The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth

Nonlinear Processes in Geophysics

Volumn 16, Issue 1, 2009, Pages 131-139

  Toffoli, A ^a   Benoit, M ^b   Onorato, M ^c   Bitner Gregersen, E M ^a  

^a DNV GL   (Norway)

^b UNIVERSITÉ PARIS EST   (France)

^c UNIVERSITY OF TURIN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EULERIAN ANALYSIS; GAUSSIAN METHOD; GRAVITY WAVE; NONLINEARITY; NUMERICAL MODEL; WATER DEPTH; WAVE DIRECTION; WAVE ENERGY; WAVE FIELD;

EID: 77949481353     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-16-131-2009     Document Type: Article

References (44)

1. Annenkov S. Y. Shrira V. I.: Numerical modeling of water-wave evolution based on the Zakharov equation J. Fluid. Mech. 449, 341-371, 2001.
2. Benjamin, T. B.: Instability of periodic wave trains in nonlinear dispersive systems, Proc. Roy. Soc. London, A299, 59-75, 1967.
3. Clamond, D. and Grue, J.: A fast method for fully nonlinear water-wave computations, J. Fluid Mech., 447, 337-355, 2001.
4. Clamond, D., Francius, M., Grue, J., and Kharif, C.: Long time interaction of envelope solitons and freak wave formations, Europ. J. Mech. B-Fluids, 25, 536-553, 2006.
5. Davey, A. and Stewartson, K.: On three-dimensional packets of surface waves, Proc. R. Soc. Lond. A, 338, 101-110, 1974.
6. Dommermuth, D. G. and Yue, D. K. P.: A high-order spectral method for the study of nonlinear gravity waves, J. Fluid Mech., 184, 267-288, 1987.
7. Ducrozet, G., Bonnefoy, F., Le Touzé, D., and Ferrant, P.: 3-D HOS simulations of extreme waves in open seas, Nat. Hazards Earth Syst. Sci., 7, 109-122, 2007, http://www.nat-hazards-earth-syst-sci.net/7/109/2007/.
8. Dysthe, K. B., Trulsen, K., Krogstad, H., and Socquet-Juglard, H.: Evolution of a narrow-band spectrum of random surface gravity waves, J. Fluid Mech., 478, 1-10, 2003.
9. Forristall, G.: Wave Crests Distributions: Observations and Second-Order Theory, J. Phys. Ocean., 30, 1931-1943, 2000.
10. Francius, M. and Kharif, C.: Three dimensional instabilities of periodic gravity waves in shallow water, J. Fluid Mech., 561, 417-437, 2006.
11. Gramstad, O. and Trulsen, K.: Influence of crest and group length on the occurrence of freak waves, J. Fluid Mech., 582, 463-472, 2007.
12. Hasselmann, K.: On the non-linear energy transfer in a gravity-wave spectrum. Part 1: General theory, J. Fluid Mech., 12, 481-500, 1962.
13. Herbers, T. H. C., Orzech, M., Elgar, S., and Guza, R. T.: Shoaling transformation of wave frequency-directional spectra, J. Geo-phys. Res., 108(C1), 3013, doi:10.1029/2001JC001304, 2003.
14. Holthuijsen, L. H.: Waves in oceanic and coastal waters, Cambridge University Press, Cambridge, UK, 2007.
15. Hwang, P. A., Wang, D. W., Walsh, E. J., Krabill, W. B., and Swift, R. N.: Airborne measurements of the wavenumber spectra of ocean surface waves. Part II: Directional distribution, J. Phys. Oceanogr., 30, 2768-2787, 2000.
16. Janssen, P. A. E. M.: Nonlinear Four-Wave Interaction and Freak Waves, J. Phys. Ocean., 33, 863-884, 2003.
17. Janssen, P. A. E. M. and Onorato, M.: The intermediate water depth limit of the Zakharov equation and consequences for wave prediction, J. Phys. Oceanogr., 37, 2389-2400, 2007.
18. Komen, G., Cavaleri, L., Donelan, M., Hasselmann, K., Hassel-mann, S., and Janssen, P. A. E. M.: Dynamics and modeling of ocean waves, Cambridge University Press, Cambridge, UK, 1994.
19. Longuet-Higgins, M. S.: The effect of non-linearities on statistical distribution in the theory of sea waves, J. Fluid Mech., 17, 459-480, 1963.
20. Longuet-Higgins, M. S.: On the nonlinear transfer of energy in the peak of a gravity-wave spectrum: a simplified model, Proc. Roy. Soc. London A, 347, 311-328, 1976.
21. Mori, N. and Janssen, P. A. E. M.: On kurtosis and occurrence probability of freak waves, J. Phys. Ocean., 36, 1471-1483, 2006.
