Rogue wave
Rogue waves are large and unpredictable surface waves that can be extremely dangerous to ships and isolated structures such as lighthouses. They are distinct from tsunamis, which are long-wavelength waves, often almost unnoticeable in deep waters and caused by the displacement of water due to other phenomena. A rogue wave at the shore is sometimes called a sneaker wave.
In oceanography, rogue waves are more precisely defined as waves whose heights are more than twice the significant wave height, which is itself defined as the mean of the largest third of waves in a wave record. Rogue waves do not appear to have a single distinct cause but occur where physical factors such as high winds and strong currents cause waves to merge to create a single large wave. Research published in 2023 suggests sea state crest-trough correlation leading to linear superposition may be a dominant factor in predicting the frequency of rogue waves.
Among other causes, studies of nonlinear waves such as the Peregrine soliton, and waves modeled by the nonlinear Schrödinger equation, suggest that modulational instability can create an unusual sea state where a "normal" wave begins to draw energy from other nearby waves, and briefly becomes very large. Such phenomena are not limited to water and are also studied in liquid helium, nonlinear optics, and microwave cavities. A 2012 study reported that, in addition to the Peregrine soliton reaching up to about three times the height of the surrounding sea, a hierarchy of higher-order wave solutions could also exist having progressively larger sizes and demonstrated the creation of a "super rogue wave" in a water-wave tank.
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. Although it is often claimed that rogue holes have never been observed in nature despite replication in wave tank experiments, there is a rogue hole recording from an oil platform in the North Sea, revealed in Kharif et al. The same source also reveals a recording of what is known as the "Three Sisters", in which three successive large waves form.
Background
Rogue waves are waves in open water that are much larger than surrounding waves. More precisely, rogue waves have a height which is more than twice the significant wave height. They can be caused when currents or winds cause waves to travel at different speeds, and the waves merge to create a single large wave, or when nonlinear effects cause energy to move between waves to create a single extremely large wave.Once considered mythical and lacking hard evidence, rogue waves are now proven to exist and are known to be natural ocean phenomena. Eyewitness accounts from mariners and damage inflicted on ships have long suggested they occur. Still, the first scientific evidence of their existence came with the recording of a rogue wave by the Gorm 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 accuracy of the wave-height reading made by a downwards-pointing laser sensor.
The existence of rogue waves has since been confirmed by videos, photographs, satellite imagery, radar of the ocean surface, stereo wave-imaging systems, pressure transducers on the seafloor, 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 an 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. These are also different from the wave known as a "hundred-year wave", which is a purely statistical description of a particularly high wave with a 1% chance to occur in any given year in a particular body of water.
Rogue waves have now been proven to cause the sudden loss of some ocean-going vessels. Well-documented instances include the freighter MS München, lost in 1978. Rogue waves have been implicated in the loss of other vessels, including the Ocean Ranger, a semisubmersible mobile offshore drilling unit that sank in Canadian waters on 15 February 1982. In 2007, the United States' National Oceanic and Atmospheric Administration compiled a catalog 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 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, the thought 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. Still, these were not linked conceptually to sailors' stories of encounters with giant rogue ocean waves, as the latter were believed to be scientifically implausible.Since the 19th century, oceanographers, meteorologists, engineers, and ship designers have used a statistical model known as the Gaussian function 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 an SWH of, the model suggests that a wave higher than would hardly ever occur. It suggests one of could indeed happen, but only once in 10,000 years. This basic assumption was well-accepted, though acknowledged to be an approximation. Using a Gaussian form to model waves has been the sole basis of virtually every text on that topic for the past 100 years.
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.
Research on cross-swell waves and their contribution to rogue wave studies
Before the Draupner wave was recorded in 1995, early research had already made significant strides in understanding extreme wave interactions. In 1979, Dik Ludikhuize and Henk Jan Verhagen at TU Delft successfully generated cross-swell waves in a wave basin. Although only monochromatic waves could be produced at the time, their findings, reported in 1981, showed that individual wave heights could be added together even when exceeding breaker criteria. This phenomenon provided early evidence that waves could grow significantly larger than anticipated by conventional theories of wave breaking.This work highlighted that in cases of crossing waves, wave steepness could increase beyond usual limits. Although the waves studied were not as extreme as rogue waves, the research provided an understanding of how multidirectional wave interactions could lead to extreme wave heights—a key concept in the formation of rogue waves. The crossing-wave phenomenon studied in the Delft Laboratory therefore had direct relevance to the unpredictable rogue waves encountered at sea.
