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Rogue wave


Rogue wave

The Draupner wave, a single giant wave measured on New Year's Day 1995, finally confirmed the existence of freak waves, which had previously been considered near-mythical.[1]

Rogue waves (also known as freak waves, monster waves, episodic waves, killer waves, extreme waves, and abnormal waves) are relatively large and spontaneous surface waves that occur far out in open water, and are a threat even to large ships and ocean liners.[2]

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 12-meter wave in the usual "linear" model would have a breaking force of 6 million tons per square metre (MT/m2) and modern ships are designed to tolerate a breaking wave of 15 MT/m2, but a rogue wave can dwarf both of these figures with a breaking force of 100 MT/m2.[3]

In oceanography, rogue waves are more precisely defined as waves whose height is more than twice the significant wave height (Hs or SWH), which is itself defined as the mean of the largest third of waves in a wave record. Therefore, rogue waves are not necessarily the biggest waves found on the water; they are, rather, unusually large waves for a given sea state. Rogue waves seem not 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 exceptionally large wave.[2]

Rogue waves can occur in other media than water. In particular, optical rogue waves allow study of the phenomenon in the laboratory. A 2015 paper studied the wave behavior around a rogue wave, including optical, and the Draupner wave, and concluded that "rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order".[4]


  • Background 1
  • History of rogue wave knowledge 2
  • Occurrence 3
  • Causes 4
  • Scientific applications 5
  • Reported encounters 6
    • 19th century 6.1
    • 20th century 6.2
    • 21st century 6.3
  • See also 7
  • References 8
  • External links 9
    • MaxWave report and WaveAtlas 9.1
    • Other 9.2
  • Further reading 10


Rogue waves are an open water phenomenon, in which winds, currents, non-linear phenomena such as solitons, and other circumstances cause a wave to briefly form that is far larger than the "average" large occurring wave (the significant wave height or 'SWH') of that time and place. The basic underlying physics that makes phenomena such as rogue waves possible is that different gravity waves can travel at different speeds, and so they can "pile up" in certain circumstances - known as "constructive interference". (In deep ocean the speed of a gravity wave is proportional to the square root of its wavelength--the distance peak-to-peak.) However other situations can also give rise to rogue waves, particularly situations where non-linear effects or instability effects can cause energy to move between waves and be concentrated in one or very few extremely large waves before returning to "normal" conditions.

Once considered mythical and lacking hard evidence for their existence, rogue waves are now proven to exist and known to be a natural ocean phenomenon. Eyewitness accounts from mariners and damage inflicted on ships have long suggested they occurred; however, their scientific measurement was only positively confirmed following measurements of the "Draupner wave", a rogue wave at the Draupner platform in the North Sea on January 1, 1995, with a maximum wave height of 25.6 metres (84 ft) (peak elevation of 18.5 metres (61 ft)) . During that event, minor damage was also inflicted on the platform, far above sea level, confirming that the reading was valid. Their existence has also since been confirmed by satellite imagery of the ocean surface.[5]

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.[2] 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 designers, and can overwhelm the usual capabilities of ocean-going vessels which are not designed for such encounters.

Rogue waves are therefore distinct from tsunamis.[2] Tsunamis are caused by massive displacement of water, often resulting from sudden movement of the ocean floor, after which they propagate at high speed over a wide area. They are more or less unnoticeable in deep water and only become dangerous as they approach the shoreline and the ocean floor becomes shallower; therefore tsunamis do not present a threat to shipping at sea (the only ships lost in the 2004 Asian tsunami were in port). They are also distinct from megatsunamis, which are single massive waves caused by sudden impact, such as meteor impact or landslides within enclosed or limited bodies of water. They are also different from the waves described as "hundred-year waves", which is a purely statistical prediction of the highest wave likely to occur in a hundred-year period in a particular body of water.

In February 2000, a British oceanographic research vessel, the RRS Discovery, sailing in the Rockall Trough west of Scotland encountered the largest waves ever recorded by scientific instruments in the open ocean, with a SWH of 18.5 metres (61 ft) and individual waves up to 29.1 metres (95 ft).[6] "In 2004 scientists using three weeks of radar images from European Space Agency satellites found ten rogue waves, each 25 metres (82 ft) or higher."[7]

Rogue waves have been cited in the media as a likely cause of the sudden, inexplicable disappearance of many ocean-going vessels. One of the very few cases in which evidence exists that may indicate a rogue wave incident is the case of the freighter MS München, lost in 1978.

