reprint-screen.pdf |title=Monster waves threaten rescue helicopters }}&nbsp;{{small|(35.7&nbsp;[[Kibibyte|KiB]])}}, [[U.S. Naval Institute]], December 15, 2006</ref>
* MS ''[[Louis Majesty]]'' ([[Mediterranean Sea]], March 2010) was struck by three successive {{convert|8|m|adj=on|abbr=on}} waves while crossing the [[Gulf of Lion]] on a [[Mediterranean Sea|Mediterranean cruise]] between [[Cartagena, Spain|Cartagena]] and [[Marseille]]. Two passengers were killed by flying glass when the second and third waves shattered a lounge window. The waves, which struck without warning, were all abnormally high in respect to the [[Swell (ocean)|sea swell]] at the time of the incident.<ref>{{cite news
 | url       = http://www.lavanguardia.es/sucesos/noticias/20100303/53896565674/dos-muertos-y-16-heridos-por-una-ola-gigante-en-un-crucero-con-destino-a-cartagena.html
 | title       = Dos muertos y 16 heridos por una ola gigante en un crucero con destino a Cartagena
 | newspaper       = La Vanguardia
 | date       = 3 March 2010
 | access-date       = 4 March 2010
 | archive-date       = 6 March 2010
 | archive-url       = https://web.archive.org/web/20100306063537/http://www.lavanguardia.es/sucesos/noticias/20100303/53896565674/dos-muertos-y-16-heridos-por-una-ola-gigante-en-un-crucero-con-destino-a-cartagena.html
 | url-status       = dead
 }}</ref><ref>{{cite news
 |url          = https://www.foxnews.com/story/giant-rogue-wave-slams-into-ship-off-french-coast-killing-2
 |title        = Giant rogue wave slams into ship off French coast, killing 2
 |work    = [[Fox News]]
 |date         = 3 March 2010
 |access-date  = 2010-03-04
 |archive-url  = https://web.archive.org/web/20100306155220/http://www.foxnews.com/story/0,2933,587885,00.html
 |archive-date = 2010-03-06
 |url-status     = live
}}</ref>
* In 2011, the [[Sea Shepherd Conservation Society|Sea Shepherd]] vessel ''[[MV Brigitte Bardot]]''{{Spaces}}was damaged by a rogue wave of 11&nbsp;m (36.1&nbsp;ft) while [[Sea Shepherd Conservation Society operations#Operation Divine Wind (2011–2012)|pursuing the Japanese whaling fleet]] off the western coast of Australia on 28 December 2011.<ref>{{cite web|url=https://thewest.com.au/news/wa/brigitte-bardot-finally-back-in-port-ng-ya-336845|title=Brigitte Bardot finally back in port|work=Jane Hammond|publisher=[[The West Australian]]|date=5 January 2012|accessdate=30 January 2012}}</ref> The MV ''Brigitte Bardot'' was escorted back to [[Fremantle, Western Australia|Fremantle]] by the SSCS flagship, [[MV Steve Irwin|MV ''Steve Irwin'']]. The main hull was cracked, and the port side [[Pontoon (boat)|pontoon]] was being held together by straps. The vessel arrived at Fremantle Harbor on 5 January 2012. Both ships were followed by the [[Institute of Cetacean Research|ICR]] security vessel [[MV Shōnan Maru 2|MV ''Shōnan Maru 2'']] at a distance of 5 nautical miles (9&nbsp;km).<ref>[[Jiji Press]], "Sea Shepherd scouting vessel badly damaged", ''[[Japan Times]]'', 30 December 2011, p. 2.</ref>
* In 2019, [[Hurricane Dorian]]'s [[extratropical cyclone|extratropical remnant]] generated a {{convert|100|ft|m|order=flip|adj=on|abbr=on}} rogue wave off the coast of [[Newfoundland (island)|Newfoundland]].<ref name="100 foot rogue wave">{{cite news|url=https://www.washingtonpost.com/weather/2019/09/09/hurricane-dorian-likely-whipped-up-foot-rogue-wave-near-newfoundland/|title=Hurricane Dorian probably whipped up a 100-foot rogue wave near Newfoundland|author=Matthew Cappucci|newspaper=The Washington Post|date=September 9, 2019|access-date=September 10, 2019}}</ref>
* In 2022, the [[Viking Cruises|Viking]] cruise ship ''[[Viking Octantis|Viking Polaris]]'' was hit by a rogue wave on its way to [[Ushuaia]], Argentina. One person died, four more were injured, and the ship's scheduled route to [[Antarctica]] was canceled.<ref name="viking cruise incident">{{cite news|url=https://www.usatoday.com/story/news/world/2022/12/02/rogue-wave-death-antartica-viking-cruise/10816288002/|title=Giant 'rogue wave' hits Antarctica-bound cruise ship, leaving one dead and four injured|author=Wyatte Grantham-Philips|newspaper=USA Today|date=December 2, 2022|access-date=December 2, 2022}}</ref>