Research published in 2024 by TU Delft and other institutions has subsequently demonstrated that waves coming from multiple directions can grow up to four times steeper than previously imagined.
The 1995 Draupner wave
The Draupner wave was the first rogue wave to be detected by a measuring instrument. The wave was recorded in 1995 at Unit E of the Draupner platform, a gas-pipeline support complex located in the North Sea about southwest from the southern tip of Norway.At 15:24 UTC on 1 January 1995, the device recorded a rogue wave with a maximum wave height of. Its peak elevation above still water level was. The reading was confirmed by the other sensors. In the area, the SWH at the time was about, 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. Still, in shallow waters during high-energy events, extremely high waves are rarer than this particular model predicts. From about 1997, most leading authors acknowledged the existence of rogue waves with the caveat that wave models could not 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 but were the typical realizations of a rare and strongly non-gaussian sea surface population of waves. A workshop of leading researchers in the world attended the first Rogue Waves 2000 workshop held in Brest in November 2000.
In 2000, 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 SWH 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 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." In simple terms, a scientific model 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 10 individual giant waves above in height during a short survey period of three weeks in a limited area of the South Atlantic. 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. Rogue waves are now known to occur in all of the world's oceans many times each day.
Rogue waves are now accepted as a common phenomenon. Professor Akhmediev of the Australian National University has stated that 10 rogue waves exist in the world's oceans at any moment. Some researchers have speculated that roughly three of every 10,000 waves on the oceans achieve rogue status, yet in certain spots—such as coastal inlets and river mouths—these extreme waves can make up three 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, and the third incoming wave adds to the two accumulated backwashes and suddenly overloads the ship deck with large amounts of water. The phenomenon is one of various theorized causes of the sinking of the on Lake Superior in November 1975.
A 2012 study reported that, in addition to the Peregrine soliton reaching up to about 3 times the height of the surrounding sea, a hierarchy of higher-order wave solutions could also exist having progressively larger sizes, and demonstrated the creation of a "super rogue wave"—a breather around 5 times higher than surrounding waves—in a water tank. Also in 2012, researchers at the Australian National University proved the existence of "rogue wave holes", an inverted profile of a rogue wave. Their research created rogue wave holes on the water surface in a water-wave tank. In maritime folklore, stories of rogue holes are as common as stories of rogue waves. They had followed from theoretical analysis but had never been proven experimentally.
"Rogue wave" has become a near-universal term used by scientists to describe isolated, large-amplitude waves that occur more frequently than expected for normal, Gaussian-distributed, statistical events. Rogue waves appear ubiquitous and are not limited to the oceans. They appear in other contexts and have been reported in liquid helium, nonlinear optics, and microwave cavities. Marine researchers universally now accept that these waves belong to a specific kind of sea wave, not considered by conventional models for sea wind waves. A 2015 paper studied the wave behavior around a rogue wave, including optical and the Draupner wave, and concluded, "rogue events do not necessarily appear without warning but are often preceded by a short phase of relative order".
In 2019, researchers succeeded in producing a wave with similar characteristics to the Draupner wave, and proportionately greater height, using multiple wavetrains meeting at an angle of 120°. Previous research had strongly suggested that the wave resulted from an interaction between waves from different directions. Their research also highlighted that wave-breaking behavior was not necessarily as expected. If waves met at an angle less than about 60°, then the top of the wave "broke" sideways and downwards. Still, from about 60° and greater, the wave began to break vertically upwards, creating a peak that did not reduce the wave height as usual but instead increased it. They also showed that the steepness of rogue waves could be reproduced in this manner. Lastly, they observed that optical instruments such as the laser used for the Draupner wave might be somewhat confused by the spray at the top of the wave if it broke, and this could lead to uncertainties of around in the wave height. They concluded, "... the onset and type of wave breaking play a significant role and differ significantly for crossing and noncrossing waves. Crucially, breaking becomes less crest-amplitude limiting for sufficiently large crossing angles and involves the formation of near-vertical jets".