This paper investigates the effect of third-order nonlinearities on the statistical distributions of wave heights, crests, and troughs of waves mechanically generated in a deep-water basin and simulating two crossing systems characterized by bimodal spectra. The observed statistics exhibits various effects of third-order nonlinearities, in a manner dependent on both the distance from the wave-maker and the angle between the mean directions of the component wave systems. In order to isolate and demonstrate the effects of third-order nonlinearities by themselves, the vertically asymmetric distortions induced by second-order bound waves are removed from the observed time series. It appears then that the distributions of wave crests, troughs and heights extracted from the nonskewed records clearly deviate from the Rayleigh distribution, suggesting that the waves are characterized by nonlinear corrections of higher-order than the typical of second-order waves. Nonetheless, some models developed for weakly nonlinear second-order waves can still be used in describing wave heights, crests and troughs in mixed seas, provided that the relevant distribution parameters are modified, so as to reflect the effects of third-order corrections and some basic characteristics of the mixed seas.
Issue Section:
CFD and VIV
References
References
1.
Forristall
, G.
2005
, “Understanding Rogue Waves: Are New Physics Really Necessary?
,” Proceedings of the 14th Áha Hulikoá Hawaiian Winter Workshop on Rogue Waves
.2.
Tayfun
, M. A.
Fedele
, F.
2007
, “Wave-Height Distributions and Nonlinear Effects
,” Ocean Eng.
, 34
, pp. 1631
–1649
.10.1016/j.oceaneng.2006.11.0063.
Tayfun
, M. A.
2006
, “Statistics of Nonlinear Wave Crests and Groups
,” Ocean Eng.
, 33
, pp. 1589
–1622
.10.1016/j.oceaneng.2005.10.0074.
Tayfun
, M. A.
2008
, “Distribution of Wave Envelope and Phase in Wind Waves
,” J. Phys. Oceanogr.
, 38
, pp. 2784
–2800
.10.1175/2008JPO4008.15.
Haver
, S.
2005
, “Design of Offshore Structures: Impact of the Possible Existence of Freak Waves
,” Proceedings of the 14th Áha Hulikoá Hawaiian Winter Workshop on Rogue Waves
.6.
Petrova
, P.
Cherneva
, Z.
Guedes Soares
, C.
2007
, “On the Adequacy of Second-Order Models to Predict Abnormal Waves
,” Ocean Eng.
, 34
(7
), pp. 956
–961
.10.1016/j.oceaneng.2006.06.0067.
Petrova
, P.
Guedes Soares
, C.
2008
, “Maximum Wave Crest and Height Statistics of Irregular and Abnormal Waves in an Offshore Basin
,” Appl. Ocean Res.
, 30
, pp. 144
–152
.10.1016/j.apor.2008.08.0048.
Onorato
, M.
Osborne
, A.
Serio
, M.
Bertone
, S.
2001
, “Freak Waves in Random Oceanic Sea States
,” Phys. Rev. Lett.
, 86
(25
), pp. 5831
–5834
.10.1103/PhysRevLett.86.58319.
Onorato
, M.
Osborne
, A.
Serio
, M.
Cavaleri
, L.
Brandini
, C.
Stansberg
, C.
2004
, “Observation of Strongly Non-Gaussian Statistics for Random Sea Surface Gravity Waves in Wave Flume Experiments
,” Phys. Rev. E
, 70
, p. 067302
.10.1103/PhysRevE.70.06730210.
Janssen
, P.
2003
, “Nonlinear Four-Wave Interactions and Freak Waves
,” J. Phys. Oceanogr.
, 33
, pp. 863
–884
.10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;211.
Onorato
, M.
Osborne
, A.
Serio
, M.
Cavaleri
, L.
2005
, “Modulational Instability and Non-Gaussian Statistics in Experimental Random Water-Wave Trains
,” Phys. Fluids
, 17
, p. 078101
.10.1063/1.194676912.
Mori
, N.
Yasuda
, T.
2002
, “Effects of High Order Nonlinear Interactions on Unidirectional Wave Trains
,” Ocean Eng.
, 9
(10
), pp. 1233
–1245
.10.1016/S0029-8018(01)00074-913.
Forristall
, G.
2007
, “Wave Crest Heights and Deck Damage in Hurricanes Ivan, Katrina, and Rita
,” Offshore Technology Conference
, OTC
Paper No. 18620-MS. 10.4043/18620-MS14.
Onorato
, M.
Osborne
, A.
Serio
, M.
