Rogue waves (also known as freak waves or killer waves) are large and unpredictable surface waves that can be extremely dangerous to ships and isolated structures such as lighthouses. [1] They are distinct from tsunamis, which are long wavelength waves, often almost unnoticeable in deep waters and are caused by the displacement of water due to other phenomena (such as earthquakes). A rogue wave at the shore is sometimes called a sneaker wave. [2]
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. 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. [1] Recent research suggests sea state crest-trough correlation leading to linear superposition may be a dominant factor in predicting the frequency of rogue waves. [3]
Among other causes, studies of nonlinear waves such as the Peregrine soliton, and waves modeled by the nonlinear Schrödinger equation (NLS), suggest that modulational instability can create an unusual sea state where a "normal" wave begins to draw energy from other nearby waves, and briefly becomes very large. Such phenomena are not limited to water and are also studied in liquid helium, nonlinear optics, and microwave cavities. A 2012 study reported that in addition to the Peregrine soliton reaching up to about three times the height of the surrounding sea, a hierarchy of higher order wave solutions could also exist having progressively larger sizes and demonstrated the creation of a "super rogue wave" (a breather around five times higher than surrounding waves) in a water-wave tank. [4]
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. [5] 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. [6] The same source also reveals a recording of what is known as the 'Three Sisters'.
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 (Hs or SWH). 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 11 m (36 ft) in a relatively low sea state. [7] 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 25.6 m (84 ft) and peak elevation of 18.5 m (61 ft). 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. [8]
The existence of rogue waves has since been confirmed by video and photographs, satellite imagery, radar of the ocean surface, [9] stereo wave imaging systems, [10] pressure transducers on the sea-floor, and oceanographic research vessels. [11] 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 18.5 metres (61 ft) and individual waves up to 29.1 metres (95 ft). [12] 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. [13]
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. [1] 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. [1] 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; [14] therefore, tsunamis do not present a threat to shipping at sea (e.g., the only ships lost in the 2004 Asian tsunami were in port.). 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. [15] 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. [16] 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. [17]
In 1826, French scientist and naval officer Jules Dumont d'Urville reported waves as high as 33 m (108 ft) 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 9 m (30 ft). [18] [19] 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 100-foot [30 m] rogue waves generally weren't coming back to tell people about it." [20]
Unusual waves have been studied scientifically for many years (for example, John Scott Russell's wave of translation, an 1834 study of a soliton wave). Still, these were not linked conceptually to sailors' stories of encounters with giant rogue ocean waves, as the latter were believed to be scientifically implausible.
Since the 19th century, oceanographers, meteorologists, engineers, and ship designers have used a statistical model known as the Gaussian function (or Gaussian Sea or standard linear model) to predict wave height, on the assumption that wave heights in any given sea are tightly grouped around a central value equal to the average of the largest third, known as the significant wave height (SWH). [21] In a storm sea with an SWH of 12 m (39 ft), the model suggests hardly ever would a wave higher than 15 m (49 ft) occur. It suggests one of 30 m (98 ft) 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. [21] [22] [ when? ][ why? ]
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 20 metres (67 ft). Draper also described freak wave holes. [23] [24] [25]
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. [26]
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. [27]
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. [28]
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 160 km (100 miles) southwest from the southern tip of Norway. [29] [a]
The rig was built to withstand a calculated 1-in-10,000-years wave with a predicted height of 20 m (64 ft) and was fitted with state-of-the-art 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 25.6 m (84 ft). Peak elevation above still water level was 18.5 m (61 ft). [30] The reading was confirmed by the other sensors. [31] The platform sustained minor damage in the event.
