Rogue wave
Rogue waves (also known as freak waves, monster waves, episodic waves, killer waves, extreme waves, and abnormal waves) are unusually large, unpredictable and suddenly appearing surface waves that can be extremely dangerous to ships, even to large ones. They are distinct from tsunamis, which are often almost unnoticeable in deep waters and are caused by the displacement of water due to other phenomena (such as earthquakes). A rogue wave appearing at the shore is sometimes referred to as a sneaker wave. In oceanography, rogue waves are more precisely defined as waves whose height is more than twice the  significant wave height ("H" 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. Rogue waves can occur in media other than water. They appear to be ubiquitous in nature and have also been  reported in liquid helium, in quantum mechanics, in nonlinear optics, in microwave cavities, in Bose–Einstein condensation, in heat and diffusion, and in finance. 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. Rogue holes have been replicated in experiments using water wave tanks, but have not been confirmed in the real world. 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 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 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 peak-to-peak distance between adjacent waves.) 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 that they occur. The first scientific evidence of their existence came with the recording of a rogue wave by the Gorm platform in the central North Sea in 1984. A stand-out wave was detected with a wave height of  in a relatively low sea state. 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 and peak elevation of . During that event, minor damage was inflicted on the platform far above sea level, confirming the validity of the reading made by a down-pointing laser sensor. Their existence has also since been confirmed by video and photographs, satellite imagery, radar of the ocean surface, stereo wave imaging systems , pressure transducers on the sea-floor, and oceanographic research vessels. 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 any scientific instruments in the open ocean, with a SWH of and individual waves up to . "In 2004 scientists using three weeks of radar images from European Space Agency satellites found ten rogue waves, each or higher." 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. 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. Tsunamis are caused by a massive displacement of water, often resulting from sudden movements 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; 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 are a purely statistical prediction of the highest wave likely to occur in a hundred-year period in a particular body of water. 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. Rogue waves have been implicated in the loss of other vessels, including the "Ocean Ranger", a semi-submersible mobile offshore drilling unit that sank in Canadian waters on 15 February 1982. 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. History of rogue wave knowledge. Early reports. In 1826, French scientist and naval officer Captain Jules Dumont d'Urville reported waves as  high as in the Indian Ocean with three colleagues as witnesses, yet he was publicly ridiculed by fellow scientist François Arago. In that era it was widely held that no wave could exceed . Author Susan Casey wrote that much of that disbelief came because there were very few people who had seen a rogue wave and survived; until the advent of steel double-hulled ships of the 20th century "people who encountered rogue waves generally weren't coming back to tell people about it." 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), but 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 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. In a  storm sea with a significant wave height of , the model suggests there will hardly ever be a wave higher than . It suggests one of could indeed happen – but only once in ten thousand years. This basic assumption was well accepted, though acknowledged to be an approximation. The use of a Gaussian form to model waves had been the sole basis of virtually every text on that topic for the past 100 years. 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 Institute of  Oceanography in the early 1960s to record wave height, and the highest wave recorded at that time, which was about . Draper also described "freak wave holes". However, even as late as the mid-1990s, most popular texts on oceanography such as that by Pirie did not contain any mention of rogue or freak waves. Even after the 1995 Draupner wave, the popular text on "Oceanography" by Gross (1996) only gave rogue waves a mention and simply stated that "Under extraordinary circumstances unusually large waves called rogue waves can form" without providing any further detail. The 1995 Draupner wave. The Draupner wave  (or New Year's 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 southwest from the southern tip of Norway. The rig was built to withstand a calculated 1-in-10,000-years wave with a predicted height of and was fitted with a state-of-the-art set of sensors, including a laser rangefinder wave recorder on the platform's underside. At 3 pm on 1 January 1995, the device recorded a rogue  wave with a maximum wave height of . Peak elevation above still water level was . The reading was confirmed by the other sensors. The platform sustained minor damage in the event. In the area, the significant wave height was approximately , 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. 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. 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. 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. 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 rather they were the typical realizations of a rare and strongly non-gaussian sea surface population of waves ("freak" extreme waves). A workshop of leading researchers in the world attended the first Rogue Waves 2000 workshop held in Brest in November 2000. In 2000 the British oceanographic vessel RRS "Discovery" recorded a 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 a ship-borne wave recorder measured individual waves up to from crest to trough, and  a maximum significant wave height of . 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) above . 