History of rogue wave knowledge

Merchant ship labouring in heavy seas as a huge wave looms ahead. Huge waves are common near the 100-fathom line in the Bay of Biscay.

It is common for mid-ocean storm waves to reach 7 metres (23 ft) in height, and in extreme conditions such waves can reach heights of 15 metres (49 ft). However, for centuries maritime folklore told of the existence of much larger waves — up to 30 metres (98 ft) in height (approximately the height of a 10-story building) — that could appear without warning in mid-ocean, against the prevailing current and wave direction, and often in perfectly clear weather. Such waves were said to consist of an almost vertical wall of water preceded by a trough so deep that it was referred to as a "hole in the sea"; a ship encountering a wave of such magnitude would be unlikely to survive the tremendous pressures exerted by the weight of the breaking water, and would almost certainly be sunk in a matter of seconds or minutes.

Some research confirms that observed wave height distribution in general follows well the Rayleigh distribution, but in shallow waters during high energy events, extremely high waves are more rare than this particular model predicts.[7]

Rogue waves seem to occur in all of the world's oceans many times every year. This has caused reconsideration of the ocean-going ship design.

Rogue waves may also occur in lakes. 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 tons of water. The phenomenon was implicated in the sinking of the SS Edmund Fitzgerald on Lake Superior in November 1975.[8]


In the course of Project MaxWave, researchers from the GKSS Research Centre, using data collected by ESA satellites, identified a large number of radar signatures that have been portrayed as evidence for rogue waves. Further research is under way to develop better methods of translating the radar echoes into sea surface elevation, but at present this technique is not proven.[9][10]


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.

The linear part solution of the Nonlinear Schrödinger equation describing the evolution of a complex wave envelope in deep water.

Because the phenomenon of rogue waves is still a matter of active research, it is premature to state clearly what the most common causes are or whether they vary from place to place. The areas of highest predictable risk appear to be where a strong 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. However, since this thesis does not explain the existence of all waves that have been detected, several different mechanisms are likely, with localised variation. Suggested mechanisms for freak waves include the following:

Diffractive focusing
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.[11]
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.[11] This happens off the South African coast, where the Agulhas Current is countered by westerlies.
Nonlinear effects (modulational instability)
It seems possible to have a rogue wave occur by natural, nonlinear processes from a random background of smaller waves.[12] In such a case, it is hypothesised, 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 after. 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 equation. These equations also have non-linear contributions and show solitary-wave solutions. A small-scale rogue wave consistent with the nonlinear Schrödinger equation was produced in a laboratory water tank in 2011.[13] In particular, the study of solitons, and especially Peregrine solitons, have supported the idea that non-linear effects could arise in bodies of water.
Normal part of the wave spectrum
Rogue waves are not freaks at all but are part of normal wave generation process, albeit a rare extremity.[11]
Wind waves
While it is unlikely that wind alone can generate a rogue wave, its effect combined with other mechanisms may provide a fuller explanation of freak wave phenomena. As wind blows over the ocean, energy is transferred to the sea surface. When strong winds from a storm happen to blow in the opposing direction of the ocean current the forces might be strong enough to randomly generate rogue waves. Theories of instability mechanisms for the generation and growth of wind waves—although not on the causes of rogue waves—are provided by Phillips[14] and Miles.[15]
Thermal expansion
When a stable wave group in a warm water column moves into a cold water column the size of the waves must change because energy must be conserved in the system. So each wave in the wave group become smaller because cold water holds more wave energy based on density. The waves are now spaced further apart and because of gravity they will propagate into more waves to fill up the space and become a stable wave group. If a stable wave group exists in cold water and moves into a warm water column the waves will get larger and the wavelength will be shorter. The waves will seek equilibrium by attempting to displace the waves amplitude because of gravity. However, by starting with a stable wave group the wave energy can displace towards the center of the group. If both the front and back of the wave group are displacing energy towards the center it can become a rogue wave. This would happen only if the wave group is very large.

