module ocean efim pelinovsky freak waves vagues géantes Волны - убийцы

Module OceanModule Ocean

Efim Pelinovsky

Freak WavesVagues géantesВолны - убийцы

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 hautL`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

Agulhas Current

“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…”

Rogue Waves, 2000Brest, France

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 ofnavigating 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

LocationDepth

m Height, mMax

Height, m Hmax / Hs Registration Year

Gork, Eire 20 5,0 12,8 2,6 Waverider 1969

Gulf of Mexico 100 10,4 19,4 1,9 Wave staff 1969

Gulf of Mexico 350 10,0 23,0 2,3 Wave staff 1969

Gorm Field, DK 40 6,8 17,8 2,6 Radar 1981

Gorm Field, DK 40 7,8 16,5 2,1 Radar 1981

Ekofish, N 70 20 – 22 > 2,5 Damage 1984

Gorm Field 40 5,0 12,0 2,4 Radar 1984

Gorm Field 40 5,0 11,3 2,3 Radar 1984

Gorm Field 40 5,0 11,0 2,2 Radar 1984

Gorm Field 40 4,8 13,1 2,7 Radar 1984

Hanstholm, DK 20 2 6 – 7 3 Visual 1985

Hanstholm, DK 40 3,5 7,6 2,2 Waverider 1985

Instrumental Data

Records

0 4 8 1 2 1 6 2 0

tim e (m in )

-1 0

0

1 0

2 0

elev

atio

n (

m)

“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

24 0 25 0 26 0 27 0 28 0 2 90

tim e (sec )

-10

0

10

20

elev

atio

n (

m)

time-4

0

4

8

12dis

pla

cem

ent

Freak Wave Definition

Hfreak > 2 Hsignificant

No data for large deviations

or they are not representative

Why does large wave appear?

Wind wave field is quasi-Gaussian random process

2

2

2exp

2

1)(

f

sea e lev a tio n

den

sity

of

dis

trib

uti

on f

un

ctio

n

3

is mean wave height

gW /~ 2W – wind speed

Wind wave field has narrow spectrum

2

4exp)(

meanH

HHF

0 1 2 3

w a v e h e ig h t, H /H m ea n

0

0 .5

1

dis

trib

uti

on f

un

ctio

n

for H = 3Hmean 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 knowsextreme 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 interactionfocuses, random caustics.

shallow water only

deep water only

Wave – Current Interactions

Blocking on opposite current

wave number

fre

qu

ency

U=0

U>0

U<0

)(xkUgk

)(xUcgr blocking at

Models: energy balance equation, nonlinear Schrodinger equation

Random Caustics

RandomFocuses,Caustics

Wave Bottom Interactions Wind direction is varied casually

Shallow Water only

Forced model

Evolution model – free waves

Large background

Small backgroundStorm Area

“Itself” wave dynamics

Mechanism of Wave Focusing

start finish

Wave as each from ushas own speed

Mechanism of Wave Focusing

start finish

Meeting point

focus

DispersionDispersion Enhancement

Physics:Physics: Phase speed is c(k)

negative time positive time

t = 0 (wave focus)

Kinematic Model

t

cxgr ( ) 0

c

tc

c

xgr

grgr 0

cx x

t Tgr ( )

0

x

cgr

x0

t=T

collapse, focus

before after

Increased wind

A

t

i A

x

2

2

2

Deep Water Waves

Narrow spectrumDisplacement

( , ) ( , ) exp ( ) . . ...x t A x t i t k x c c 0 0

Wave EnvelopeEnvelope - parabolic equation

(non-dimensional variables)