==Quantifying the impact of rogue waves on ships==

The loss of the {{MS|München}} in 1978 provided some of the first physical evidence of the existence of rogue waves. ''München'' was a state-of-the-art cargo ship with multiple water-tight compartments and an expert crew. She was lost with all crew, and the wreck has never been found. The only evidence found was the starboard lifeboat recovered from floating wreckage sometime later. The lifeboats hung from forward and aft blocks {{convert|20|m|ft|abbr=on}} above the waterline. The pins had been bent back from forward to aft, indicating the lifeboat hanging below it had been struck by a wave that had run from fore to aft of the ship and had torn the lifeboat from the ship. To exert such force, the wave must have been considerably higher than {{convert|20|m|ft|abbr=on}}. At the time of the inquiry, the existence of rogue waves was considered so statistically unlikely as to be near impossible. Consequently, the Maritime Court investigation concluded that the severe weather had somehow created an "unusual event" that had led to the sinking of the ''München''.<ref name="BBCFreak">{{cite web
 | url        = http://www.bbc.co.uk/science/horizon/2002/freakwave.shtml
 | title      = Freak Wave – programme summary
 | date       = 14 November 2002
 | website    = www.bbc.co.uk/
 | publisher  = BBC
 | access-date= 15 January 2016
 }}</ref><ref name="McCloskey2014">{{cite book
 | author     = Keith McCloskey
 | title      = The Lighthouse: The Mystery of the Eilean Mor Lighthouse Keepers
 | url        = https://books.google.com/books?id=cOn3AwAAQBAJ
 | date       = 2014
 | publisher  = History Press Limited
 | isbn       = 978-0-7509-5741-0}}</ref>