2006
, “Modulational Instability in Crossing Sea States: A Possible Mechanism for the Formation of Freak Waves
,” Phys. Rev. Lett.
, 96
, p. 014503
.10.1103/PhysRevLett.96.01450315.
Shukla
, P.
Kourakis
, I.
Eliasson
, B.
Marklund
, M.
Stenflo
, L.
2006
, “Instability and Evolution of Nonlinearly Interacting Water Waves
,” Phys. Rev. Lett.
, 97
, p. 094501
.10.1103/PhysRevLett.97.09450116.
Toffoli
, A.
Bitner-Gregersen
, E. M.
Osborne
, A. R.
Serio
, M.
Monbaliu
, J.
Onorato
, M.
2011
, “Extreme Waves in Random Crossing Seas: Laboratory Experiments and Numerical Simulations
,” Geophys. Res. Lett.
, 38
, p. L06605
.10.1029/2011GL04682717.
Onorato
, M.
Proment
, D.
Toffoli
, A.
2010
, “Freak Waves in Crossing Seas
,” Eur. Phys. J. Spec. Top.
, 185
, pp. 45
–55
.10.1140/epjst/e2010-01237-818.
Guedes Soares
, C.
1991
, “On the Occurrence of Double Peaked Wave Spectra
,” Ocean Eng.
, 18
(1–2
), pp. 167
–171
.10.1016/0029-8018(91)90040-W19.
Guedes Soares
, C.
1984
, “Representation of Double-Peaked Sea Wave Spectra
,” Ocean Eng.
, 11
, pp. 185
–207
.10.1016/0029-8018(84)90019-220.
Boukhanovski
, A.
Guedes Soares
, C.
2009
, “Modelling of Multipeaked Directional Wave Spectra
,” Appl. Ocean Res.
, 31
(2
), pp. 132
–141
.10.1016/j.apor.2009.06.00121.
Rodriguez
, G.
Guedes Soares
, C.
Pacheco
, M.
Pérez-Martell
, E.
2002
, “Wave Height Distribution in Mixed Sea States
,” ASME J. Offshore Mech. Arct. Eng.
, 124
(1
), pp. 34
–40
.10.1115/1.144579422.
Guedes Soares
, C.
Carvalho
, A. N.
2003
, “Probability Distributions of Wave Heights and Periods in Measured Combined Sea-States From the Portuguese Coast
,” ASME J. Offshore Mech. Arct. Eng.
, 125
(3
), pp. 198
–204
.10.1115/1.157681623.
Petrova
, P.
Guedes Soares
, C.
2011
, “Wave Height Distributions in Bimodal Sea States From Offshore Basins,”
Ocean Eng.
, 38
(4)
, pp. 658
–672
10.1016/j.oceaneng.2010.12.018.24.
Arena
, F.
Guedes Soares
, C.
2009
, “Nonlinear Crest, Trough, and Wave Height Distributions in Sea States with Double-Peaked Spectra
,” ASME J. Offshore Mech. Arct. Eng.
, 131
(4
), p. 041105
.10.1115/1.316065725.
Toffoli
, M.
Onorato
, M.
Monbaliu
, J.
2006
, “Wave Statistics in Unimodal and Bimodal Seas From a Second-Order Model
,” Eur. J. Mech. B/Fluids
, 25
, pp. 649
–661
.10.1016/j.euromechflu.2006.01.00326.
Tamura
, H.
Waseda
, T.
Miyazawa
, Y.
2009
, “Freakish Sea State and Swell-Wind Sea Coupling: Numerical Study of the Suwa-Maru Incident
,” Geophys. Res. Lett.
, 36
, p. L01607
10.1029/2008GL036280.27.
Rice
, S.
1945
, “Mathematical Analysis of Random Noise
,” Bell Syst. Tech. J.
, 24
, pp. 46
–156
.28.
Longuet-Higgins
, M.
1975
, “On the Joint Distribution of the Periods and Amplitudes of Sea Waves
,” J. Geophys. Res.
, 80
(18
), pp. 2688
–2694
.10.1029/JC080i018p0268829.
Tayfun
, M. A.
Lo
, J.-M.
1990
, “Nonlinear Effects on Wave Envelope and Phase
,” J. Waterway, Port, Coastal, Ocean Eng.
, 116
(1
), pp. 79
–100
.10.1061/(ASCE)0733-950X(1990)116:1(79)30.
Longuet-Higgins
, M.
1952
, “On the Statistical Distribution of the Heights of Sea Waves
,” J. Marine Res.
, 11
(3
), pp. 245
–266
.31.
Tayfun
, M. A.
