Module Ocean

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Module Ocean
Freak Waves
Vagues géantes
????? - ??????
Efim Pelinovsky
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Léré 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 détre publiée. Parce que le phénomène
nest pas rare en mer du Nord et ne halt pas du
vent, comme la houle.
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Vagues géantes en mer du Nord  Les ferries
rapides créent des vagues dangereuses pouvant
atteindre jusqu'à cinq mètres de haut Léré
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
détre publiée. Parce que le phénomène nest pas
rare en mer du Nord et ne halt pas du vent, comme
la houle. Il résulte de la présence dun ferry
rapide, un de ces gros catamarans qui assurent
aujourdhui la moitié du trafic entre la
Grande-Bretagne, lIrlande et le
continent. Comment un bateau peur-il engendrer un
rel monstre? Sa vitesse en est la causc.
Lorsquelle 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. Dune faible
amplitude, elle est peu décelable. Lorsque les
fonds commencer à remonter, à lapproche de la
cote, londe ralentit mass se redresse, gonfle,
déferle. Devient destructrice. En meurtriére pour
le pècheur qui ne la voit pas venir.
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Gulf Stream, off of Charleston
February of 1986
three waves, 56 feet 17 m
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.
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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
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12 events
(Lavrenov, 1998)
South Africa
1952-1973, 1984
Indian Ocean
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Agulhas Current
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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 didnt change
during the next three hours. Wave height didnt
exceed 5 m, its length was 4045 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 56 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
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Rogue Waves, 2000 Brest, France
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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 1130 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.
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Rogue Waves Tsunami Waves?
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.
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Ocean Platform
Helicopter desk
Drill floor
Pilot house
Upper desk
Upper hull
Ballast control room
Columns and braces
Pump and propulsion room
Pontoons
Transverse brace
Ballast tank
Chain locker
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Instrumental Data
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Records
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New Year Wave at Draupner (Statoil
operated jacket platform, Norway)
Depth 70 m, Duration 12 sec, Height 26 m
January 1, 1995 at 1520
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Freak Wave Definition
Hfreak gt 2 Hsignificant
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Why does large wave appear?
Wind wave field is quasi-Gaussian random process
No data for large deviations or they are not
representative
s is mean wave height
W wind speed
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Gaussian Prediction
Wind wave field has narrow spectrum
for H 3Hmean
P 10-3
One wave from 1000 waves is a freak wave!
Wave Period 10 s,
Freak wave each 3 hr!
But who knows extreme statistics?
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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
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Mechanisms

• Wave current interaction

• wave blocking,
• random caustics.

• Wave bottom interaction

• focuses,
• random caustics.

shallow water only

• Itself wave dynamics

• temporal-spatial focusing,
• modulation instability.

deep water only
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Wave Current Interactions

• Blocking on opposite current

blocking at
Models energy balance equation,
nonlinear Schrodinger equation

• Random Caustics

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Wave Bottom Interactions
Wind direction is varied casually
Shallow Water only
Random Focuses, Caustics
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Itself wave dynamics
Small background
Storm Area
Large background
Evolution model free waves
Forced model
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Mechanism of Wave Focusing
Wave as each from us has own speed
finish
start
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Mechanism of Wave Focusing
finish
focus
start
Meeting point
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Dispersion Enhancement
Physics Phase speed is c(k)
t 0 (wave focus)
negative time
positive time
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Kinematic Model
cgr
tT
before
after
x0
x
collapse, focus
Increased wind
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Deep Water Waves
Narrow spectrum
Displacement
Wave Envelope - parabolic equation
(non-dimensional variables)
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Gaussian Envelope
t 0
t - 20
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Wave Random Field
12 harmonics
different times
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Real Wave Field with the Freak Wave
collapse
t - 10
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Transient Random
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Wave focus
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3D Freak Waves
exp(-kz)
2D parabolic equation
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Regular Wave
collapse
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Random Wave Field
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Real 3D Wave Field
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Conclusions (linear focusing)
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

• Detection of Weak Coherent Components

• Influence of Nonlinearity

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KdV model for shallow water
Inverse scattering method
Discrete l - solitons
Continuous l dispersive tail
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solitons dispersive train
Initial disturbance
evolves
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
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Soliton-like disturbance
- Ursell parameter
Number of solitons
Maximal soliton
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Large Ursell number
?max 2 ?0

Inverting - no generation of freak wave!
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Small Ursell number
One small soliton
?0(freak) gt 2?1
Freak wave is almost linear wave in spite of its
large amplitude!
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Freak Wave as a deep hole (depression)
h(x) lt 0 solitonless potential
Only dispersive tail
Similar to linear problem
No limitations on characteristics
of deep holes!
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Numerical simulation
Inverted
direct
Freak wave
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Rare and short-lived character of freak wave
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Non-optimal focusing
Freak wave
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freak wave
Non-optimal focusing
wave train only, no soliton
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Nonlinear wave train within linearised KdV eq.
in KdV crest only, amplitude 0.4
Nonlinearity important for optimal focusing
freak wave
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Korteweg de Vries equation
Modulated wave field no Benjamin Feir
instability
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Demodulation no freak wave
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Wind Wave Distribution
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Random field evolution
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random deterministic
direct
inverted
freak wave
freak wave
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Non-Expected Freak Wave
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Expected Freak Wave
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Nonlinear waves in deep water
Nonlinear Schrodinger Equation for kA
Integrable model
Benjamin Feir instability
Sine wave transforms to solitons and breathers
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Nonlinear abnormal waves
time
(exact breathers)
Peregrine
Akhmediev
kA
3
Ma
1
coordinate
time
space
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Nonlinear Schrodinger equation
Modelling of the Benjamin Feir
instability amplitude modulation
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Giant waves
Deep holes
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Double Freak Wave Packets
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Three Freak Wave Groups
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Nonlinear Schrodinger equation
Modelling of wave focusing phase (frequency)
and amplitude modulation
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Freak wave
Nonlinear Spatial Temporal
Focusing
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Second Focusing
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freak waves
solitons, breathers
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Benjamin-Feir limit
First Freak Wave Appearance
linear focusing
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Freak Waves in Laboratory, IRPHE/IOA, Marseille,
France
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Freak Waves in Laboratory, IRPHE/IOA, Marseille,
France
Weak-amplitude packet
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Freak Waves in Laboratory, IRPHE/IOA, Marseille,
France
Visible freak wave
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Freak Waves in Laboratory, IRPHE/IOA, Marseille,
France
Steep Freak Waves with Wind
20 December 2000
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Conclusions
Huge Freak Wave is a Focus of
Nonlinear-Dispersive Wave Trains
Rare and short-lived character of freak wave