In 1980, the [[MV Derbyshire|MV ''Derbyshire'']] was lost during [[Typhoon Orchid (1980)|Typhoon Orchid]] south of Japan, along with all of her crew. The ''Derbyshire'' was an ore-bulk oil combination carrier built in 1976. At 91,655 gross register tons, she remains the largest British ship ever lost at sea. The wreck was found in June 1994. The survey team deployed a remotely operated vehicle to photograph the wreck. A private report published in 1998 prompted the British government to reopen a formal investigation into the sinking. The investigation included a comprehensive survey by the [[Woods Hole Oceanographic Institution]], which took 135,774 pictures of the wreck during two surveys. The formal forensic investigation concluded that the ship sank because of structural failure and absolved the crew of any responsibility. Most notably, the report determined the detailed sequence of events that led to the structural failure of the vessel. A third comprehensive analysis was subsequently done by Douglas Faulkner, professor of marine architecture and ocean engineering at the [[University of Glasgow]]. His 2001 report linked the loss of the ''Derbyshire'' with the emerging science on freak waves, concluding that the ''Derbyshire'' was almost certainly destroyed by a rogue wave.<ref name="FaulknerD"/><ref name="FaulknerConference">{{cite conference
 |url          = http://www.ifremer.fr/web-com/molagnon/bv/Faulkner_w.pdf
 |title        = Rogue Waves – Defining Their Characteristics for Marine Design
 |first        = Douglas
 |last         = Faulkner
 |year         = 2000
 |conference   = Rogue Waves 2000 Workshop
 |publisher    = French Research Institute for Exploitation of the Sea
 |location     = Brest
 |pages        = 16
 |access-date  = 15 January 2016
 |quote        = This paper introduces the need for a paradigm shift in thinking for the design of ships and offshore installations to include a Survival Design approach additional to current design requirements.
 |archive-date = 15 February 2018
 |archive-url  = https://web.archive.org/web/20180215024344/http://www.ifremer.fr/web-com/molagnon/bv/Faulkner_w.pdf
 |url-status   = dead
}}</ref><ref name = EuropeanUnionSurvey >{{cite web
 | url        = http://www.worldnavalships.com/forums/showthread.php?t=13867
 | title      = The Loss of the 'DERBYSHIRE'
 | last1      = Brown
 | first1     = David
 | year       = 1998
 | publisher  = Crown
 | archive-url = https://web.archive.org/web/20130322054007/http://www.worldnavalships.com/forums/showthread.php?t=13867
 | archive-date = 2013-03-22
 | type       = Technical Report }}</ref><ref name = HansardJune2002>
{{Cite Hansard
 | house      = House of Commons
 | title      = Ships and Seafarers (Safety)
 | url        = https://www.theyworkforyou.com/whall/?id=2002-06-25.193.1
 | date       = 25 June 2002
 | column_start= 193WH
 | column_end = 215WH
 | quote      = The MV ''Derbyshire'' was registered at Liverpool and, at the time, was the largest ship ever built; it was twice the size of the ''Titanic''. }}</ref><ref name = WoodsHoleNavigation>{{cite web
 | url        = https://apps.dtic.mil/sti/pdfs/ADA370001.pdf
 | archive-url = https://web.archive.org/web/20170204151313/http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA370001
 | url-status = live
 | archive-date = February 4, 2017
 | title      = Navigation for the ''Derbyshire'' Phase2 Survey
 | last1      = Lerner
 | first1     = S.
 | last2      = Yoerger
 | first2     = D.
 | last3      = Crook
 | first3     = T.
 | date       = May 1999
 | publisher  = Woods Hole Oceanographic Institution MA
 | pages      = 28
 | type       = Technical Report
 | id         = WHOI-99-11
 | quote =In 1997, the Deep Submergence Operations Group of the Woods Hole Oceanographic Institution conducted an underwater forensic survey of the UK bulk carrier MV ''Derbyshire'' with a suite of underwater vehicles. This report describes the navigation systems and methodologies used to position the vessel and vehicles precisely. Precise navigation permits the survey team to control the path of the subsea vehicle to execute the survey plan, provides the ability to return to specific targets, and allows the assessment team to correlate observations made at different times from different vehicles. This report summarizes the techniques used to locate Argo and the repeatability of those navigation fixes. To determine repeatability, we selected a number of instances where the vehicle lines crossed. We can determine the true position offset by registering two images from overlapping areas on different track lines. We can determine the navigation error by comparing the position offset derived from the images to the offsets obtained from navigation. The average error for 123 points across a single tie line was 3.1 meters, the average error for a more scattered selection of 18 points was 1.9 meters.
 | ref        = WHOI-99-11}}</ref>

Work by sailor and author Craig B. Smith in 2007 confirmed prior forensic work by Faulkner in 1998 and determined that the ''Derbyshire'' was exposed to a [[hydrostatic pressure]] of a "static head" of water of about {{convert|20|m|ft|abbr=on}} with a resultant [[static pressure]] of {{convert|201|kPa|bar psi}}.{{efn|Equivalent to {{nowrap|20,500 kgf/m<sup>2</sup>}} or {{nowrap|20.5 t/m<sup>2</sup>}}.}} This is in effect {{convert|20|m|abbr=on}} of seawater (possibly a super rogue wave){{efn|The term "super rogue wave" had not yet been coined by ANU researchers at that time.}} flowing over the vessel. The deck cargo hatches on the ''Derbyshire'' were determined to be the key point of failure when the rogue wave washed over the ship. The design of the hatches only allowed for a static pressure less than {{convert|2|m|ft|abbr=on}} of water or {{convert|17.1|kPa|bar psi |abbr=on}},{{efn|Equivalent to {{nowrap|1,744 kgf/m<sup>2</sup>}} or {{nowrap|1.7 t/m<sup>2</sup>}}.}} meaning that the typhoon load on the hatches was more than 10 times the design load. The forensic structural analysis of the wreck of the ''Derbyshire'' is now widely regarded as irrefutable.<ref name="SmithConference"/>

