Rogue wave

This article is about the deep water rogue waves which occur far out into open water. For tsunami and tidal wave phenomena, see those respective articles. For other uses, see Rogue wave (disambiguation).
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 large and spontaneous surface waves that occur far out in open water, and can be extremely dangerous, 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 metric tons per square metre (MT/m2). Although modern ships are designed to tolerate a breaking wave of 15 MT/m2, 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

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 nearly unnoticeable in deep water and only become dangerous as they approach the shoreline and the ocean floor becomes shallower;[6] 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).[7] "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."[8]

Rogue waves have now been proven to be the cause of the sudden loss of some ocean-going vessels. Well documented instances include the freighter MS München, lost in 1978[9] and the MV Derbyshire lost in 1980, the largest British ship ever lost at sea.[10][11] A rogue wave has been implicated in the loss of other vessels including the Ocean Ranger which was a semi-submersible mobile offshore drilling unit that sank in Canadian waters on 15 February 1982.[12] In 2007 the US National Oceanic and Atmospheric Administration compiled a catalogue of more than 50 historical incidents probably associated with rogue waves.[13]

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.[8]

Rogue waves seem to occur in all of the world's oceans many times every year. In 2004 the ESA MaxWave project identified more than ten individual giant waves above 25 metres in height during a short survey period. The ESA's ERS satellites have helped to establish the widespread existence of these 'rogue' waves.[14][15]

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.[16]

Occurrence

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.[14][17]

Causes

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.[18]
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.[18] 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.[9] 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.[19] 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.[18]
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[20] and Miles.[21]
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.[22]

There are three categories of freak waves:

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.[25]

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.[26] 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.[27][28]

Reported encounters

Main article: List of rogue waves

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

20th century

21st century

Rogue waves and ship design

Scientific acknowledgement of the existence of rogue waves is a relatively recent paradigm. In 1826 the famous French scientist and naval officer, Captain Jules Dumont d'Urville reported waves as high as '33 metres' in the Indian Ocean with three colleagues as witnesses, yet he was publicly ridiculed by François Arago, the 25th Prime Minister of France. In that era it was widely held that no wave could exceed 30 feet.[50][35] That opinion persisted until recently because most scientists did not believe they existed. Casey recently wrote that much of that disbelief came because there were very few people who had seen a rogue wave, and people who encountered 100-foot [30.5-metre] rogue waves generally weren't coming back to tell people about it.[51]

The loss of the MS München in 1978 provided some of the first physical evidence of the existence of rogue waves. The MS München was a state-of-the-art cargo ship with multiple water-tight compartments, an expert crew and was considered unsinkable. It was lost with all crew. The key evidence found was the starboard lifeboat which was recovered from the wreckage. The lifeboat hangs from forward and aft blocks 20 metres 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 which had torn the lifeboat from the ship. To exert such force the wave must have been considerably higher than 20m. At that time, 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.[9][52]

Oceanographers, meteorologists and ship designers at that time used a mathematical system commonly called the Gaussian Sea (or standard linear model) to predict wave height.[53] This model assumes that waves vary in a regular way around the average (so-called 'significant') wave height. In a storm sea with a significant wave height of 12m, the model suggests there will hardly ever be a wave higher than 15m. One of 30m could indeed happen - but only once in ten thousand years (of wave height of 12m). The science has now developed to acknowledge the existence of rogue waves despite the fact that they cannot plausibly be explained by even state-of-the-art wave statistics.[54] Most popular texts on oceanography up until the mid 1990's such as that by Pirie made no mention of rogue or freak waves.[55] The popular text on Oceanography by Gross (1996) only gave rogue waves a mention and stated that Under extraordinary circumstances unusually large waves called rogue waves can form without providing any further detail.[56] From about 1997 most leading authors acknowledged the existence of rogue waves with the caveat that wave models had been unable to replicate rogue waves.[35] The first scientific research which comprehensively proved that waves exist that are clearly outside the range of Gaussian waves was published in 1997.[57]