In the area, the SWH at the time was about 12 m (39 ft), so the Draupner wave was more than twice as tall and steep as its neighbors, with characteristics that fell outside any known wave model. The wave caused enormous interest in the scientific community. [29] [31]
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. [32] 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. [13] From about 1997, most leading authors acknowledged the existence of rogue waves with the caveat that wave models could not replicate rogue waves. [18]
Statoil researchers presented a paper in 2000, collating evidence that freak waves were not the rare realizations of a typical or slightly non-gaussian sea surface population (classical extreme waves) but were the typical realizations of a rare and strongly non-gaussian sea surface population of waves (freak extreme waves). [33] A workshop of leading researchers in the world attended the first Rogue Waves 2000 workshop held in Brest in November 2000. [34]
In 2000, British oceanographic vessel RRS Discovery recorded a 29 m (95 ft) 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 21 metres per second (41 kn), a ship-borne wave recorder measured individual waves up to 29.1 m (95.5 ft) from crest to trough, and a maximum SWH of 18.5 m (60.7 ft). 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 (39.4 ft). 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 (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". [1] [12] [29] [35] [36]
In 2004, the ESA MaxWave project identified more than 10 individual giant waves above 25 m (82 ft) in height during a short survey period of three weeks in a limited area of the South Atlantic. [37] [38] By 2007, it was further proven via satellite radar studies that waves with crest-to-trough heights of 20 to 30 m (66 to 98 ft) occur far more frequently than previously thought. [39] 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. [40] 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. [41]
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 large amounts of water. The phenomenon is one of various theorized causes of the sinking of the SS Edmund Fitzgerald on Lake Superior in November 1975. [42]
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. [4] 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. [5] In maritime folklore, stories of rogue holes are as common as stories of rogue waves. They had followed from theoretical analysis but had never been proven experimentally.
"Rogue wave" has become a near-universal term used by scientists to describe isolated, large-amplitude waves that occur more frequently than expected for normal, Gaussian-distributed, statistical events. Rogue waves appear ubiquitous and are not limited to the oceans. They appear in other contexts and have recently been reported in liquid helium, nonlinear optics, and microwave cavities. Marine researchers universally now accept that these waves belong to a specific kind of sea wave, not considered by conventional models for sea wind waves. [43] [44] [45] [46] 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". [47]
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°. Previous research had strongly suggested that the wave resulted from an interaction between waves from different directions ("crossing seas"). Their research also highlighted that wave-breaking behavior was not necessarily as expected. If waves met at an angle less than about 60°, then the top of the wave "broke" sideways and downwards (a "plunging breaker"). Still, from about 60° and greater, the wave began to break vertically upwards, creating a peak that did not reduce the wave height as usual but instead increased it (a "vertical jet"). They also showed that the steepness of rogue waves could be reproduced in this manner. Lastly, they observed that optical instruments such as the laser used for the Draupner wave might be somewhat confused by the spray at the top of the wave if it broke, and this could lead to uncertainties of around 1.0 to 1.5 m (3 to 5 ft) 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". [48] [49]
On 17 November 2020, a buoy moored in 45 metres (148 ft) of water on Amphitrite Bank in the Pacific Ocean 7 kilometres (4.3 mi; 3.8 nmi) off Ucluelet, Vancouver Island, British Columbia, Canada, at 48°54′N125°36′W / 48.9°N 125.6°W recorded a lone 17.6-metre (58 ft) tall wave among surrounding waves about 6 metres (20 ft) in height. [50] The wave exceeded the surrounding significant wave heights by a factor of 2.93. When the wave's detection was revealed to the public in February 2022, one scientific paper [50] and many news outlets christened the event as "the most extreme rogue wave event ever recorded" and a "once-in-a-millennium" event, claiming that at about three times the height of the waves around it, the Ucluelet wave set a record as the most extreme rogue wave ever recorded at the time in terms of its height in proportion to surrounding waves, and that a wave three times the height of those around it was estimated to occur on average only once every 1,300 years worldwide. [51] [52] [53]
The Ucluelet event generated controversy. Analysis of scientific papers dealing with rogue wave events since 2005 revealed the claims for the record-setting nature and rarity of the wave to be incorrect. The paper Oceanic rogue waves [54] by Dysthe, Krogstad and Muller reports on an event in the Black Sea in 2004 which was far more extreme than the Ucluelet wave, where the Datawell Waverider buoy reported a wave whose height was 10.32 metres (33.86 ft) higher and 3.91 times the significant wave height, as detailed in the paper. Thorough inspection of the buoy after the recording revealed no malfunction. The authors of the paper that reported the Black Sea event [55] assessed the wave as "anomalous" and suggested several theories on how such an extreme wave may have arisen. The Black Sea event differs in the fact that it, unlike the Ucluelet wave, was recorded with a high-precision instrument. The Oceanic rogue waves paper also reports even more extreme waves from a different source, but these were possibly overestimated, as assessed by the data's own authors. The Black Sea wave occurred in relatively calm weather.