In addition, fast-moving waves are now known to also exert extremely high dynamic pressure. Plunging or breaking waves are known to cause short-lived impulse pressure spikes called [[Gifle peaks]]. These can reach pressures of {{convert|200|kPa|bar psi|abbr=on}} (or more) for milliseconds, which is sufficient pressure to lead to brittle fracture of mild steel. Evidence of failure by this mechanism was also found on the ''Derbyshire''.<ref name="FaulknerD">{{cite book
 |last      = Faulkner
 |first     = Douglas
 |date      = 1998
 |title     = An Independent Assessment of the Sinking of the M.V. ''Derbyshire''
 |url       = http://www.sname.org/HigherLogic/System/DownloadDocumentFile.ashx?DocumentFileKey=df0dc59b-5d4e-43a2-9c97-f2a031de8ca6
 |archive-url = https://web.archive.org/web/20160418161247/http://www.sname.org/HigherLogic/System/DownloadDocumentFile.ashx?DocumentFileKey=df0dc59b-5d4e-43a2-9c97-f2a031de8ca6
 |url-status  = dead
 |archive-date = 2016-04-18
 |publisher = SNAME Transactions, Royal Institution of Naval Architects
 |pages     = 59–103
 |quote     = The author's starting point, therefore, was to look for an extraordinary cause. He reasoned that nothing could be more extraordinary than the violence of a fully arisen and chaotic storm-tossed sea. He therefore studied the meteorology of revolving tropical storms and freak waves and found that steep elevated waves of 25 to 30 m or more were quite likely to have occurred during Typhoon Orchid.
}}</ref> Smith documented scenarios where hydrodynamic pressure up to {{convert|5650|kPa|bar psi |abbr=on}} or over 500&nbsp;metric tonnes/m<sup>2</sup> could occur.{{efn|Equivalent to {{nowrap|576,100 kgf/m<sup>2</sup>}} or {{nowrap|576.1 t/m<sup>2</sup>}}.}}<ref name="SmithConference"/>

In 2004, an extreme wave was recorded impacting the Alderney Breakwater, [[Alderney]], in the [[Channel Islands]]. This [[Breakwater (structure)|breakwater]] is exposed to the Atlantic Ocean. The peak pressure recorded by a shore-mounted transducer was {{Convert|745|kPa|bar psi |abbr=on}}. This pressure far exceeds almost any design criteria for modern ships, and this wave would have destroyed almost any merchant vessel.<ref name="MyUser_Soest.hawaii.edu_April_16_2016c">{{cite web
 | url        = http://www.soest.hawaii.edu/PubServices/Muller_Rogue_Wave.pdf
 | title      = Rogue Waves: The Fourteenth 'Aha Huliko'A Hawaiian Winter Workshop
 | newspaper  = Soest.hawaii.edu
 | date       = 3 September 2005
 | publisher  = Oceanography
 | volume     = 18
 | issue      = 3
 | pages      = 66–70
 | access-date = April 16, 2016}}</ref>

==Design standards==

In November 1997, the [[International Maritime Organization]] (IMO) adopted new rules covering survivability and structural requirements for bulk carriers of {{convert|150|m|ft|abbr=on}} and upwards. The bulkhead and double bottom must be strong enough to allow the ship to survive flooding in hold one unless loading is restricted.<ref>{{cite web
 |title=Improving the safety of bulk carriers
 |publisher=IMO
 |url=http://www.imo.org/includes/blastDataOnly.asp/data_id%3D6609/BULK.PDF
 |archive-url=http://arquivo.pt/wayback/20090707145541/http://www.imo.org/includes/blastDataOnly.asp/data_id%3D6609/BULK.PDF
 |url-status=dead
 |archive-date=2009-07-07
 |access-date=2009-08-11
}}</ref>