The loss in 1980 of the MV Derbyshire during Typhoon Orchid south of Japan with the loss of all crew marked a turning point for ship design. The Derbyshire was an ore-bulk-oil combination carrier built in 1976 and was only a few years old. The carrier was relatively new and at 91,655 gross register tons, she was—and remains—the largest British ship ever to have been 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 was published in 1998 which prompted the British government to reopen a formal investigation into the sinking. The British government investigation included a comprehensive survey by the Woods Hole Oceanographic Institution which took 135,774 pictures of the wreck during two surveys. The formal investigation concluded that the ship sank because of structural failure and absolved the crew of any responsibility. A third comprehensive analysis was subsequently done by Douglas Faulkner, professor of marine architecture and ocean engineering at the University of Glasgow. His highly analytical and scientific report published in 2001 examined and linked the loss of the MV Derbyshire with what he called the emerging body of scientific evidence regarding the mechanics of freak waves. Professor Faulkner concluded that it was almost certain that Derbyshire would have encountered a wave of sufficient size to destroy her. Faulkner's conclusions have not been refuted in the more than 15 years since they were first presented, indeed subsequent analysis by others has corroborated his findings. Faulkner's finding that the Derbyshire was lost because of a rogue wave has had widespread implications on ship design.[10] Faulkner has subsequently proposed the need for a paradigm shift in thinking for the design of ships and offshore installations to include what he calls a Survival Design approach additional to current design requirements.[11][58] [59][60]

In 1995, additional strong scientific evidence came with the recording of what is universally known as the Draupner wave. The Draupner was an oil-drilling platform operated by Statoil about 100 miles off the tip of Norway. The rig was built to withstand a calculated 1 in 10,000 years wave with a predicted height of 64-feet and was also fitted with state-of-the-art laser wave recorder on the platform’s underside. At 3 p.m. on 1 January 1995 it recorded an 85-foot rogue wave that hit the rig at 45 mph. This was the first confirmed measurement of a freak wave, more than twice as tall and steep as its neighbors with characteristics that fell outside any known wave model.[61]

Since the mid-1990's there has been considerable research on extreme or rogue waves, and it is now proven via satellite radar studies that waves with crest to trough heights of 20 to 30 meters, occur far more frequently than previously thought.[62]

In 2000 the British oceanographic vessel RRS Discovery (1962) recorded a 29-metre wave off the coast of Scotland near Rockall. This was a scientific research vessel and was fitted with high quality instruments. The subsequent analysis determined that under severe gale force conditions with wind speeds averaging 21 metres per second (m/s) a ship-borne wave recorder measured individual waves up to 29.1 m from crest to trough, and a maximum significant wave height of 18.5 m. 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 (Hs) above 12 m. 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—the information upon which all ships, oil rigs, fisheries, and passenger boats rely—had predicted these behemoths. Put simply, 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.[2][7][61][63][51]

More recent work by Smith in 2007 confirmed prior work by Faulkner in 1998 and determined that the MV Derbyshire was exposed to a Hydrostatic pressure of a Static head of water of about 20 m with a resultant static pressure of 201 kN/m2.[nb 1] This is in effect 20 metres of green water (huge rogue wave) 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 of less than two metres of water or 17.1 kN/m2,[nb 2] in other words the typhoon load on the hatches was more than ten (10) times the design load. The structural analysis of the wreck of the Derbyshire is now widely regarded as irrefutable.[62]

In addition fast moving waves are now known to also exert extremely high dynamic pressure. It is known that plunging or breaking waves can cause short-lived impulse pressure spikes called Gifle peaks. These can reach pressures of 200 kN/m2 (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.[10] Smith has documented scenarios where hydrodynamic pressure of up to 5,650 kN/m2 or over 500 metric tonnes per square metre could occur.[nb 3][62]

In November 1997 the International Maritime Organization (IMO) adopted new rules covering survivability and structural requirements for bulk carriers of 150 metres 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.[64]

As the science of rogue waves has developed, so too has ship design. It is now widely held that 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 metric tons per square metre (MT/m2). Although modern ships are designed to (typically) tolerate a breaking wave of 15 MT/m2, a rogue wave can dwarf both of these figures with a breaking force far exceeding 100 MT/m2.[3][nb 4] Smith has presented calculations using the International Association of Classification Societies (IACS) Common Structural Rules (CSR) for a typical bulk carrier which are consistent.[nb 5][62]

Challenor, a leading scientists in this field has stated that We don’t have that random messy theory for nonlinear waves. At all he says. People have been working actively on this for the past 50 years at least. We don’t even have the start of a theory.[61][51]

In 2006 Smith proposed that the International Association of Classification Societies (IACS) recommendation 34 pertaining to standard wave data be modified so that the minimum design wave height be increased to 65 feet. He presented analysis that there was 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. Smith has also proposed that the dynamic force of wave impacts should be included in the structural analysis.[65]

