In this paper, some abnormal or rogue wave events registered in the North Sea by means of the surface elevation measurements are reconstructed with the help of theoretical models for water waves and numerical simulations of wave evolution. Time series of surface elevation, which are measured at a single point, provide incomplete information about the waves. The registered time series are used to restore the wave dynamics under reasonable assumptions. Different frameworks associated with the relation between the surface elevation and the fluid velocity fields are considered, and different numerical models are used to simulate the wave dynamics in time and space. It is shown that for some abnormal or rogue wave records the result of the extreme event reconstruction is robust. In particular, the verification of approximate approaches versus the fully nonlinear numerical simulation is performed. The reconstructed rogue wave is generally less steep than the measured one. Possible reasons for this discrepancy are suggested.

References

References
1.
Kharif
,
C.
, and
Pelinovsky
,
E.
,
2003
, “
Physical Mechanisms of the Rogue Wave Phenomenon
,”
Eur. J. Mech. B/Fluids
,
22
, pp.
603
634
.10.1016/j.euromechflu.2003.09.002
2.
Dysthe
,
K.
,
Krogstad
,
H. E.
, and
Müller
,
P.
,
2008
, “
Oceanic Rogue Waves
,”
Annu. Rev. Fluid Mech.
,
40
, pp.
287
310
.10.1146/annurev.fluid.40.111406.102203
3.
Kharif
,
C.
,
Pelinovsky
,
E.
, and
Slunyaev
,
A.
,
2009
,
Rogue Waves in the Ocean
,
Springer-Verlag
,
Berlin
.
4.
Rosenthal
,
W.
,
Lehner
,
S.
,
Dankert
,
H.
,
Guenther
,
H.
,
Hessner
,
K.
,
Horstmann
,
J.
,
Niedermeier
,
A.
,
Nieto-Borge
,
J. C.
,
Schulz-Stellenfleth
,
J.
, and
Reichert
,
K.
,
2003
, “
Detection of Extreme Single Waves and Wave Statistics
,”
MaxWave. Rogue Waves – Forecast and Impact on Marine Structures
, Final Meeting and Workshop. Working Group Reports.
5.
Lawton
,
G.
,
2001
, “
Monsters of the Deep (The Perfect Wave)
,”
New Scientist
,
170
(
2297
), pp.
28
32
. Available at: http://www.newscientist.com/article/mg17022974.900-monsters-of-the-deep.html
6.
Guedes Soares
,
C.
, and
Teixeira
,
A. P.
,
2001
, “
Risk Assessment in Maritime Transportation
,”
Reliab. Eng. Syst. Saf.
,
74
, pp.
299
309
.10.1016/S0951-8320(01)00104-1
7.
Toffoli
,
A.
,
Lefevre
,
J. M.
,
Bitner-Gregersen
,
E.
, and
Monbaliu
,
J.
,
2005
, “
Towards the Identification of Warning Criteria: Analysis of a Ship Accident Database
,”
Appl. Ocean Res.
,
27
, pp.
281
291
.10.1016/j.apor.2006.03.003
8.
Guedes Soares
,
C.
,
Bitner-Gregersen
,
E.
, and
Antão
,
P.
2001
, “
Analysis of the Frequency of Ship Accidents Under Severe North Atlantic Weather Conditions
,”
Proceedings of the Conference on Design and Operation for Abnormal Conditions II
, RINA, London, pp.
221
230
.
9.
Bitner-Gregersen
,
E.
,
Guedes Soares
,
C.
, and
Silvestre
,
A.
,
1998
, “
On the Average Wave Steepness
,”
Proceedings of the Ocean Wave Kinematics, Dynamics and Loads on Ship Structures (Wave’98)
, ASCE, Houston, TX, pp.
513
520
.
10.
Guedes Soares
,
C.
,
Fonseca
,
N.
, and
Pascoal
,
R.
,
2008
, “
Abnormal Wave Induced Load Effects in Ship Structures
,”
J. Ship Res.
,
52
(
1
), pp.
30
44
. Available at: http://www.ingentaconnect.com/content/sname/jsr/2008/00000052/00000001/art00003#expand/collapse
11.