Furthermore, a paper [56] by I. Nikolkina and I. Didenkulova also reveals waves more extreme than the Ucluelet wave. In the paper, they infer that in 2006 a 21-metre (69 ft) wave appeared in the Pacific Ocean off the Port of Coos Bay, Oregon, with a significant wave height of 3.9 metres (13 ft). The ratio is 5.38, almost twice that of the Ucluelet wave. The paper also reveals the MV Pont-Aven incident as marginally more extreme than the Ucluelet event. The paper also assesses a report of an 11-metre (36 ft) wave in a significant wave height of 1.9 metres (6 ft 3 in), but the authors cast doubt on that claim. A paper written by Craig B. Smith in 2007 reported on an incident in the North Atlantic, in which the submarine Grouper was hit by a 30-meter wave in calm seas. [57]
Because the phenomenon of rogue waves is still a matter of active research, clearly stating what the most common causes are or whether they vary from place to place is premature. The areas of highest predictable risk appear to be where a strong current runs counter to the primary direction of travel of the waves; the area near Cape Agulhas off the southern tip of Africa is one such area. The warm Agulhas Current runs to the southwest, while the dominant winds are westerlies, but since this thesis does not explain the existence of all waves that have been detected, several different mechanisms are likely, with localized variation. Suggested mechanisms for freak waves include:
The spatiotemporal focusing seen in the NLS equation can also occur when the non-linearity is removed. In this case, focusing is primarily due to different waves coming into phase rather than any energy-transfer processes. Further analysis of rogue waves using a fully nonlinear model by R. H. Gibbs (2005) brings this mode into question, as it is shown that a typical wave group focuses in such a way as to produce a significant wall of water at the cost of a reduced height.
A rogue wave, and the deep trough commonly seen before and after it, may last only for some minutes before either breaking or reducing in size again. Apart from a single one, the rogue wave may be part of a wave packet consisting of a few rogue waves. Such rogue wave groups have been observed in nature. [73]
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A number of research programmes are currently underway or have concluded whose focus is/was on rogue waves, including:
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. [95] Research in optics has pointed out the role played by a Peregrine soliton that may explain those waves that appear and disappear without leaving a trace. [96] [97]
Rogue waves in other media appear to be ubiquitous and have also been reported in liquid helium, in quantum mechanics, [98] in nonlinear optics, in microwave cavities, [99] in Bose–Einstein condensate, [100] in heat and diffusion, [101] and in finance. [102] [103]
Many of these encounters are reported only in the media, and are not examples of open-ocean rogue waves. Often, in popular culture, an endangering huge wave is loosely denoted as a "rogue wave", while the case has not been established that the reported event is a rogue wave in the scientific sense – i.e. of a very different nature in characteristics as the surrounding waves in that sea state] and with a very low probability of occurrence.
This section lists a limited selection of notable incidents.