The spatio-temporal focusing seen in the NLS equation can also occur when the nonlinearity 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 wavegroup 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 one single rogue wave, the rogue wave may be part of a wave packet consisting of a few rogue waves. Such rogue wave groups have been observed in nature.[16]

There are three categories of freak waves:

  • "Walls of water" travelling up to 10 km (6 mi) through the ocean
  • "Three Sisters", groups of three waves[17]
  • Single, giant storm waves, building up to fourfold the storm's waves height and collapsing after some seconds[18]

A research group at the Umeå University, Sweden 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.[19]

Scientific applications

The possibility of the artificial stimulation of rogue wave phenomena has attracted research funding from DARPA, an agency of the United States Department of Defense. Bahram Jalali and other researchers at UCLA studied microstructured optical fibers near the threshold of soliton supercontinuum generation and observed rogue wave phenomena. After modelling the effect, the researchers announced that they had successfully characterized the proper initial conditions for generating rogue waves in any medium.[20] Additional works carried out in optics have pointed out the role played by a nonlinear structure called Peregrine soliton that may explain those waves that appear and disappear without leaving a trace.[21][22]

Reported encounters

It should be noted that many of these encounters are only reported 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 it has not been (and most often cannot be) established that the reported event is a rogue wave in the scientific sense — i.e. of a very different nature in characteristics as the surrounding waves in that sea state and with very low probability of occurrence (according to a Gaussian process description as valid for linear wave theory).

This section lists a limited selection of notable incidents.

19th century

  • The Eagle Island lighthouse (1861) – water broke the glass of the structure's east tower and flooded it, implying a wave that surmounted the 40 m (130 ft) cliff and overwhelmed the 26 m (85 ft) tower.[23]
  • Flannan Isles (1900) – three lighthouse keepers vanished after a storm that resulted in wave-damaged equipment being found 34 metres (112 ft) above sea level.[24][25]

20th century

  • SS Kronprinz Wilhelm, September 18, 1901 – the most modern German ocean liner in 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.[26]
  • SS Waratah - In 1909, it left Durban, South Africa with 211 passengers and crew but did not reach Cape Town, South Africa.[2]
  • [27]
  • USS Ramapo (1933) – triangulated at 112 feet (34 m).[28]
  • RMS Queen Mary (1942) – broadsided by a 92-foot (28 m) wave and listed briefly about 52 degrees before slowly righting.
  • SS Flying Enterprise (1951) – Ripped apart amidships and eventually sank 40 miles (64 km) from Falmouth, England.
  • SS Michelangelo (1966) – hole torn in superstructure, heavy glass smashed 80 feet (24 m) above the waterline, and three deaths.[28]
  • SS Edmund Fitzgerald (1975) – lost on Lake Superior. A Coast Guard report blamed water entry to the hatches, which gradually filled the hold, or alternatively errors in navigation or charting causing damage from running onto shoals. 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 ten minutes later.[8]
  • MS München (1978) – lost at sea leaving only "a few bits of wreckage" and signs of sudden damage including extreme forces 66 feet (20 m) above the water line. Although more than one wave was probably involved, this remains the most likely sinking due to a freak wave.[12]
  • Esso Languedoc A 25-to-30-metre (80 to 100 ft) wave washed across the deck from the stern of the French supertanker near Durban, South Africa, and was photographed by the first mate, Philippe Lijour, in 1980.[29]
  • Fastnet Lighthouse Struck by 48 m (157 ft) wave in 1985 [30]
  • MV Derbyshire (1980) 91,655 GRT bulk freighter - the largest British ship ever lost at sea - disappears without trace during Typhoon Orchid on 9 September 1980, with the loss of 44 lives. Wreck located and extensively surveyed in 1994. One subsequent analysis (which won the 2001 Royal Institution of Naval Architects award for excellence) demonstrated 1) that given the weather conditions pertaining, Derbyshire would almost certainly have encountered waves of at least 28 metres (92 ft), and 2) that even a much smaller rogue wave would have easily destroyed one or more of Derbyshire's cargo hatch covers, leading to the rapid loss of the ship.[31]
  • Draupner wave (North Sea, 1995) – First rogue wave confirmed with scientific evidence, it had a maximum height of 25.6 metres (84 ft).[32]
  • RMS Queen Elizabeth 2 – North Atlantic, September 1995, 29-metre (95 ft) wave, during Hurricane Luis: The Master said it "came out of the darkness" and "looked like the White Cliffs of Dover." [3] Newspaper reports at the time described the cruise liner as attempting to "surf" the near-vertical wave in order not to be sunk.