It is notable that the Norwegian offshore standards now take into account extreme severe wave conditions and require that a 10,000-year wave does not endanger the ships integrity.[66] Rosenthal notes that as at 2005 rogue waves were not explicitly accounted for in Classification Societies’ Rules for ships’ design.[66] As an example, DNV GL, one of the world's largest international certification body 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 at January 2016 still has not included any allowance for rogue waves.[67]

The U.S. Navy historically took the design position that the largest wave likely to be encountered was 21.4 m (70 ft). 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 as a consequence of new knowledge of waves greater than 21.4 m (70 ft) because they build to higher standards.[62]

A characteristic of the shipping industry is that there are no uniform codes or international standards. There are more than 50 classification societies worldwide, each has different rules. Ship design has historically largely been led by the ship insurers who inspected, classified and insured vessels. Hence the widespread adoption of new rules to allow for the existence of rogue waves is likely to take many years.[62]

See also

Oceanography, currents and regions
Waves

Footnotes

  1. ↑ A failure load pressure of 201 kN/m2 is the same as 20,500 kgf/m2 or 20.5 Mt/m2 (metric tonnes per square metre).
  2. ↑ A design load pressure (of the hatches) of 17.1 kN/m2 is the same as 1,744 kgf/m2 or 1.7 Mt/m2 (metric tonnes per square metre).
  3. ↑ A hydrostatic pressure of 5,650 kN/m2 is the same as 576,100 kgf/m2 or 576.1 Mt/m2 (metric tonnes per square metre).
  4. ↑ Note that MT/m refers to metric tonnes per square metre.
  5. ↑ Smith has presented calculations for a hypothetical bulk carrier with a length of 275m and a displacement of 161,000 metric tonnes, the design Hydrostatic pressure, 8.75 m below waterline is 88 kN/m2 or 88 kPa or 8.9 MT/m2 (metric tonnes per square metre). For the same carrier the design Hydrodynamic pressure is 122 kN/m2 or 122 kPa or 12,440 kgf/m2 (kilograms of force per square metre) or 12.44 Mt/m2 (metric tonnes per square metre).