The loss of the MS München in 1978 provided some of the first physical evidence of the existence of rogue waves. München was a state-of-the-art cargo ship with multiple water-tight compartments and an expert crew. She was lost with all crew, and the wreck has never been found. The only evidence found was the starboard lifeboat recovered from floating wreckage sometime later. The lifeboats hung from forward and aft blocks 20 m (66 ft) 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 20 m (66 ft). 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. [15] [128]
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 to be— the largest British ship ever lost at sea. The wreck was found in June 1994. The survey team deployed a remotely operated vehicle to photograph the wreck. A private report published in 1998 prompted the British government to reopen a formal investigation into the sinking. The investigation included a comprehensive survey by the Woods Hole Oceanographic Institution, which took 135,774 pictures of the wreck during two surveys. The formal forensic investigation concluded that the ship sank because of structural failure and absolved the crew of any responsibility. Most notably, the report determined the detailed sequence of events that led to the structural failure of the vessel. A third comprehensive analysis was subsequently done by Douglas Faulkner, professor of marine architecture and ocean engineering at the University of Glasgow. His 2001 report linked the loss of the Derbyshire with the emerging science on freak waves, concluding that the Derbyshire was almost certainly destroyed by a rogue wave. [129] [130] [131] [132] [133]
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 20 m (66 ft) with a resultant static pressure of 201 kilopascals (2.01 bar; 29.2 psi). [b] This is in effect 20 m (66 ft) of seawater (possibly a super rogue wave) [c] flowing over the vessel. The deck cargo hatches on the Derbyshire were determined to be the key point of failure when the rogue wave washed over the ship. The design of the hatches only allowed for a static pressure less than 2 m (6.6 ft) of water or 17.1 kPa (0.171 bar; 2.48 psi), [d] meaning that the typhoon load on the hatches was more than 10 times the design load. The forensic structural analysis of the wreck of the Derbyshire is now widely regarded as irrefutable. [39]
In addition, fast-moving waves are now known to also exert extremely high dynamic pressure. Plunging or breaking waves are known to cause short-lived impulse pressure spikes called Gifle peaks. These can reach pressures of 200 kPa (2.0 bar; 29 psi) (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. [129] Smith documented scenarios where hydrodynamic pressure up to 5,650 kPa (56.5 bar; 819 psi) or over 500 metric tonnes/m2 could occur. [e] [39]
In 2004, an extreme wave was recorded impacting the Alderney Breakwater, Alderney, in the Channel Islands. This breakwater is exposed to the Atlantic Ocean. The peak pressure recorded by a shore-mounted transducer was 745 kPa (7.45 bar; 108.1 psi). This pressure far exceeds almost any design criteria for modern ships, and this wave would have destroyed almost any merchant vessel. [7]
In November 1997, the International Maritime Organization (IMO) adopted new rules covering survivability and structural requirements for bulk carriers of 150 m (490 ft) 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. [134]
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 m (39 ft) wave in the usual "linear" model would have a breaking force of 6 metric tons per square metre [t/m2] (8.5 psi). Although modern ships are typically designed to tolerate a breaking wave of 15 t/m2, a rogue wave can dwarf both of these figures with a breaking force far exceeding 100 t/m2. [117] Smith presented calculations using the International Association of Classification Societies (IACS) Common Structural Rules for a typical bulk carrier. [f] [39]
Peter Challenor, a scientist 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." [29] [35]
In 2006, Smith proposed that the IACS recommendation 34 pertaining to standard wave data be modified so that the minimum design wave height be increased to 19.8 m (65 ft). He presented analysis that sufficient evidence exists to conclude that 20.1 m (66 ft) high waves can be experienced in the 25-year lifetime of oceangoing vessels, and that 29.9 m (98 ft) high waves are less likely, but not out of the question. Therefore, a design criterion based on 11.0 m (36 ft) high waves seems inadequate when the risk of losing crew and cargo is considered. Smith also proposed that the dynamic force of wave impacts should be included in the structural analysis. [135] The Norwegian offshore standards now consider extreme severe wave conditions and require that a 10,000-year wave does not endanger the ships' integrity. [136] W. Rosenthal noted that as of 2005, rogue waves were not explicitly accounted for in Classification Society's rules for ships' design. [136] As an example, DNV GL, one of the world's largest international certification bodies and classification society with main expertise in technical assessment, advisory, and risk management publishes their Structure Design Load Principles which remain largely based on the Significant Wave Height, and as of January 2016, still have not included any allowance for rogue waves. [137]
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 due to new knowledge of waves greater than 21.4 m because the ships are built to higher standards than required. [39]
The more than 50 classification societies worldwide each has different rules. However, most new ships are built to the standards of the 12 members of the International Association of Classification Societies, which implemented two sets of common structural rules - one for oil tankers and one for bulk carriers, in 2006. These were later harmonised into a single set of rules. [138]
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The Challenger Deep is the deepest known point of the seabed of Earth, located in the western Pacific Ocean at the southern end of the Mariana Trench, in the ocean territory of the Federated States of Micronesia.