21st century

  • MS Bremen and Caledonian Star (South Atlantic, 2001) encountered 30-metre (98 ft) freak waves. Bridge windows on both ships were smashed, and all power and instrumentation lost.[3]
  • U.S. Naval Research Laboratory ocean-floor pressure sensors detected a freak wave caused by Hurricane Ivan in the Gulf of Mexico, 2004. The wave was around 27.7 metres (91 ft) high from peak to trough, and around 200 metres (660 ft) long.[33]
  • [35] Four passengers were slightly injured in this incident.[34]
  • Aleutian Ballad, (Bering Sea, 2005) footage of what is identified as a 60-foot (18 m) 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.[36]
  • In 2006, researchers from U.S. Naval Institute theorise 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.[37]
  • On January 24, 2009 the Augusto González de Linares buoy, located 22 miles north of Santander, Spain reported a wave of 26.13 meters, equivalent to 8 floors high, during a storm.[38]
  • MS Louis Majesty (Mediterranean Sea, March 2010) was struck by three successive 8-metre (26 ft) waves while crossing the Gulf of Lion on a Mediterranean cruise between Cartagena and Marseille. Two passengers were killed by flying glass when a lounge window was shattered by the second and third waves. The waves, which struck without warning, were all abnormally high in respect to the sea swell at the time of the incident.[39][40]
  • The Spanish Deepwater Buoys Network, in January 2014, measured a wave height of 27.81 metres (91.2 ft). The data was taken at the buoy Vilán-Sisargas (Cape Vilan) in Galicia (Spain) during the winter storms, which were particularly severe in Atlantic waters.[41]
  • MS Marco Polo was struck by a rogue wave on the English Channel (February 2014), and killed a 85-year-old man and injured a woman in her 70s.[42]