1994
, “Distributions of Envelope and Phase in Weakly Nonlinear Random Waves
,” J. Eng. Mech.
, 120
(4
), pp. 1009
–1025
.10.1061/(ASCE)0733-9399(1994)120:5(1009)32.
Tayfun
, M. A.
1980
, “Narrow-Band Nonlinear Sea Waves
,” J. Geophys. Res.
, 85
(C3
), pp. 1548
–1552
.10.1029/JC085iC03p0154833.
Fedele
, F.
Tayfun
, M. A.
2009
, “On Non-Linear Wave Groups and Crest Statistics
,” J. Fluid Mech.
, 620
, pp. 221
–229
.10.1017/S002211200800442434.
Tayfun
, M. A.
1990
, “Distribution of Large Wave Heights
,” J. Waterway, Port, Coastal, Ocean Eng.
, 116
(6
), pp. 686
–707
.10.1061/(ASCE)0733-950X(1990)116:6(686)35.
Boccotti
, P.
1989
, “On Mechanics of Irregular Gravity Waves
,” Atti Accad. Naz. Lincei, Mem. VIII
, 19
, pp. 11
–170
.36.
Forristall
, G.
1984
, “The Distribution of Measured and Simulated Wave Heights as a Function of Spectral Shape
,” J. Geophys. Res.
, 89
, pp. 10547
–10552
.10.1029/JC089iC06p1054737.
Boccotti
, P.
2000
, Wave Mechanics for Ocean Engineering
, Elsevier Science
, Amsterdam
.38.
Zheng
, G.
Cong
, P.
Pei
, Y.
2006
, “On the Improvements to the Wave Statistics of Narrowbanded Waves When Applied to Broadbanded Waves
,” J. Geophys. Res.
, 111
, p. C11016
.10.1029/2005JC00310639.
Casas-Prat
, M.
Holthuijsen
, L. H.
2010
, “Short-Term Statistics of Waves Observed in Deep Water
,” J. Geophys. Res.
, 115
, p. C09024
.10.1029/2009JC00574240.
Mori
, N.
Onorato
, M.
Janssen
, P.
Osborne
, A.
Serio
, M.
2007
, “On the Extreme Statistics of Long-Crested Deep Water Waves: Theory and Experiments
,” J. Geophys. Res.
, 112
, p. C09011
10.1029/2006JC004024.41.
Guedes Soares
, C.
Nolasco
, M.
1992
, “Spectral Modeling of Sea States With Multiple Wave Systems
,” ASME J. Offshore Mech. Arct. Eng.
, 114
, pp. 278
–284
.10.1115/1.291998142.
Donelan
, M.
Magnusson
, K.
2005
, “The Role of Meteorological Focusing in Generating Rogue Wave Conditions
,” Proceedings of the 14th Áha Hulikoá Hawaiian Winter Workshop on Rogue Waves
.43.
Stansberg
, C.
1995
, “Second-Order Random Wave Modelling in Space and Time, With Comparison to Experiments
,” Proceedings of 14th International Conference on Offshore Mechanics and Arctic Engineering (OMAE), ASME, Vol. 1 (Pt. A)
, pp. 37
–44
.44.
Cherneva
, Z.
Tayfun
, M. A.
Guedes Soares
, C.
2009
, “Statistics of Nonlinear Waves Generated in an Offshore Wave Basin
,” J. Geophys. Res.
, 114
, p. C08005
10.1029/2009JC005332.45.
Shemer
, L.
Sergeeva
, A.
2009
, “An Experimental Study of Spatial Evolution of Statistical Parameters in a Unidirectional Narrow-Banded Random Wavefield
,” J. Geophys. Res.
, 114
, p. C01015
10.1029/2008JC005077.46.
Dean
, R.
1990
, “Abnormal Waves: A Possible Explanation
,” A.
Torum
O.
Gudmestat
Kluwer
, Amsterdam
, pp. 609
–612
.47.
Toffoli
, A.
Bitner-Gregersen
, E.
Onorato
, M.
Babanin
, A.
2008
, “Wave Crest and Trough Distributions in a Broad-Banded Directional Wave Field
,” Ocean Eng.
, 35
, pp. 1784
–1792
.10.1016/j.oceaneng.2008.08.01048.
Fedele
, F.
Cherneva
, Z.
Tayfun
, M. A.
Guedes Soares
, C.
2010
, “Nonlinear Schrödinger Invariants and Wave Statistics
,” Phys. Fluids
, 22
, p. 036601
.10.1063/1.3325585Copyright © 2013 by ASME
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