Rogue waves present considerable danger for several reasons: they are rare, unpredictable, may appear suddenly or without warning, and can impact with tremendous force. A {{convert|12|m|adj=on|abbr=on}} wave in the usual "linear" model would have a breaking force of {{convert|6|MT/m2|psi|abbr=~}}. Although modern ships are typically designed to tolerate a breaking wave of 15 t/m<sup>2</sup>, a rogue wave can dwarf both of these figures with a breaking force far exceeding 100 t/m<sup>2</sup>.<ref name="skuld" /> Smith presented calculations using the International Association of Classification Societies (IACS) Common Structural Rules <!-- (CSR) --> for a typical bulk carrier.{{efn|Smith has presented calculations for a hypothetical bulk carrier with a length of 275 m and a displacement of 161,000 metric tons where the design hydrostatic pressure 8.75 m below the waterline would be {{nowrap|88 kN/m<sup>2</sup>}} ({{nowrap|8.9 t/m<sup>2</sup>}}). For the same carrier the design hydrodynamic pressure would be {{nowrap|122 kN/m<sup>2</sup>}} ({{nowrap|12.44 t/m<sup>2</sup>}}).}}<ref name="SmithConference"/>

Peter Challenor, a scientist from the [[National Oceanography Centre]] in the United Kingdom, was quoted in [[Susan Casey|Casey]]'s book in 2010 as saying: "We don't have that random messy theory for nonlinear waves. At all." He added, "People have been working actively on this for the past 50 years at least. We don't even have the start of a theory."<ref name="TheWeek"/><ref name="Casey2010"/>

In 2006, Smith proposed that the IACS recommendation 34 pertaining to standard wave data be modified so that the minimum design wave height be increased to {{convert|65|ft|m|1|order=flip|abbr=on}}. He presented analysis that sufficient evidence exists to conclude that {{convert|66|ft|m|1|order=flip|abbr=on}} high waves can be experienced in the 25-year lifetime of oceangoing vessels, and that {{convert|98|ft|m|1|order=flip|abbr=on}} high waves are less likely, but not out of the question. Therefore, a design criterion based on {{convert|36|ft|m|1|order=flip|abbr=on}} high waves seems inadequate when the risk of losing crew and cargo is considered. Smith also proposed that the dynamic force of wave impacts should be included in the structural analysis.<ref name="SmithBook">{{cite book  | last      =  Smith
 | first      = Craig
 | date       = 2006
 | title      = Extreme Waves
 | url        = https://archive.org/details/extremewaves00smit
 | url-access =  registration
 | publisher  = Joseph Henry Press
 | isbn       = 978-0309100625
 | quote      = There is sufficient evidence to conclude that 66-foot-high waves can be experienced in the 25-year lifetime of oceangoing vessels and that 98-foot-high waves are less likely, but not out of the question. Therefore, a design criterion based on 36-foot-high waves seems inadequate when the risk of losing crew and cargo is considered. }}</ref>
The Norwegian offshore standards now consider extreme severe wave conditions and require that a 10,000-year wave does not endanger the ships' integrity.<ref name="rosenthal"/> W. Rosenthal noted that as of 2005, rogue waves were not explicitly accounted for in Classification Society's rules for ships' design.<ref name="rosenthal">{{cite web
 | url        = http://www.soest.hawaii.edu/PubServices/2005pdfs/Rosenthal.pdf
 | title      = Results of the MAXWAVE project
 | last       = Rosenthal
 | first      = W
 | date       = 2005
 | website    = www.soest.hawaii.edu
 | access-date= 14 January 2016
 | quote      = The Norwegian offshore standards consider extreme severe wave conditions by requiring that a 10,000-year wave does not endanger the structure’s integrity (Accidental Limit State, ALS).}}</ref> As an example, [[DNV GL]], one of the world's largest international certification bodies and classification society with main expertise in technical assessment, advisory, and risk management publishes their Structure Design Load Principles which remain largely based on the Significant Wave Height, and as of January 2016, still have not included any allowance for rogue waves.<ref name="DNVGL">{{cite web
 |url         = http://www.gl-group.com/infoServices/rules/pdfs/gl_i-2-2_e.pdf
 |archive-url = https://web.archive.org/web/20140912042308/http://www.gl-group.com/infoServices/rules/pdfs/gl_i-2-2_e.pdf
 |url-status    = dead
 |archive-date = 2014-09-12
 |title       = Rules for Classification and Construction
 |date        = 2011
 |website     = www.gl-group.com/
 |publisher   = Germanischer Lloyd SE
 |location    = Hamburg, Germany
 |access-date = 13 January 2016
 |quote       = General Terms and Conditions of the respective latest edition will be applicable. See Rules for Classification and Construction, I – Ship Technology, Part 0 – Classification and Surveys.
}}</ref>