A tsunami is a series of waves in a water body caused by the displacement of a large volume of water, generally in an ocean or a large lake. Earthquakes, volcanic eruptions and underwater explosions above or below water all have the potential to generate a tsunami. Unlike normal ocean waves, which are generated by wind, or tides, which are in turn generated by the gravitational pull of the Moon and the Sun, a tsunami is generated by the displacement of water from a large event.
In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remarkable stability can be traced to a balanced cancellation of nonlinear and dispersive effects in the medium. Solitons were subsequently found to provide stable solutions of a wide class of weakly nonlinear dispersive partial differential equations describing physical systems.
An iceberg is a piece of freshwater ice more than 15 meters long that has broken off a glacier or an ice shelf and is floating freely in open water. Smaller chunks of floating glacially derived ice are called "growlers" or "bergy bits". Much of an iceberg is below the water's surface, which led to the expression "tip of the iceberg" to illustrate a small part of a larger unseen issue. Icebergs are considered a serious maritime hazard.
A seiche is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbors, caves, and seas. The key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave.
In fluid dynamics, a wind wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result of the wind blowing over the water's surface. The contact distance in the direction of the wind is known as the fetch. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small ripples to waves over 30 m (100 ft) high, being limited by wind speed, duration, fetch, and water depth.
MV Derbyshire was a British ore-bulk-oil combination carrier built in 1976 by Swan Hunter, as the last in the series of the Bridge-class sextet. She was registered at Liverpool and owned by Bibby Line.
In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose–Einstein condensates confined to highly anisotropic, cigar-shaped traps, in the mean-field regime. Additionally, the equation appears in the studies of small-amplitude gravity waves on the surface of deep inviscid (zero-viscosity) water; the Langmuir waves in hot plasmas; the propagation of plane-diffracted wave beams in the focusing regions of the ionosphere; the propagation of Davydov's alpha-helix solitons, which are responsible for energy transport along molecular chains; and many others. More generally, the NLSE appears as one of universal equations that describe the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state. The 1D NLSE is an example of an integrable model.
In physical oceanography, the significant wave height (SWH, HTSGW or Hs) is defined traditionally as the mean wave height (trough to crest) of the highest third of the waves (H1/3). It is usually defined as four times the standard deviation of the surface elevation – or equivalently as four times the square root of the zeroth-order moment (area) of the wave spectrum. The symbol Hm0 is usually used for that latter definition. The significant wave height (Hs) may thus refer to Hm0 or H1/3; the difference in magnitude between the two definitions is only a few percent. SWH is used to characterize sea state, including winds and swell.
Weather buoys are instruments which collect weather and ocean data within the world's oceans, as well as aid during emergency response to chemical spills, legal proceedings, and engineering design. Moored buoys have been in use since 1951, while drifting buoys have been used since 1979. Moored buoys are connected with the ocean bottom using either chains, nylon, or buoyant polypropylene. With the decline of the weather ship, they have taken a more primary role in measuring conditions over the open seas since the 1970s. During the 1980s and 1990s, a network of buoys in the central and eastern tropical Pacific Ocean helped study the El Niño-Southern Oscillation. Moored weather buoys range from 1.5–12 metres (5–40 ft) in diameter, while drifting buoys are smaller, with diameters of 30–40 centimetres (12–16 in). Drifting buoys are the dominant form of weather buoy in sheer number, with 1250 located worldwide. Wind data from buoys has smaller error than that from ships. There are differences in the values of sea surface temperature measurements between the two platforms as well, relating to the depth of the measurement and whether or not the water is heated by the ship which measures the quantity.
In hydrodynamics, a clapotis is a non-breaking standing wave pattern, caused for example, by the reflection of a traveling surface wave train from a near vertical shoreline like a breakwater, seawall or steep cliff. The resulting clapotic wave does not travel horizontally, but has a fixed pattern of nodes and antinodes. These waves promote erosion at the toe of the wall, and can cause severe damage to shore structures. The term was coined in 1877 by French mathematician and physicist Joseph Valentin Boussinesq who called these waves 'le clapotis' meaning "the lapping".
