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Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin

Published online by Cambridge University Press:  25 May 2009

M. ONORATO ,
L. CAVALERI ,
S. FOUQUES ,
O. GRAMSTAD ,
P. A. E. M. JANSSEN ,
J. MONBALIU ,
A. R. OSBORNE ,
C. PAKOZDI ,
M. SERIO  and
C. T. STANSBERG
...Show all authors
M. ONORATO
Affiliation:
Dipartimento di Fisica Generale, Università di Torino, Via P. Giuria 1, Torino, Italy
L. CAVALERI
Affiliation:
ISMAR, Castello 1364/A, Venezia, Italy
S. FOUQUES
Affiliation:
Norwegian Marine Technology Research Institute A.S. (MARINTEK), PO Box 4125, Valentinlyst, Trondheim, Norway
O. GRAMSTAD
Affiliation:
Department of Mathematics, University of Oslo, PO Box 1053, Blindern, Oslo, Norway
P. A. E. M. JANSSEN
Affiliation:
ECMWF, Shinfield Park, Reading, UK
J. MONBALIU
Affiliation:
K.U. Leuven, Kasteelpark Arenberg 40, Heverlee, Belgium
A. R. OSBORNE
Affiliation:
Dipartimento di Fisica Generale, Università di Torino, Via P. Giuria 1, Torino, Italy
C. PAKOZDI
Affiliation:
Norwegian Marine Technology Research Institute A.S. (MARINTEK), PO Box 4125, Valentinlyst, Trondheim, Norway
M. SERIO
Affiliation:
Dipartimento di Fisica Generale, Università di Torino, Via P. Giuria 1, Torino, Italy
C. T. STANSBERG
Affiliation:
Norwegian Marine Technology Research Institute A.S. (MARINTEK), PO Box 4125, Valentinlyst, Trondheim, Norway
A. TOFFOLI
Affiliation:
Det Norske Veritas, Veritasveien 1, Høvik, Norway
K. TRULSEN
Affiliation:
Department of Mathematics, University of Oslo, PO Box 1053, Blindern, Oslo, Norway
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Abstract