References

  1. ↑ Haver, Sverre (2003). Freak wave event at Draupner jacket January 1 1995 (PDF) (Report). Statoil, Tech. Rep. PTT-KU-MA. Retrieved 2015.
  2. 1 2 3 4 5 6 "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. 1 2 3 4 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. ↑ "Physics of Tsunamis". NOAA.gov. US Dept of Commerce. 27 January 2016. Retrieved 29 January 2016. They can not be felt aboard ships nor can they be seen from the air in the open ocean.
  7. 1 2 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
  8. 1 2 Laird, Anne Marie (December 2006). "Observed Statistics of Extreme Waves". Doctoral dissertation, Monterey, California Naval Postgraduate School: 2.
  9. 1 2 3 4 "Freak Wave - programme summary". http://www.bbc.co.uk/. BBC. 14 November 2002. Retrieved 15 January 2016. External link in |website= (help)
  10. 1 2 3 Faulkner, Douglas (1998). An Independent Assessment of the Sinking of the M.V. Derbyshire. SNAME Transactions, Royal Institution of Naval Architects. pp. 59–103. 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 m to 30 m or more were quite likely to have occurred during typhoon Orchid.
  11. 1 2 Faulkner, Douglas (2000). Rogue Waves - Defining Their Characteristics for Marine Design (PDF). Rogue Waves 2000 Workshop. Brest: French Research Institute for Exploitation of the Sea. p. 16. Retrieved 15 January 2016. 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.
  12. ↑ Royal Commission on the Ocean Ranger Marine Disaster (Canada) (1985). Safety offshore Eastern Canada, summary of studies & seminars. The Commission.
  13. ↑ Liu, Paul C. (2007). "A Chronology of Freaque Wave Encounters" (PDF). Geofizika 24 (1): 57–70. Retrieved October 8, 2012.
  14. 1 2 "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.
  15. ↑ "Observing the Earth: Ship-Sinking Monster Waves revealed by ESA Satellites". www.ESA.int. ESA. 21 July 2004. Retrieved 14 January 2016.
  16. 1 2 Wolff, Julius F. (1979). "Lake Superior Shipwrecks", p. 28. Lake Superior Marine Museum Association, Inc., Duluth, Minnesota, USA. ISBN 0-932212-18-8.
  17. ↑ "Freak waves spotted from space". BBC News Online. 22 July 2004. Retrieved May 8, 2006.
  18. 1 2 3 "Rogue Waves". Ocean Prediction Center. National Weather Service. April 22, 2005. Retrieved May 8, 2006.
  19. ↑ Adrian Cho (13 May 2011). "Ship in Bottle, Meet Rogue Wave in Tub". Science Now 332: 774. Retrieved 2011-06-27.
  20. ↑ Phillips 1957, Journal of Fluid Mechanics
  21. ↑ Miles, 1957, Journal of Fluid Mechanics
  22. ↑ Frederic-Moreau. The Glorious Three, translated by M. Olagnon and G.A. Chase / Rogue Waves-2004, Brest, France
  23. ↑ Endeavour or Caledonian Star report, March 2, 2001, 53°03′S 63°35′W / 53.050°S 63.583°W
  24. ↑ MS Bremen report, February 22, 2001, 45°54′S 38°58′W / 45.900°S 38.967°W
  25. ↑ 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)
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  27. ↑ 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). Bibcode:2010NatPh...6..790K. doi:10.1038/nphys1740.
  28. ↑ "Peregrine's 'Soliton' observed at last". bris.ac.uk. Retrieved 2010-08-24.
  29. ↑ "Eagle Island Lighthouse". Commissioners of Irish Lights. Retrieved 28 October 2010.
  30. ↑ Haswell-Smith, Hamish (2004). The Scottish Islands. Edinburgh: Canongate. pp. 329–31. ISBN 978-1-84195-454-7.
  31. ↑ Munro, R.W. (1979) Scottish Lighthouses. Stornoway. Thule Press. ISBN 0-906191-32-7. Munro (1979) pages 170-1
  32. ↑ The New York Times, September 26, 1901, p. 16
  33. ↑ , Müller, et al., "Rogue Waves," 2005
  34. 1 2 Rogue Giants at Sea, Broad, William J, New York Times, July 11, 2006
  35. 1 2 3 Bruce Parker (13 March 2012). The Power of the Sea: Tsunamis, Storm Surges, Rogue Waves, and Our Quest to Predict Disasters. St. Martin's Press. ISBN 978-0-230-11224-7.
  36. ↑ "Ship-sinking monster waves revealed by ESA satellites", ESA News, July 21, 2004, accessed June 18, 2010
  37. ↑ "The Story of the Fastnet - The Economist Magazine December 18th 2008"
  38. ↑ Douglas Faulkner, "An Analytical Assessment of the Sinking of the M.V. Derbyshire," RINA Transactions 2001, Royal Institution of Naval Architects.
  39. ↑ http://www.esa.int/esaCP/SEMOKQL26WD_index_0.html
  40. ↑ Hurricane Ivan prompts rogue wave rethink, The Register, 5 August 2005
  41. ↑ Reuters (April 18, 2005). Freak wave pummels cruise ship.
  42. ↑ "NTSB – Brief MAB-05/03". Archived from the original on 2009-03-08. Retrieved 2009-03-08.
  43. ↑ 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 Discovery.com
  44. ↑ Monster waves threaten rescue helicopters PDF (35.7 KiB), U.S. Naval Institute, December 15, 2006
  45. ↑ "Olas de récord en Cantabria". El Diario Montañés. 3 February 2009.
  46. ↑ "Dos muertos y 16 heridos por una ola gigante en un crucero con destino a Cartagena". La Vanguardia. 3 March 2010.
  47. ↑ "Giant rogue wave slams into ship off French coast, killing 2". FoxNews. 3 March 2010.
  48. ↑ "Nuevo récord de altura de ola máxima registrada en España". Puertos del Estado. 21 October 2014.
  49. ↑ 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.