MS Stolt Surf was a chemical tanker, operated by Stolt-Nielsen Inc. She achieved a measure of infamy when she was struck and damaged by a rogue wave, an event that was photographed by a crew member and subsequently added to the ongoing debate over the possibility of such waves out in the deep ocean.
In fluid dynamics, wind wave modeling describes the effort to depict the sea state and predict the evolution of the energy of wind waves using numerical techniques. These simulations consider atmospheric wind forcing, nonlinear wave interactions, and frictional dissipation, and they output statistics describing wave heights, periods, and propagation directions for regional seas or global oceans. Such wave hindcasts and wave forecasts are extremely important for commercial interests on the high seas. For example, the shipping industry requires guidance for operational planning and tactical seakeeping purposes.
Internal tides are generated as the surface tides move stratified water up and down sloping topography, which produces a wave in the ocean interior. So internal tides are internal waves at a tidal frequency. The other major source of internal waves is the wind which produces internal waves near the inertial frequency. When a small water parcel is displaced from its equilibrium position, it will return either downwards due to gravity or upwards due to buoyancy. The water parcel will overshoot its original equilibrium position and this disturbance will set off an internal gravity wave. Munk (1981) notes, "Gravity waves in the ocean's interior are as common as waves at the sea surface-perhaps even more so, for no one has ever reported an interior calm."
The Peregrine soliton is an analytic solution of the nonlinear Schrödinger equation. This solution was proposed in 1983 by Howell Peregrine, researcher at the mathematics department of the University of Bristol.
Wind-wave dissipation or "swell dissipation" is process in which a wave generated via a weather system loses its mechanical energy transferred from the atmosphere via wind. Wind waves, as their name suggests, are generated by wind transferring energy from the atmosphere to the ocean's surface, capillary gravity waves play an essential role in this effect, "wind waves" or "swell" are also known as surface gravity waves.
Optical rogue waves are rare pulses of light analogous to rogue or freak ocean waves. The term optical rogue waves was coined to describe rare pulses of broadband light arising during the process of supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input waveform—in nonlinear optical fiber. In this context, optical rogue waves are characterized by an anomalous surplus in energy at particular wavelengths or an unexpected peak power. These anomalous events have been shown to follow heavy-tailed statistics, also known as L-shaped statistics, fat-tailed statistics, or extreme-value statistics. These probability distributions are characterized by long tails: large outliers occur rarely, yet much more frequently than expected from Gaussian statistics and intuition. Such distributions also describe the probabilities of freak ocean waves and various phenomena in both the man-made and natural worlds. Despite their infrequency, rare events wield significant influence in many systems. Aside from the statistical similarities, light waves traveling in optical fibers are known to obey the similar mathematics as water waves traveling in the open ocean, supporting the analogy between oceanic rogue waves and their optical counterparts. More generally, research has exposed a number of different analogies between extreme events in optics and hydrodynamic systems. A key practical difference is that most optical experiments can be done with a table-top apparatus, offer a high degree of experimental control, and allow data to be acquired extremely rapidly. Consequently, optical rogue waves are attractive for experimental and theoretical research and have become a highly studied phenomenon. The particulars of the analogy between extreme waves in optics and hydrodynamics may vary depending on the context, but the existence of rare events and extreme statistics in wave-related phenomena are common ground.
Roman Evsey Glazman was a Russian American physicist and oceanographer.
The nonlinearity of surface gravity waves refers to their deviations from a sinusoidal shape. In the fields of physical oceanography and coastal engineering, the two categories of nonlinearity are skewness and asymmetry. Wave skewness and asymmetry occur when waves encounter an opposing current or a shallow area. As waves shoal in the nearshore zone, in addition to their wavelength and height changing, their asymmetry and skewness also change. Wave skewness and asymmetry are often implicated in ocean engineering and coastal engineering for the modelling of random sea states, in particular regarding the distribution of wave height, wavelength and crest length. For practical engineering purposes, it is important to know the probability of these wave characteristics in seas and oceans at a given place and time. This knowledge is crucial for the prediction of extreme waves, which are a danger for ships and offshore structures. Satellite altimeter Envisat RA-2 data shows geographically coherent skewness fields in the ocean and from the data has been concluded that large values of skewness occur primarily in regions of large significant wave height.