A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30° at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests. Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 235 - 257
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Alber, I. E. 1978 The effects of randomness on the stability of two dimensional surface wave trains. Proc. R. Soc. Lond. A 636, 525–546.Google Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. J. Fluid Mech. 27, 417–430.CrossRefGoogle Scholar
Brandini, C. 2001 Nonlinear interaction processes in extreme wave dynamics. PhD thesis, Universitá Di Firenze.Google Scholar
Denissenko, P., Lukaschuk, S. & Nazarenko, S. 2007 Gravity wave turbulence in a laboratory flume. Phys. Rev. Lett. 99, 014501.CrossRefGoogle Scholar
Donelan, M. A., Drennan, W. M. & Magnusson, A. K. 1996 Nonstationary analysis of the directional properties of propagating waves. J. Phys. Oceanogr. 26, 1901–1914.2.0.CO;2>CrossRefGoogle Scholar
Donelan, M. A., Hamilton, J. & Hui, W. H. 1985 Directional spectra pf wind-generated waves. Philos. Trans. R. Soc. Lond. A 315, 509–562.Google Scholar
Dysthe, K. B. 1979 Note on the modification of the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105–114.Google Scholar
Dysthe, K. B., Trulsen, K., Krogstad, H. & Socquet-Juglard, H. 2003 Evolution of a narrow–band spectrum of random surface gravity waves. J. Fluid Mech. 478, 1–10.Google Scholar
Emery, W. J. & Thomson, R. E. 2001 Data Analysis Methods in Physical Oceanography. Elsevier Science B.VGoogle Scholar
Forristall, G. Z. 2000 Wave crests distributions: Observations and second-order theory. J. Phys. Oceanogr. 30, 1931–1943.Google Scholar
Gramstad, O. & Trulsen, K. 2007 Influence of crest and group length on the occurrence of freak waves. J. Fluid Mech. 582, 463–472.CrossRefGoogle Scholar
Hasselmann, K. 1962 On the non–linear energy transfer in a gravity-wave spectrum. Part I. General theory. J. Fluid Mech. 12, 481–500.CrossRefGoogle Scholar
Hasselmann, D. E., Dunckel, M. & Ewing, J. A. 1980 Directional wave spectra observed during jonswap 1973. J. Phys. Oceanogr. 10, 1264–1280.2.0.CO;2>CrossRefGoogle Scholar
Hauser, D., Kahma, K. K., Krogstad, H. E., Lehner, S., Monbaliu, J. & Wyatt, L. W. (Ed.) 2005 Measuring and Analysing the Directional Spectrum of Ocean Waves. Cost OfficeGoogle Scholar
Hwang, P. A., Wang, D. W., Walsh, E. J., Krabill, W. B. & Swift, R. N 2000 Airborne measurements of the wavenumber spectra of ocean surface waves. Part II. Directional distribution. J. Phys. Oceanogr. 30, 2768–2787.2.0.CO;2>CrossRefGoogle Scholar
Janssen, P. A. E. M. 2003 Nonlinear four-wave interaction and freak waves. J. Phys. Oceanogr. 33 (4), 863–884.2.0.CO;2>CrossRefGoogle Scholar
Janssen, P. A. E. M. & Onorato, M. 2007 The intermediate water depth limit of the Zakharov equation and consequences for wave prediction. J. Phys. Oceanogr. 37, 2389–2400.CrossRefGoogle Scholar
Kharif, C., Giovanangeli, J. P., Touboul, J., Grare, L. & Pelinovsky, E. 2008 Influence of wind on extreme wave events: experimental and numerical approaches. J. Fluid Mech. 594, 209–247.Google Scholar
Komen, G. J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, H. & Janssen, P. A. E. M. 1994 Dynamics and Modeling of Ocean Waves. Cambridge University PressGoogle Scholar
Longuet-Higgins, M. S. 1963 The effect of non-linearities on statistical distribution in the theory of sea waves. J. Fluid Mech. 17, 459–480.Google Scholar
Longuet-Higgins, M. S. 1980 On the distribution of the heights of sea waves: some effects of nonlinearity and finite band width. J. Geophys. Res. 85, 1519–1523.CrossRefGoogle Scholar
Mitsuyasu, H., Tasai, F., Suhara, T., Mizuno, S., Ohkusu, M., Honda, T. & Rikiishi, K. 1975 Observations of the directional spectrum of ocean waves using a cloverleaf buoy. J. Phys. Oceanogr. 5, 750–760.2.0.CO;2>CrossRefGoogle Scholar
Mori, N. & Janssen, P. A. E. M. 2006 On kurtosis and occurrence probability of freak waves. J. Phys. Oceanogr. 36, 1471–1483.CrossRefGoogle Scholar
Mori, N., Onorato, M., Janssen, P. A. E. M., Osborne, A. R. & Serio, M. 2007 On the extreme statistics of long-crested deep water waves: theory and experiments. J. Geophys. Res. 112 (C9), C09011.CrossRefGoogle Scholar
Mori, N. & Yasuda, T. 2002 Effects of high–order nonlinear interactions on unidirectional wave trains. Ocean Engng 29, 1233–1245.Google Scholar
Onorato, M., Osborne, A. R. & Serio, M. 2006 a Modulation instability in crossing sea states: A possible machanism for the formation of freak waves. Phys. Rev. Lett. 96, 014503.CrossRefGoogle Scholar
Onorato, M., Osborne, A. R. & Serio, M. 2002 a Extreme wave events in directional random oceanic sea states. Phys. Fluids 14 (4), 25–28.Google Scholar
Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. 2001 Freak wave in random oceanic sea states. Phys. Rev. Lett. 86 (25), 5831–5834.Google Scholar
Onorato, M., Osborne, A. R., Serio, M. & Cavaleri, L. 2005 Modulational instability and non-gaussian statistics in experimental random water-wave trains. Phys. Fluids 17, 078101–4.Google Scholar
Onorato, M., Osborne, A. R., Serio, M., Cavaleri, L., Brandini, C. & Stansberg, C. T. 2004 Observation of strongly non-gaussian statistics for random sea surface gravity waves in wave flume experiments. Phys. Rev. E 70, 067302.Google ScholarPubMed
Onorato, M., Osborne, A., Serio, M., Cavaleri, L., Brandini, C. & Stansberg, C. T. 2006 b Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves. Eur. J. Mech. B/Fluids 25, 586–601.Google Scholar
Onorato, M., Osborne, A. R., Serio, M., Resio, D., Puskarev, A., Zakharov, V. E. & Brandini, C. 2002 b Freely decaying weak turbulence for sea surface gravity waves. Phys. Rev. Lett. 89, 4.144501.CrossRefGoogle ScholarPubMed
Socquet-Juglard, H., Dysthe, K., Trulsen, K., Krogstad, H. E. & Liu, J. 2005 Distribution of surface gravity waves during spectral changes. J. Fluid Mech. 542, 195–216.Google Scholar
Song, J. & Banner, M. L. 2002 On determining the onset and strength of breaking for deep water waves. Part I. Unforced irrotational wave groups. J. Phys. Oceanogr. 32, 2541–2558.Google Scholar
Stansberg, C. T. 1992 On spectral instabilities and development of nonlinearities in propagating deep-water wave trains. In Coastal Engineering, Proceedings of the XXIII International Conference Venice, Italy, pp. 658–671. American Society of Civil Engineers.Google Scholar
Stansberg, C. T. 1994 Effects from directionality and spectral bandwidth on non-linear spatial modulations of deep-water surface gravity waves. In Proceedings, Vol. 1, the 24th International Conference on Coastal Engineering, Kobe, Japan, pp. 579–593. American Society of Civil Engineers.Google Scholar
Tayfun, M. A. 1980 Narrow–band nonlinear sea waves. J. Geophys. Res. 85 (C3), 1548–1552.Google Scholar
Tayfun, M. A. & Fedele, F. 2007 Wave-height distributions and nonlinear effects. Ocean Engng 34, 1631–1649.CrossRefGoogle Scholar
Tayfun, M. A. & Lo, J.-M. 1990 Nonlinear effects on wave envelope and phase. J. Water. Port Coastal Ocean Engng, ASCE 116, 79–100.Google Scholar
Toffoli, A., Onorato, M. & Monbaliu, J. 2006 Wave statistics in unimodal and bimodal seas from a second–order model. Eur. J. Mech. B/Fluids 25, 649–661.CrossRefGoogle Scholar
Trulsen, K. & Dysthe, K. B. 1997 Freak waves – a three-dimensional wave simulation. In Proceedings of the 21st Symposium on Naval Hydrodynamics, Washington, DC, pp. 550–560. National Academy Press.Google Scholar
Waseda, T. 2006 Impact of directionality on the extreme wave occurrence in a discrete random wave system. In Proceedings of 9th International Workshop on Wave Hindcasting and Forecasting, Victoria, Canada.Google Scholar
Young, I. R. 1994 On the measurement of directional wave spectra. Appl. Ocean Res. 16, 283–294.CrossRefGoogle Scholar
Zakharov, V. 1968 Stability of period waves of finite amplitude on surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190–194.CrossRefGoogle Scholar