22. Mori, N. and Yasuda, T.: Effects of high-order nonlinear interactions on unidirectional wave trains, Ocean Eng., 29, 1233-1245, 2002.
23. Mori, N., Onorato, M., Janssen, P. A. E. M., Osborne, A. R., and Serio, M.: On the extreme statistics of long-crested deep water waves: Theory and experiments, J. Geophys. Res., 112, C09011, doi:10.1029/2006JC004024, 2007. (Pubitemid 350120730)
24. Onorato, M., Osborne, A. R., Serio, M., and Bertone, S.: Freak waves in random oceanic sea states, Phys. Rev. Lett., 86, 5831-5834, 2001.
25. Onorato, M., Osborne, A. R., and Serio, M.: Extreme wave events in directional random oceanic sea states, Phys. Fluids, 14, 25-28, 2002.
26. Onorato, M., Osborne, A. R., Serio, M., and Cavaleri, L.: Modulational instability and non-Gaussian statistics in experimental random water-wave trains, Phys. Fluids, 17, 078101, doi:10.1063/1.1946769, 2005. (Pubitemid 41057241)
27. Onorato, M., Osborne, A., Serio, M., Cavaleri, L., Brandini, C., and Stansberg, C. T.: Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves, Eur. J. Mech. B-Fluid, 25, 586-601, 2006.
28. Pelinovsky, E. and Sergeeva, A.: Numerical modeling of the KdV random wave field, Eur. J. Mech. B-Fluid, 25, 425-434, 2006.
29. Prevosto, M., Krogstad, H., and Robin, A.: Probability distributions for maximum wave and crest heights, Coast. Eng., 40, 329-360, 2000.
30. Socquet-Juglard, H., Dysthe, K., Trulsen, K., Krogstad, H., and Liu, J.: Distribution of surface gravity waves during spectral changes, J. Fluid Mech., 542, 195-216, 2005.
31. Tanaka, M.: A method of studying nonlinear random field of surface gravity waves by direct numerical simulations, Fluid Dyn. Res., 28, 41-60, 2001a.
32. Tanaka, M.: Verification of Hasselmann's energy transfer among surface gravity waves by direct numerical simulations of primitive equations, J. Fluid Mech., 444, 199-221, 2001b.
33. Tayfun, M. A.: Narrow-band nonlinear sea waves, J. Geophys. Res., 85(C3), 1548-1552, 1980.
34. Tayfun, M. A. and Fedele, F.: Wave-height distributions and nonlinear effects, Ocean Eng., 34, 1631-1649, 2007.
35. Toffoli, A., Onorato, M., and Monbaliu, J.: Wave statistics in uni-modal and bimodal seas from a second-order model, Eur. J. Mech. B-Fluid, 25, 649-661, 2006.
36. Toffoli, A., Onorato, M., Babanin, A. V., Bitner-Gregersen, E., Os-borne, A. R., and Monbaliu, J.: Second-order theory and set-up in surface gravity waves: a comparison with experimental data, J. Phys. Ocean., 37, 2726-2739, 2007.
37. Toffoli, A., Bitner-Gregersen, E., Onorato, M., and Babanin, A. V.: Wave crest and trough distributions in a broad-banded directional wave field, Ocean Eng., 35, 1784-1792, 2008a.
38. Toffoli, A., Onorato, M., Bitner-Gregersen, E., Osborne, A. R., and Babanin, A. V.: Surface gravity waves from direct numerical simulations of the Euler equations: a comparison with second-order theory, Ocean Eng., 35, 367-379, 2008b.
39. Toffoli, A., Onorato, M., Osborne, A. R., and Monbaliu, J.: Non-Gaussian properties of shallow water waves in crossing seas, in: Extreme ocean waves, edited by: Pelinovsky, E. and Kharif, C., Springer Netherlands, The Netherlands, 53-69, 2008c.
40. Waseda, T.: Impact of directionality on the extreme wave occurrence in a discrete random wave system, in: Proc. 9th Int. Workshop on Wave Hindcasting and Forecasting, Victoria, Canada, 2006.
41. West, B. J., Brueckner, K. A., Janda, R. S., Milder, D. M., and Milton, R. L.: A new method for surface hydrodynamics, J. Geo-phys. Res., 92, 11803-11824, 1987.
42. Whitham, G.: Linear and Nonlinear Waves, Wiley Interscience, New York, USA, 636 pp., 1974.
43. Zakharov, V. E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid, J. Appl. Mech. Tech. Phys., 9, 190-194, 1968.
44. Zakharov, V. E., Dyachenko, A. I., and Vasilyev, O. A.: New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface, Eur. J. Mech. B-Fluid, 21, 283-291, 2002.