The U.S. Navy historically took the design position that the largest wave likely to be encountered was {{convert|21.4|m|ft|abbr=on}}. Smith observed in 2007 that the navy now believes that larger waves can occur and the possibility of extreme waves that are steeper (i.e. do not have longer wavelengths) is now recognized. The navy has not had to make any fundamental changes in ship design due to new knowledge of waves greater than 21.4&nbsp;m because the ships are built to higher standards than required.<ref name="SmithConference"/>

The more than 50 classification societies worldwide each has different rules. However, most new ships are built to the standards of the 12 members of the [[International Association of Classification Societies]], which implemented two sets of common structural rules - one for oil tankers and one for bulk carriers, in 2006. These were later harmonised into a single set of rules.<ref name="IACS Common Structural Rules">{{cite web |title=International Association of Classification Societies |url=http://www.iacs.org.uk/publications/common-structural-rules/ |website=IACS |access-date=1 June 2020}}</ref>

==See also==
{{Col-begin}}
{{Col-1-of-2}}
; Oceanography, currents and regions:
* {{annotated link|Antarctic Circumpolar Current}}
* {{annotated link|Agulhas Current}}
* {{annotated link|Bermuda Triangle}}
* {{annotated link|Gulf Stream}}
* {{annotated link|Kuroshio Current}}
* {{annotated link|Ocean current}}
* {{annotated link|Wind wave}}
* {{annotated link|Wave–current interaction}}
{{Col-2-of-2}}
{{portal|Oceans}}
; Waves:
* {{annotated link|Branched flow}}
* {{annotated link|Extreme value theory}}
* {{annotated link|Clapotis}}
* {{annotated link|Sneaker wave}}
* {{annotated link|Soliton}} (and especially, {{annotated link|Peregrine soliton}})
* {{annotated link|White squall}}
* {{annotated link|Resonance}}
* {{annotated link|Meteotsunami}}
{{col-end}}

