L`éré dernier, au large du port anglais de Harwich, John Sibley et Denis Hayman pèchent paisiblement. La mer est calme. Soudain, une vague de cinq mètres de haut surgit. Sibley périt, noyé. Depuis, Hayman provoque enquète sur enquète. La vérité sur cette vague extraordinaire vient d’étre publiée. Parce que le phénomène n’est pas rare en mer du Nord et ne halt pas du vent, comme la houle.
Vagues géantes en mer du Nord Les ferries rapides créent des vagues dangereuses pouvant atteindre jusqu'à cinq mètres de haut L`éré dernier, au large du port anglais de Harwich, John Sibley et Denis Hayman pèchent paisiblement. La mer est calme. Soudain, une vague de cinq mètres de haut surgit. Sibley périt, noyé. Depuis, Hayman provoque enquète sur enquète. La vérité sur cette vague extraordinaire vient d’étre publiée. Parce que le phénomène n’est pas rare en mer du Nord et ne halt pas du vent, comme la houle. Il résulte de la présence d’un ferry rapide, un de ces gros catamarans qui assurent aujourd’hui la moitié du trafic entre la Grande-Bretagne, l’Irlande et le continent. Comment un bateau peur-il engendrer un rel monstre? Sa vitesse en est la causc. Lorsqu’elle dépasse soixantèdix kilomèttes/heure, elle provoque un choc violent entre la proue du ferry et la mer. Une vague en nait. Pas forcément géante. Elle fonce vers la cote au-dessus de fonds de trente à quarante mètres. D’une faible amplitude, elle est peu décelable. Lorsque les fonds commencer à remonter, à l’approche de la cote, l’onde ralentit mass se redresse, gonfle, déferle. Devient destructrice. En meurtriére pour le pècheur qui ne la voit pas venir.
Gulf Stream, off of Charleston February of 1986 It was actually a nice day with light breezes and no significant sea. Only the very long swell, of about 15 feet high and probably 600 to 1000 feet long. three waves, ~ 56 feet = 17 m
Taken aboard the SS Spray (ex-Gulf Spray) in about February of 1986, in the Gulf Stream, off of Charleston. Circumstances: A substantial gale was moving across Long Island, sending a very long swell down our way, meeting the Gulf Stream. We saw several rogue waves during the late morning on the horizon, but thought they were whales jumping. It was actually a nice day with light breezes and no significant sea. Only the very long swell, of about 15 feet high and probably 600 to 1000 feet long. This one hit us at the change of the watch at about noon. The photographer was an engineer (name forgotten), and this was the last photo on his roll of film. We were on the wing of the bridge, with a height of eye of 56 feet, and this wave broke over our heads. This shot was taken as we were diving down off the face of the second of a set of three waves, so the ship just kept falling into the trough, which just kept opening up under us. It bent the foremast (shown) back about 20 degrees, tore the foreword firefighting station (also shown) off the deck (rails, monitor, platform and all) and threw it against the face of the house. It also bent all the catwalks back severely. Later that night, about 19-30, another wave hit the after house, hitting the stack and sending solid water down into the engine room through the forced draft blower intakes. Captain G. Andy Chase
South Africa Indian Ocean 12 events (Lavrenov, 1998) 1952-1973, 1984
“April 27, 1985 tanker-refrigerator “Taganrogsky Zaliv” (length 164, m, dead-weight 12000 tons) was sailing from Indian ocean to the south-eastern region of Atlantic ocean. After 12.00 wind diminished up to 12 m/sec. Wind sea became to be calmer as well. Wind didn’t change during the next three hours. Wave height didn’t exceed 5 m, its length was 40–45 m. To overcome wave impact the boatswain and three seamen were sent to fore-deck. Speed of the ship was diminished to a minimum value which was enough for safe control of ship motion. The fore-deck and deck were not flooded with water. By 1pm the job was almost done at the fore-deck. At this moment the front part suddenly went down and close to fore-deck the crest of a very large wave appeared. It was 5–6 meters higher than fore-deck. The wave crest fell down at the ship. Seamen were spread out. One of them was killed and washed overboard. It was impossible to save him. Nobody was able to foresee the wave appearance. When the ship went down riding on the wave and burrowed into its frontal part nobody felt the wave impact. Wave easy rolled over fore-deck covering it with more than 2 m water layer…”
NOAA VESSEL SWAMPED BY ROGUE WAVE At November 4, 2000, the 56-foot R/V Ballena capsized in a rogue wave south of Point Arguello, California. The Channel Islands National Marine Sanctuary's research vessel was engaged in a routine side-scan sonar survey for the U. S. Geological Survey of the seafloor along the 30-foot-depth contour approximately 1/4 nautical mile from the shore. The crew of the R/V Ballena, all of whom survived, consisted of the captain, LCdr. Pickett, research scientist Dr. Cochrane, and research assistant, Boyle. According to NOAA, the weather was good, with clear skies and glassy swells. The actual swell appeared to be 5-7 feet. At approximately 11:30 a.m., Pickett and Boyle said they observed a 15-foot swell begin to break 100 feet from the vessel. The wave crested and broke above the vessel, caught the Ballena broadside, and quickly overturned her. All crewmembers were able to escape the overturned vessel and deploy the vessel's liferaft. The crew attempted to paddle to the shore, but realized the possibility of navigating the raft safely to shore was unlikely due to strong near-shore currents. The crew abandoned the liferaft approximately 150 feet from shore and attempted to swim to safety. The crew climbed the rocky cliffs along the shore and walked approximately 2 miles before they encountered a vehicle from Vandenberg Air Force Base, which immediately called for emergency services. The R/V Ballena is a total loss.