Dyachenko
,
A. I.
, and
Zakharov
,
V. E.
,
2008
, “
On the Formation of Freak Waves on the Surface of Deep Water
,”
JETP Lett.
,
88
, pp.
307
311
.10.1134/S0021364008170049
12.
Slunyaev
,
A. V.
,
2009
, “
Numerical Simulation of “Limiting” Envelope Solitons of Gravity Waves on Deep Water
,”
JETP
,
109
, pp.
676
686
.10.1134/S1063776109100148
13.
Chabchoub
,
A.
,
Hoffmann
,
N. P.
, and
Akhmediev
,
N.
,
2011
, “
Rogue Wave Observation in a Water Wave Tank
,”
Phys. Rev. Lett.
,
106
, p.
204502
.10.1103/PhysRevLett.106.204502
14.
Chabchoub
,
A.
,
Hoffmann
,
N.
,
Onorato
,
M.
,
Slunyaev
,
A.
,
Sergeeva
,
A.
,
Pelinovsky
,
E.
, and
Akhmediev
,
N.
,
2012
, “
Observation of a Hierarchy of Up to Fifth-Order Rogue Waves in a Water Tank
,”
Phys. Rev. E
,
86
, p.
056601
.10.1103/PhysRevE.86.056601
15.
Slunyaev
,
A.
,
Clauss
,
G. F.
,
Klein
,
M.
, and
Onorato
,
M.
,
2013
, “
Simulations and Experiments of Short Intense Envelope Solitons of Surface Water Waves
,”
Phys. Fluids
,
25
, p.
067105
.10.1063/1.4811493
16.
Trulsen
,
K.
,
2001
, “
Simulating the Spatial Evolution of a Measured Time Series of a Freak Wave
,”
Proc. of the Workshop “Rogue Waves 2000
,”
M.
Olagnon
and
G. A.
Athanassoulis
, eds.,
Ifremer
,
Brest, France
, pp.
265
274
.
17.
Dysthe
,
K. B.
,
1979
, “
Note on a Modification to the Nonlinear Schrödinger Equation for Application to Deep Water Waves
,”
Proc. R. Soc. London, Ser. A
,
369
, pp.
105
114
.10.1098/rspa.1979.0154
18.
Trulsen
,
K.
, and
Dysthe
,
K. B.
,
1996
, “
A Modified Nonlinear Schrödinger Equation for Broader Bandwidth Gravity Waves on Deep Water
,”
Wave Motion
,
24
, pp.
281
289
.10.1016/S0165-2125(96)00020-0
19.
Trulsen
,
K.
,
Gudmestad
,
O. T.
, and
Velarde
,
M. G.
,
2001
, “
The Nonlinear Schrödinger Method for Water Wave Kinematics on Finite Depth
,”
Wave Motion
,
33
, pp.
379
395
.10.1016/S0165-2125(00)00077-9
20.
Trulsen
,
K.
,
2006
, “
Weakly Nonlinear and Stochastic Properties of Ocean Wave Fields: Application to an Extreme Wave Event
,”
J.
Grue
and
K.
Trulsen
, eds.,
Waves in Geophysical Fluids: Tsunamis, Rogue Waves, Internal Waves and Internal Tides
, CISM Courses and Lectures No. 489,
Springer
,
New York
.
21.
Clauss
,
G. F.
, and
Klein
,
M.
,
2009
, “
The New Year Wave: Spatial Evolution of an Extreme Sea State
,”
ASME J. Offshore Mech. Arct. Eng.
,
131
, p.
041001
.10.1115/1.3160533
22.
Divinsky
,
B. V.
,
Levin
,
B. V.
,
Lopatukhin
,
L. I.
,
Pelinovsky
,
E. N.
, and
Slyunyaev
,
A. V.
,
2004
, “
A Freak Wave in the Black Sea: Observations and Simulation
,”
Dokl. Earth Sci.
,
395A
, pp.
438
443
.
23.
Slunyaev
,
A.
,
Pelinovsky
,
E.
, and
Guedes Soares
,
C.
,
2005
, “
Modeling Freak Waves From the North Sea
,”
Appl. Ocean Res.
,
27
, pp.
12
22
.10.1016/j.apor.2005.04.002
24.
Slunyaev
,
A.