==Notes==
{{Notelist}}

==References==
{{Reflist| 30em }}

==Further reading==
{{Refbegin}}
* {{cite news
 | title      = Rogue Waves – Monsters of the deep
 | newspaper    = The Economist
 | date       = September 17, 2009
 | page       = 94 }}
* {{cite book
 |title     = The Wave: In Pursuit of the Rogues, Freaks and Giants of the Ocean
 |url       = https://books.google.com/books?isbn=140708707X
 |author    = Susan Casey
 |publisher = Anchor Canada
 |year      = 2011
 |isbn      = 978-0-385-66668-8
}}
* {{cite book
 |title      = Extreme Waves
 |url        = https://archive.org/details/extremewaves00smit
 |url-access = registration
 |author     = Craig B. Smith
 |publisher  = Joseph Henry Press, Washington, D.C.
 |year       = 2006
 |isbn       = 978-0-309-10062-5
}}
* {{cite book
 |title     = Rogue Waves in the Ocean
 |url       = https://books.google.com/books?id=LR-IjCcUkfIC
 |author1   = Christian Kharif
 |author2   = Efim Pelinovsky
 |author3   = Alexey Slunyaev
 |year      = 2008
 |publisher = Springer Science & Business Media
 |isbn      = 978-3-540-88419-4
}}
* {{cite book
 |title     = Waves in Geophysical Fluids: Tsunamis, Rogue Waves, Internal Waves and Internal Tides
 |url       = https://books.google.com/books?id=CtXBBAAAQBAJ
 |author1   = John Grue
 |author2   = Karsten Trulsen
 |year      = 2007
 |publisher = Springer Science & Business Media
 |isbn      = 978-3-211-69356-8
}}
* {{cite book
 |title     = Extreme Ocean Waves
 |url       = https://books.google.com/books?id=vH2BCgAAQBAJ
 |author1   = Efim Pelinovsky
 |author2   = Christian Kharif
 |year      = 2015
 |publisher = Springer
 |isbn      = 978-3-319-21575-4
}}
* {{cite book
 |title     = The Power of the Sea: Tsunamis, Storm Surges, Rogue Waves, and Our Quest to Predict Disasters
 |url       = https://books.google.com/books?id=zzlNJFc4vngC
 |author    = Bruce Parker
 |year      = 2012
 |publisher = St. Martin's Press
 |isbn      = 978-0-230-11224-7
}}
* {{cite book
 |title     = The Science of Ocean Waves: Ripples, Tsunamis, and Stormy Seas
 |url       = https://books.google.com/books?id=eTvSAQAAQBAJ
 |author    = J. B. Zirker
 |year      = 2013
 |publisher = JHU Press
 |isbn      = 978-1-4214-1079-1
}}
* {{cite book
 |title     = Nonlinear Ocean Waves & the Inverse Scattering Transform
 |url       = https://books.google.com/books?id=wdmsn9icd7YC
 |author    = Alfred Osborne
 |year      = 2010
 |publisher = Academic Press
 |isbn      = 978-0-08-092510-3
}}
* {{cite book
 |title     = Ocean Engineering Mechanics: With Applications
 |url       = https://books.google.com/books?id=CvNjW98oWbYC
 |author    = Michael E. McCormick
 |year      = 2010
 |publisher = Cambridge University Press
 |isbn      = 978-0-521-85952-3
}}
* {{cite magazine
 |author    = Charlie Wood
 |date      = 5 February 2020
 |title     = The Grand Unified Theory of Rogue Waves
 |url       = https://www.quantamagazine.org/the-grand-unified-theory-of-rogue-waves-20200205/
 |magazine  = Quanta Magazine
 |publisher = Simons Foundation
 |language  = en
}}
* {{cite web
 |first=Sverre
 |last=Haver
 |date=5 August 2003
 |url=http://www.ifremer.fr/web-com/stw2004/rw/fullpapers/walk_on_haver.pdf
 |title=Freak wave event at Draupner jacket 1&nbsp;January 1995
 |access-date=20 May 2016
 |archive-date=13 June 2018
 |archive-url=https://web.archive.org/web/20180613132223/http://www.ifremer.fr/web-com/stw2004/rw/fullpapers/walk_on_haver.pdf
 |url-status=dead
 }}
* {{cite news
 |url=http://www.ox.ac.uk/news/science-blog/crest-freak-wave
 |title=On the crest of a freak wave
 |publisher=Oxford U.
 |department=Science Blog
 |series=article on Draupner wave
 }}
* {{cite magazine
 |magazine= American Physical Society
 |date= January 2018
 |volume= {{nowrap|27, Number 1}}
 |url= https://www.aps.org/publications/apsnews/201801/history.cfm
 |title= This Month in Physics History January 1, 1995: Confirmation of the Existence of Rogue Waves; January 1995
 |access-date= 22 August 2021
 }}
{{Refend}}

== External links ==
{{wiktionary}}
{{Commons category|Rogue waves}}

===Extreme seas project===
* [http://www.mar.ist.utl.pt/extremeseas/ Design for Ship Safety in Extreme Seas]

===MaxWave report and WaveAtlas===
* [http://news.bbc.co.uk/2/hi/science/nature/3917539.stm Freak waves spotted from space], [[BBC News Online]]
* [http://www.esa.int/esaCP/SEMOKQL26WD_index_0.html Ship-sinking monster waves revealed by ESA satellites]
* [https://web.archive.org/web/20110719032700/http://coast.gkss.de/projects/maxwave/ MaxWave project]
* [https://web.archive.org/web/20070107055941/http://icms.org.uk/archive/meetings/2005/roguewaves/index.html Rogue Wave Workshop (2005)]
* [http://www.ifremer.fr/web-com/stw2004/rw/index.html Rogue Waves 2004]