In conversations with residents of the Oregon coast, it was revealed that tsunami-like wave was observed at that same time period. The wave was described as about 7 meters height and was able to damage wooden access stairs along the bluffs that were at least 200 meters from the water. While the exact height of the wave or the exact time are not known by the people describing the event, the event certainly occurred. One of the beach residents was having new access stairs built down to the beach and was coming out to the coast to see the work. The wave destroyed the stairs immediately after they were finished and before the residents arrived. Rogue Waves = Tsunami Waves?
Drill floor Upper desk Ballast control room Pump and propulsion room Ballast tank Helicopter desk Pilot house Upper hull Columns and braces Pontoons Transverse brace Chain locker Ocean Platform
Location Depth m Height, m Max Height, m H max / H s Registration Year Gork, Eire 205,012,82,6 Waverider1969 Gulf of Mexico 100 10,419,41,9 Wave staff1969 Gulf of Mexico 35010,0 23,0 2,3 Wave staff1969 Gorm Field, DK 40 6,8 17,8 2,6 Radar1981 Gorm Field, DK 40 7,816,52,1 Radar1981 Ekofish, N 70 20 – 22> 2,5 Damage 1984 Gorm Field 40 5,012,02,4 Radar1984 Gorm Field 40 5,011,32,3 Radar1984 Gorm Field 40 5,011,02,2 Radar1984 Gorm Field 40 4,813,12,7 Radar1984 Hanstholm, DK 2026 – 7 3 Visual1985 Hanstholm, DK 40 3,57,62,2 Waveride r 1985 Instrumental Data
“New Year Wave” at “Draupner” (Statoil operated jacket platform, Norway) January 1, 1995 at 15:20 Depth 70 m, Duration 12 sec, Height 26 m
Freak Wave Definition H freak > 2 H significant
No data for large deviations or they are not representative Why does large wave appear? Wind wave field is quasi-Gaussian random process is mean wave height W – wind speed
Wind wave field has narrow spectrum for H = 3H mean P ~10 -3 One wave from 1000 waves is a freak wave! Wave Period ~ 10 s, Freak wave – each 3 hr! “Gaussian” Prediction But who knows extreme statistics?
Statistical approach: - needs long-term time series (it is possible now) - but always will be incorrect for extreme values of amplitudes (its level will increasing with duration of record) Physical (Dynamical) approach: -leads to find conditions when freak waves can appear
Mechanisms: Wave – current interaction “Itself” wave dynamics wave blocking, random caustics. temporal-spatial focusing, modulation instability. Wave – bottom interaction focuses, random caustics. shallow water only deep water only
Wave – Current Interactions Blocking on opposite current blocking at Models: energy balance equation, nonlinear Schrodinger equation Random Caustics
Random Focuses, Caustics Wave Bottom InteractionsWind direction is varied casually Shallow Water only
Forced model Evolution model – free waves Large background Small background Storm Area “Itself” wave dynamics
Mechanism of Wave Focusing start finish Wave as each from us has own speed
Mechanism of Wave Focusing start finish Meeting point focus
Dispersion Dispersion Enhancement Physics: Physics: Phase speed is c(k) negative time positive time t = 0 (wave focus)
Kinematic Model x cgrcgr x0x0 t=T collapse, focus before after Increased wind
Deep Water Waves Narrow spectrum Displacement Envelope Wave Envelope - parabolic equation (non-dimensional variables)
Conclusions (linear focusing): Freak 1. Freak wave is specific frequency modulated wave 2. Exact analytical test in linear theory 3. Freak wave in 3D forms in more narrow vicinity of focusing point then in 2D Tasks: Influence of Nonlinearity Detection of Weak Coherent Components
KdV model for shallow water Inverse scattering method Discrete - solitons Continuous – dispersive tail
Initial disturbance evolves solitons + dispersive train Delta-function (as model of the freak wave) evolves in one soliton and dispersive train Inverted (in x) dispersive train + soliton will evolve in delta-function But delta-function is not weak nonlinear and dispersive wave
Soliton-like disturbance - Ursell parameter Number of solitons Maximal soliton
Large Ursell number max = 2 0 Inverting - no generation of freak wave!
Small Ursell number One small soliton Freak wave is almost linear wave in spite of its large amplitude! 0(freak) > 2 1
Freak Wave as a deep hole (depression) (x) < 0 – solitonless potential Only dispersive tail Similar to linear problem No limitations on characteristics of deep holes!
Numerical simulation direct “Inverted” Freak wave