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". In 2004 the ESA MaxWave project identified more than ten individual giant waves above in height during a short survey period of three weeks in a limited area of the South Atlantic. The ESA's ERS satellites have helped to establish the widespread existence of these "rogue" waves. By 2007, it was further proven via satellite radar studies  that waves with crest to trough heights of , occur far more frequently than previously thought. It is now known that rogue waves occur in all of the world's oceans many times each day. It is now well accepted that rogue waves are a common phenomenon. Professor Akhmediev of the Australian National University has stated that there are about 10 rogue waves in the world's oceans at any moment. Some researchers have speculated that approximately 3 of every 10,000 waves on the oceans achieve rogue status, yet in certain spots – like coastal inlets and river mouths – these extreme waves  can make up 3 out of every 1,000 waves, because wave energy can be focused. 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 is one of various theorized causes of the sinking of the on Lake Superior in November 1975. Serious studies of the  phenomenon of rogue waves only started after the 1995 Draupner wave and have intensified since about 2005. One of the remarkable features of the rogue waves is that they always appear from nowhere and quickly disappear without a trace. Recent research has suggested that there could also be "super-rogue waves", which are up to five times the average sea state. "Rogue wave" has now 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 to be ubiquitous in nature and  are not limited to the oceans. They appear in other contexts and have recently been reported in liquid helium, in nonlinear optics, and in microwave cavities. It is now universally accepted by marine researchers that these waves belong to a specific kind of sea wave, not taken into account by conventional models for sea wind waves. 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. In maritime folklore, stories of rogue holes  are as common as stories of rogue waves. They follow from theoretical analysis but had never been proven experimentally. 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". In 2019, researchers succeeded in producing a wave with similar characteristics to the Draupner wave (steepness and breaking), and proportionately greater height, using multiple wavetrains meeting at an angle of 120 degrees. 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 degrees, then the top of the wave "broke" sideways and downwards (a "plunging breaker"). But from about 60 degrees 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. Finally, 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 in the wave height. They concluded "that the onset and type of wave breaking play a significant role and differ significantly for crossing and non-crossing waves. Crucially, breaking becomes less crest-amplitude limiting for sufficiently large crossing angles and involves the formation of near-vertical jets". Research efforts. There are a number of research programmes currently underway focussed on rogue waves, including: Causes. 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 localized variation. Suggested mechanisms for freak waves include the following: 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. Other media. Researchers at UCLA observed rogue wave phenomena in microstructured optical fibers near the threshold of soliton supercontinuum generation, and characterized the initial conditions for generating rogue waves in any medium. Research in optics has 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. Reported encounters. 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 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. Quantifying the impact of rogue waves on ships. The loss of the 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, which was recovered from floating wreckage some time later. The lifeboats  hung from forward and aft blocks 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 . 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". In 1980 the MV "Derbyshire" was lost during 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 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 that prompted the British government to reopen a formal investigation into the sinking. The 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 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. 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 with a resultant static pressure of . This is in effect of seawater (possibly a "super 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 of water or , meaning that the typhoon load on the hatches was more than ten times the design load. The forensic structural analysis of the wreck of the "Derbyshire" is now widely regarded as irrefutable. 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 (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". Smith has documented scenarios where hydrodynamic pressure of up to or over 500 metric tonnes per square metre could occur. In 2004 an extreme wave was recorded impacting the Admiralty Breakwater, Alderney in the Channel Islands. This breakwater is exposed to the Atlantic Ocean. The peak pressure recorded by a shore-mounted transducer was . This pressure far exceeds almost any design criteria for modern ships and this wave would have destroyed almost any merchant vessel. Design standards. In November 1997 the International Maritime Organization (IMO) adopted new rules covering survivability and structural requirements for  bulk carriers of 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. 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 wave in the usual "linear" model would have a breaking force of . Although modern ships are designed to (typically) tolerate a breaking wave of 15 t/m, a rogue wave can dwarf both of these figures with a breaking force far exceeding 100 t/m. Smith has  presented calculations using the International Association of Classification Societies (IACS) Common Structural Rules (CSR) for a typical bulk carrier which are consistent. Peter Challenor, a leading scientist in this field from the National Oceanography Centre in the United Kingdom, was quoted in 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." 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 . He presented analysis that there was sufficient evidence to conclude that high waves can be experienced in the 25-year lifetime of oceangoing vessels, and that high waves are less likely, but not out of the question. Therefore, a design criterion based on 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. 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. Rosenthal notes that as at 2005 rogue waves were not explicitly accounted for in Classification Societies’ Rules for ships’ design. 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. The U.S. Navy historically took  the design position that the largest wave likely to be encountered was . 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 metres because they build to higher standards. There are more than 50 classification societies worldwide, each with different rules, although 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.