exp( ) kz

Gaussian Envelope

2

)2tan(41

2cos

41exp

41),(

20

40

2

40

2

40

2

220

4 40

2

0 tKKtKtx

KtxK

Kt

AtxA

-500 -250 0 250 500

coordinate

-0.5

0.0

0.5

enve

lop

e

-4 -2 0 2 4

coordinate

0

2

4

6

8

10

enve

lop

e

t = 0t = - 20

A a i K xKtn n

nn

n

exp2

1 2

Wave Random Field

-4 -2 0 2 4

-4

0

4

-4 -2 0 2 4

-4

0

4

different times

12 harmonics

-10 -5 0 5 10

-4

0

4

8

12

-10 -5 0 5 10

-4

-2

0

2

4

collapset = - 10

“Real” Wave Field with the Freak Wave

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -1 0 0

Transient + Random

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -5 0

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -1 0

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -5

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -1

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .8

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .6

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .4

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .2

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .1

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .0 5

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .0 3

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .0 2

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= -0 .0 1

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0f o cu sWave focus

-1 0 -5 0 5 10

co o rd in a te

-1 0

-5

0

5

1 0t= + 0 .0 1

-1 0 -5 0 5 1 0

co o rd in a te

-1 0

-5

0

5

1 0t= + 0 .0 5

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= + 0 .1

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= + 0 .5

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= + 1

-1 0 -5 0 5 10

coo rd in a te

-1 0

-5

0

5

1 0t= + 1 0

A

ti

A

x

A

y

1

2

2

2

2

2

3D Freak Waves exp(-kz)

2D parabolic equation

A x y tA

t K t K

K x

t K

K y

t Kx y

x

x

y

y

( , , )( )(

exp

0

2 4 24

2 2

2 4

2 2

2 41 4 1 16 1 4 1 16

2

)4(atan

2

)2(atan

161

4

41

2cos

22

42

42

42

42yx

y

y

x

xtKtK

Kt

Kty

Kt

Ktx

Regular Wave

collapse

Random Wave Field

“Real”3D WaveField

Conclusions (linear focusing):1. Freak 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

t

ch x

ch

x

13

2 60

2 3

3

KdV model for shallow water

Inverse scattering method

0),(2

2

txUdxd

323h

U

Discrete - solitons

Continuous – dispersive tail

Initialdisturbance

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

Url

h 0

2

3 - Ursell parameter

N EUr

3

2

1

4

1

21Number of solitons

m Ur

Urm

4

3

3

2

1

4

1

20

2

Maximal soliton

Large Ursell number

max = 2 0

Inverting - no generation of freak wave!

Small Ursell number

1 03 Ur One small soliton

Ur 1

6

Freak wave is almost linear wave in spite of its large amplitude!

0(freak) > 21

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!

1200 1240 1280 1320 1360 1400

0 .0

0 .4

0 400 800 1200 1600coo rd in a te

0 .0

0 .4

0 400 800 1200 1600

0 .0

0 .4

0

1 40

3 60

0 .0

0 .4

0 .0

0 .4

100 200 300 400 500 600coord in a te

0 .0

0 .4

0

1 3 0

1 4 0

1 5 0

ele

vati

on

0 .0

0 .4

Numerical simulation

direct“Inverted”

Freak wave

0 100 200 300tim e

0 .1

0 .2

0 .3

0 .4am

plitu

de

Rare and short-lived character of freak wave

0 .0

0 .2

0 .0

0 .2

200 250 300 350 400 450

0 .0

0 .2

0 200 400 600 800coord in a te

0 .0

0 .2

1 5 0

1 4 0

1 3 0

0

elev

atio

n

0 .5 0 .6 0 .7 0 .8 0 .9 1en erg y

0 .2

0 .4

0 .6

0 .8

1 .0

amp

litu

de

Non-optimal focusing

Freak wave

200 240 280 320 360 400

-0 .2

0 .0

0 .2 1 4 0

200 400 600 800 1000 1200coo rd in a te

-0 .2

0 .0

0 .2 0

elev

atio

n

wave train only, no soliton

freak wave

Non-optimal focusing

0 200 400 600 800coord in a te

-0 .1

0 .0

0 .1

0 .2

0 .3

elev

atio

n

1 4 0

Nonlinear wave train within linearised KdV eq.

freak wave

Nonlinearity – important foroptimal focusing

in KdV crest only, amplitude 0.4

Korteweg – de Vries equation

Modulated wave field:no Benjamin – Feir instability

)sin(1)0,( 0 KxmAxA