See also


  1. ^ Haver, Sverre (2003). Freak wave event at Draupner jacket Januar 1 1995 (PDF) (Report). Statoil, Tech. Rep. PTT-KU-MA. Retrieved 2015. 
  2. ^ a b c d e "Monsters of the deep -- Huge, freak waves may not be as rare as once thought". Economist Magazine. September 17, 2009. Retrieved 2009-10-04. 
  3. ^ a b c Freak waves PDF (1.07 MiB), Beacon #185, Skuld, June 2005 Archived page
  4. ^ Predictability of Rogue Events, Simon Birkholz, Carsten Brée, Ayhan Demircan, and Günter Steinmeyer, Physics Review Letters 114, 213901, 28 May 2015
  5. ^ "Freak waves spotted from space". BBC News. July 22, 2004. Retrieved May 22, 2010. 
  6. ^ Holliday, NP, MJ Yelland, RW Pascal, VR Swail, PK Taylor, CR Griffiths, and EC Kent (2006). Were extreme waves in the Rockall Trough the largest ever recorded? Geophysical Research Letters, Vol. 33, L05613
  7. ^ a b Laird, Anne Marie (December 2006). "Observed Statistics of Extreme Waves". Doctoral dissertation, Monterey, California Naval Postgraduate School: 2. 
  8. ^ a b Wolff, Julius F. (1979). "Lake Superior Shipwrecks", p. 28. Lake Superior Marine Museum Association, Inc., Duluth, Minnesota, USA. .
  9. ^ "Critical review on potential use of satellite date to find rogue waves" (PDF). European Space Agency SEASAR 2006 proceedings. April 2006. Retrieved February 23, 2008. 
  10. ^ "Freak waves spotted from space".  
  11. ^ a b c "Rogue Waves". Ocean Prediction Center.  
  12. ^ a b Freak Wave, programme summary for Horizon episode aired on 14 November 2002
  13. ^ Adrian Cho (13 May 2011). "Ship in Bottle, Meet Rogue Wave in Tub". Science Now 332: 774. Retrieved 2011-06-27. 
  14. ^ Phillips 1957, Journal of Fluid Mechanics
  15. ^ Miles, 1957, Journal of Fluid Mechanics
  16. ^ Frederic-Moreau. The Glorious Three, translated by M. Olagnon and G.A. Chase / Rogue Waves-2004, Brest, France
  17. ^ Endeavour or Caledonian Star report, March 2, 2001,
  18. ^ MS Bremen report, February 22, 2001,
  19. ^ P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund and L. Stenflo: "Instability and Evolution of Nonlinearly Interacting Water Waves" nlin.CD/0608012, Physical Review Letters (2006)
  20. ^ R. Colin Johnson (December 24, 2007). "EEs Working With Optical Fibers Demystify 'Rogue Wave' Phenomenon". Electronic Engineering Times (1507): 14, 16. 
  21. ^ Kibler, B.; Fatome, J.; Finot, C.; Millot, G.; Dias, F.; Genty, G.; Akhmediev, N.; Dudley, J.M. (2010). "The Peregrine soliton in nonlinear fibre optics". Nature Physics 6 (10).  
  22. ^ "Peregrine's 'Soliton' observed at last". Retrieved 2010-08-24. 
  23. ^ "Eagle Island Lighthouse". Commissioners of Irish Lights. Retrieved 28 October 2010. 
  24. ^ Haswell-Smith, Hamish (2004). The Scottish Islands. Edinburgh: Canongate. pp. 329–31.  
  25. ^ Munro, R.W. (1979) Scottish Lighthouses. Stornoway. Thule Press. ISBN 0-906191-32-7. Munro (1979) pages 170-1
  26. ^ The New York Times, September 26, 1901, p. 16
  27. ^ [4], Müller, et al., "Rogue Waves," 2005
  28. ^ a b Rogue Giants at Sea, Broad, William J, New York Times, July 11, 2006
  29. ^ "Ship-sinking monster waves revealed by ESA satellites", ESA News, July 21, 2004, accessed June 18, 2010 [5]
  30. ^ "The Story of the Fastnet - The Economist Magazine December 18th 2008" [6]
  31. ^ Douglas Faulkner, "An Analytical Assessment of the Sinking of the M.V. Derbyshire," RINA Transactions 2001, Royal Institution of Naval Architects.
  32. ^
  33. ^ Hurricane Ivan prompts rogue wave rethink, The Register, 5 August 2005
  34. ^ Reuters (April 18, 2005). Freak wave pummels cruise ship.
  35. ^ "NTSB – Brief MAB-05/03". Archived from the original on 2009-03-08. Retrieved 2009-03-08. 
  36. ^ Deadliest Catch Season 2, Episode 4 "Finish Line" Original airdate: April 28, 2006; approx time into episode: 0:40:00–0:42:00. Edited footage viewable online at
  37. ^ Monster waves threaten rescue helicopters PDF (35.7 KiB), U.S. Naval Institute, December 15, 2006
  38. ^ "Olas de récord en Cantabria". El Diario Montañés. 3 February 2009. 
  39. ^ "Dos muertos y 16 heridos por una ola gigante en un crucero con destino a Cartagena". La Vanguardia. 3 March 2010. 
  40. ^ "Giant rogue wave slams into ship off French coast, killing 2".  
  41. ^ "Nuevo récord de altura de ola máxima registrada en España". Puertos del Estado. 21 October 2014. 
  42. ^ Jivanda, Tomas (15 February 2014). "UK weather: Man killed after huge wave breaks window of cruise ship Marco Polo in English Channel as storms set to continue". The Independent. Retrieved 17 February 2014. 

External links

MaxWave report and WaveAtlas

  • Freak waves spotted from space, BBC News Online
  • Ship-sinking monster waves revealed by ESA satellites
  • MaxWave project
  • Rogue Wave Workshop (2005)
  • Rogue Waves 2004


  • BBC News Report on Wave Research, 21 August 2004
  • The BBC's Horizon "Freak waves" first aired in November 2002
  • '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)
  • TV program description
  • Non-technical description of some of the causes of rogue waves
  • New Scientist article 06/2001
  • Freak Wave Research in Japan
  • Rogue Giants at Sea, New York Times, July 11, 2006
  • Illustrations of the ways rogue waves can form — with descriptions for layman, photos and animations.  
  • "The Wave" - photograph of a solitary and isolated rogue wave appearing in otherwise calm ocean waters (photographer: G Foulds)

Further reading

  • Rogue Waves-Monsters of the deep, The Economist, September 17, 2009, p. 94
  • Susan Casey (2011). The Wave: In Pursuit of the Rogues, Freaks and Giants of the Ocean. Anchor Canada.  
  • Craig B. Smith (2006). Extreme Waves. Joseph Henry Press, Washington, D.C.  
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