,
2006
, “
Nonlinear Analysis and Simulations of Measured Freak Wave Time Series
,”
Eur. J. Mech. B/Fluids
,
25
, pp.
621
635
.10.1016/j.euromechflu.2006.03.005
25.
Guedes Soares
,
C.
,
Cherneva
,
Z.
, and
Antão
,
E.
,
2003
, “
Characteristics of Abnormal Waves in North Sea Storm Sea States
,”
Appl. Ocean Res.
,
25
(
6
), pp.
337
344
.10.1016/j.apor.2004.02.005
26.
West
,
B. J.
,
Brueckner
,
K. A.
,
Janda
,
R. S.
,
Milder
,
D. M.
, and
Milton
,
R. L.
,
1987
, “
A New Numerical Method for Surface Hydrodynamics
,”
J. Geophys. Res.
,
92
, pp.
11803
11824
.10.1029/JC092iC11p11803
27.
Zakharov
,
V.
,
1968
, “
Stability of Periodic Waves of Finite Amplitude on a Surface of Deep Fluid
,”
J. Appl. Mech. Tech. Phys.
,
9
, pp.
190
194
.10.1007/BF00913182
28.
Clamond
,
D.
,
Francius
,
M.
,
Grue
,
J.
, and
Kharif
,
C.
,
2006
, “
Long Time Interaction of Envelope Solitons and Freak Wave Formations
,”
Eur. J. Mech. B/Fluids
,
25
, pp.
536
553
.10.1016/j.euromechflu.2006.02.007
29.
Slunyaev
,
A. V.
,
2005
, “
A High-Order Nonlinear Envelope Equation for Gravity Waves in Finite-Depth Water
,”
JETP
,
101
, pp.
926
941
.10.1134/1.2149072
30.
Veltcheva
,
D.
,
Cavaco
,
P.
, and
Guedes Soares
,
C.
,
2003
, “
Comparison of Methods for Calculation of the Wave Envelope
,”
Ocean Eng.
,
30
, pp.
937
948
.10.1016/S0029-8018(02)00069-0
31.
Veltcheva
,
D.
, and
Guedes Soares
,
C.
,
2007
, “
Analysis of Abnormal Wave Records by the Hilbert Huang Transform Method
,”
J. Atmos. Oceanic Technol.
,
24
(
9
), pp.
1678
1689
.10.1175/JTECH2067.1
32.
Cherneva
,
Z.
, and
Guedes Soares
,
C.
,
2008
, “
Non-Linearity and Non-Stationarity of the New Year Abnormal Wave
,”
Appl. Ocean Res.
,
30
, pp.
215
220
.10.1016/j.apor.2008.08.003
33.
Petrova
,
P. G.
,
Arena
,
F.
, and
Guedes Soares
,
C.
,
2011
, “
Space-Time Evolution of Random Wave Groups With High Waves Based on the Quasi-Determinism Theory
,”
Ocean Eng.
,
38
, pp.
1640
1648
.10.1016/j.oceaneng.2011.07.021
34.
Dalzell
,
J. F.
,
1999
, “
A Note on Finite Depth Second-Order Wave-Wave Interactions
,”
Appl. Ocean Res.
,
21
, pp.
105
111
.10.1016/S0141-1187(99)00008-5
35.
Creamer
,
D. B.
,
Henyey
,
F.
,
Schult
,
R.
, and
Wright
,
L.
,
1989
, “
Improved Linear Representation of Ocean Surface Waves
,”
J. Fluid Mech.
,
205
, pp.
135
161
.10.1017/S0022112089001977
36.
Taylor
,
P. H.
,
Ohl
,
C.O.G.
, and
Sauvee
,
J.
,
1999
, “
Focused Wave Groups I: Local Structure, Kinematics, and the Creamer Transform
,”
Proc. OMAE 1999
, Paper No. OMAE99/S&R-6461.
37.
Adcock
,
T.A.A.
, and
Taylor
,
P. H.
,
2009
, “
Estimating Ocean Wave Directional Spreading From an Eulerian Surface Elevation Time History
,”
Proc. R. Soc. London, Ser. A
,
465
, pp.
3361
3381
.10.1098/rspa.2009.0031
You do not currently have access to this content.