They cannot be felt aboard ships, nor can they be seen from the air in the open ocean.
Dumont d'Urville, in his narrative, expressed the opinion that the waves reached a height of 'at least 80 to 100 feet'. In an era when opinions were expressed that no wave would exceed 30 feet, Dumont d'Urville's estimations were received, with some skepticism. No one was more outspoken in his rejection than François Arago, who, calling for a more scientific approach to the estimation of wave height in his instructions for the physical research on the voyage of the Bonité, suggested that imagination played a part in estimations as high as '33 metres' (108 feet). Later, in his 1841 report on the results of the Vénus expedition, Arago made further reference to the 'truly prodigious waves with which the lively imagination of certain navigators delights in covering the seas'
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: CS1 maint: unfit URL (link)"Draupner E had only been operating in the North Sea for around half a year, when a huge wave struck the platform like a hammer. When we first saw the data, we were convinced it had to be a technological error," says Per Sparrevik. He is the head of the underwater technology, instrumentation, and monitoring at the Norwegian NGI ... but the data were not wrong. When NGI looked over the measurements and calculated the effect of the wave that had hit the platform, the conclusion was clear: The wave that struck the unmanned platform Draupner E on 1 January 1995 was indeed extreme.
The area of the Central North Sea is notorious for very high waves in certain wave trains. The short-term distribution of these wave trains includes waves far steeper than the Rayleigh distribution predicted. Such waves are often termed "extreme waves" or "freak waves". An analysis of the extreme statistical properties of these waves has been made. The analysis is based on more than 12 years of wave records from the Mærsk Olie og Gas AS operated Gorm Field, located in the Danish sector of the Central North Sea. From the wave recordings, more than 400 freak wave candidates were found. The ratio between the extreme crest height and the significant wave height (20-min value) is about 1.8, and the ratio between extreme crest height and extreme wave height is 0.69. The latter ratio is clearly outside the range of Gaussian waves, and it is higher than the maximum value for steep nonlinear long-crested waves, thus indicating that freak waves are not of a permanent form, and probably of short-crested nature. The extreme statistical distribution is represented by a Weibull distribution with an upper bound, where the upper bound is the value for a depth-limited breaking wave. Based on the measured data, a procedure for determining the freak wave crest height with a given return period is proposed. A sensitivity analysis of the extreme value of the crest height is also made.
In February 2000 those onboard a British oceanographic research vessel near Rockall, west of Scotland experienced the largest waves ever recorded by scientific instruments in the open ocean. Under severe gale force conditions with wind speeds averaging 21 ms1 a shipborne wave recorder measured individual waves up to 29.1 m from crest to trough, and a maximum significant wave height of 18.5 m. The fully formed sea developed in unusual conditions as westerly winds blew across the North Atlantic for two days, during which time a frontal system propagated at a speed close to the group velocity of the peak waves. The measurements are compared to a wave hindcast that successfully simulated the arrival of the wave group, but underestimated the most extreme waves.
Recent research has demonstrated that extreme waves, waves with crest-to-trough heights of 20 to 30 m, occur more frequently than previously thought.
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: CS1 maint: archived copy as title (link), Müller, et al., "Rogue Waves," 2005The author's starting point, therefore, was to look for an extraordinary cause. He reasoned that nothing could be more extraordinary than the violence of a fully arisen and chaotic storm-tossed sea. He therefore studied the meteorology of revolving tropical storms and freak waves and found that steep elevated waves of 25 to 30 m or more were quite likely to have occurred during Typhoon Orchid.
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.
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.
There is sufficient evidence to conclude that 66-foot-high waves can be experienced in the 25-year lifetime of oceangoing vessels and that 98-foot-high waves are less likely, but not out of the question. Therefore, a design criterion based on 36-foot-high waves seems inadequate when the risk of losing crew and cargo is considered.
The Norwegian offshore standards consider extreme severe wave conditions by requiring that a 10,000-year wave does not endanger the structure's integrity (Accidental Limit State, ALS).
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.