===Other===
* {{YouTube|2ylOpbW1H-I|How Dangerous Can Ocean Waves Get? Wave Comparison}} – documentary on rogue wave sizes, impacts, and causes by [[Facts in Motion (YouTuber)]].
* [https://web.archive.org/web/20060219163057/http://www.kayotix.com/tmp/newsfeeds/21.08.04/waveresearch/ BBC News Report on Wave Research], 21 August 2004
* [http://www.bbc.co.uk/science/horizon/2002/freakwave.shtml The BBC's Horizon "Freak waves" first aired in November 2002]
* [https://web.archive.org/web/20081206165607/http://www.gresham.ac.uk/event.asp?PageId=45&EventId=729 'Giant Waves on the Open Sea'], lecture by Professor Paul H Taylor at [[Gresham College]], 13 May 2008 (available for video, audio or text download)
* [https://web.archive.org/web/20101113032038/http://www.janson.com/rights/2009/06/25/when-nature-strikes-back-freak-waves/ TV program description]
* [https://web.archive.org/web/20151021011540/http://users.ox.ac.uk/~spet1235/Site/Freak_waves.html Non-technical description of some of the causes of rogue waves]
* [http://seastead.org/localres/misc-articles/lawton_newsci_06_30_01.html New Scientist article 06/2001]
* [http://www.oceanwave.jp/index.php?Research%2FFreak%20(Rogue)%20Wave%20Prediction Freak Wave Research in Japan]
* [https://physics.anu.edu.au/theophys/osg/ Optical Science Group, Research School of Physics and Engineering at the Australian National University]
* [https://www.nytimes.com/2006/07/11/science/11wave.html "Rogue Giants at Sea"], ''[[The New York Times]]'', July 11, 2006
* {{Skeptoid | id=4823 | number= 823| date=15 March 2022 | title=Hunting the Elusive Rogue Wave }}
* {{cite web
 | url        = http://www.math.uio.no/~karstent/waves/index_en.html
 | title        = Freak waves, rogue waves, extreme waves and ocean wave climate
 | author        = Kristian B. Dysthe
 | author-link        = Kristian B. Dysthe
 | author2        = Harald E. Krogstad
 | author3        = Hervé Socquet-Juglard
 | author4        = Karsten Trulsen
 | access-date        = 2008-11-01
 | url-status        = dead
 | archive-url        = https://web.archive.org/web/20081112065248/http://www.math.uio.no/~karstent/waves/index_en.html
 | archive-date        = 2008-11-12
 }} Illustrations of the ways rogue waves can form&nbsp;– with descriptions for layman, photos and animations.
* [http://mosaicimagesphoto.photoshelter.com/image/I0000T2wfLusQ4h8 "The Wave" – photograph of a solitary and isolated rogue wave appearing in otherwise calm ocean waters (photographer: G Foulds)]
* Katherine Noyes (25 February 2016), "[http://www.cio.com/article/3038356/a-new-algorithm-from-mit-could-protect-ships-from-rogue-waves-at-sea.html A new algorithm from MIT could protect ships from 'rogue waves' at sea] {{Webarchive|url=https://web.archive.org/web/20160228112408/http://www.cio.com/article/3038356/a-new-algorithm-from-mit-could-protect-ships-from-rogue-waves-at-sea.html |date=2016-02-28 }}", ''[[CIO magazine]]''.
* Wood, Charles, [https://www.quantamagazine.org/the-grand-unified-theory-of-rogue-waves-20200205/ The Grand Unified Theory of Rogue Waves]. Rogue waves&nbsp;– enigmatic giants of the sea&nbsp;– were thought to be caused by two different mechanisms. But a new idea that borrows from the hinterlands of probability theory has the potential to predict them all. February 5, 2020. Quanta Magazine.

{{physical oceanography}}

[[Category:Experimental physics]]
[[Category:Oceanography]]
[[Category:Ocean currents]]
[[Category:Water waves]]
[[Category:Weather hazards]]
[[Category:Rogue wave incidents| ]]
[[Category:Articles containing video clips]]
[[Category:Fluid dynamics]]
[[Category:Surface waves]]