  50. ↑ Ian Jones; Joyce Jones (2008). Oceanography in the Days of Sail (PDF). Hale & Iremonger. p. 115. ISBN 978-0-9807445-1-4. 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 being expressed that no wave would exceed 30 feet, Dumont d'Urville's estimations were received, it seemed, with some scepticism. 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'
  51. 1 2 3 Susan Casey (2010). The Wave: In the Pursuit of the Rogues, Freaks and Giants of the Ocean. Doubleday Canada. ISBN 978-0-385-66667-1.
  52. ↑ Keith McCloskey (15 July 2014). The Lighthouse: The Mystery of the Eilean Mor Lighthouse Keepers. History Press Limited. ISBN 978-0-7509-5741-0.
  53. ↑ Carlos Guedes Soares; T.A. Santos (3 October 2014). Maritime Technology and Engineering. CRC Press. ISBN 978-1-315-73159-9.
  54. ↑ John H. Steele; Steve A. Thorpe; Karl K. Turekian (26 August 2009). Elements of Physical Oceanography: A derivative of the Encyclopedia of Ocean Sciences. Academic Press. ISBN 978-0-12-375721-0.
  55. ↑ Robert Gordon Pirie (1996). Oceanography: Contemporary Readings in Ocean Sciences. Oxford University Press. ISBN 978-0-19-508768-0.
  56. ↑ M. Grant Gross (1 March 1996). Oceanography. Prentice Hall. ISBN 978-0-13-237454-5.
  57. ↑ Skourup, J; Hansen, N.-E. O.; Andreasen, K. K. (1997-08-01). "Non-Gaussian Extreme Waves in the Central North Sea". Journal of Offshore Mechanics and Arctic Engineering (ASME). doi:10.1115/1.2829061. Retrieved 15 January 2016. The area of the Central North Sea is notorious for the occurrence of very high waves in certain wave trains. The short-term distribution of these wave trains includes waves which are far steeper than predicted by the Rayleigh distribution. 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 yr of wave records from the Mærsk Olie og Gas AS operated Gorm Field which is 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) has been found to be about 1.8, and the ratio between extreme crest height and extreme wave height has been found to be 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.
  58. ↑ Brown, David (1998). "The Loss of the 'DERBYSHIRE'" (Technical Report). Crown.
  59. ↑ "Ships and Seafarers (Safety)". Parliamentary Debates (Hansard). House of Commons. 25 June 2002. col. 193WH–215WH. 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.
  60. ↑ Lerner, S.; Yoerger, D.; Crook, T. (MAY 1999). "Navigation for the Derbyshire Phase2 Survey" (PDF) (Technical Report). Woods Hole Oceanographic Institution MA. p. 28. WHOI-99-11. 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 precisely position the vessel and vehicles. Precise navigation permits the survey team to control the path of the subsea vehicle in order 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. In this report, we summarize the techniques used to locate Argo as well as the repeatability of those navigation fixes. To determine repeatability, we selected a number of instances where the vehicle lines crossed. By registering two images from overlapping areas on different tracklines, we can determine the true position offset. By comparing the position offset derived from the images to the offsets obtained from navigation, we can determine the navigation error. 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. Check date values in: |date= (help)
  61. 1 2 3 "The last word: Terrors of the sea". http://theweek.com/. 27 September 2010. Retrieved 15 January 2016. External link in |website= (help)
  62. 1 2 3 4 5 6 Smith, Craig (2007). Extreme Waves and Ship Design (PDF). 10th International Symposium on Practical Design of Ships and Other Floating Structures. Houston: American Bureau of Shipping. p. 8. Retrieved 13 January 2016. Recent research has demonstrated that extreme waves, waves with crest to trough heights of 20 to 30 meters, occur more frequently than previously thought.
  63. ↑ Holliday, N.P.; Yelland, M.Y.; Pascal, R.; Swail, V.; Taylor, P.K.; Griffiths, C.R.; Kent, E.C. (2006). "Were extreme waves in the Rockall Trough the largest ever recorded?". Geophysical Research Letters (Wiley) 33 (5): L05613. Retrieved 15 January 2016. 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 which successfully simulated the arrival of the wave group but underestimated the most extreme waves.
  64. ↑ "Improving the safety of bulk carriers" (PDF). IMO. Retrieved 2009-08-11.
  65. ↑ Smith, Craig (2006). Extreme Waves. Joseph Henry Press. ISBN 9780309100625. 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 creq and cargo is considered.
  66. 1 2 Rosenthal, W (2005). "Results of the MAXWAVE project" (PDF). www.soest.hawaii.edu. Retrieved 14 January 2016. The Norwegian offshore standards take into account extreme severe wave conditions by requiring that a 10,000-year wave does not endanger the structure’s integrity (Accidental Limit State, ALS).
  67. ↑ "Rules for Classification and Construction" (PDF). http://www.gl-group.com/. Hamburg, Germany: Germanischer Lloyd SE. 2011. Retrieved 13 January 2016. 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. External link in |website= (help)

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