Evolution of weakly nonlinear random directional waves: Laboratory experiments and numerical simulations

Journal of Fluid Mechanics

Volumn 664, Issue , 2010, Pages 313-336

  Toffoli, A ^a,e   Gramstad, O ^b   Trulsen, K ^b   Monbaliu, J ^c   Bitner Gregersen, E ^a   Onorato, M ^d  

^a DNV GL   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

^c UNIVERSITY OF LEUVEN   (Belgium)

^d UNIVERSITY OF TURIN   (Italy)

^e SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

surface gravity waves

Indexed keywords

GRAVITY WAVES; NONLINEAR EQUATIONS; NUMERICAL MODELS; WATER WAVES;

DIRECTIONAL WAVE FIELDS; LABORATORY EXPERIMENTS; MODULATIONAL INSTABILITY; NONLINEAR SCHRDINGER EQUATIONS; NUMERICAL INTEGRATIONS; PROBABILITY OF OCCURRENCE; STATISTICAL PROPERTIES; SURFACE GRAVITY WAVES;

NUMERICAL METHODS;

COMPUTER SIMULATION; EXPERIMENTAL STUDY; GRAVITY WAVE; LABORATORY METHOD; NUMERICAL MODEL; RANDOM WAVE; SURFACE WAVE; WATER WAVE;

EID: 78649960911     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211201000385X     Document Type: Article

References (68)

1. Annenkov, S. Y. & Shrira, V. I. 2001 Numerical modelling of water-wave evolution based on the Zakharov equation. J. Fluid. Mech. 449, 341-371.
2. Annenkov, S. Y. & Shrira, V. I. 2009 Evolution of kurtosis for wind waves. Geophys. Res. Lett. 36, L13603.
3. Arhan, M. & Plaisted, R. O. 1981 Non-linear deformation of sea-wave profiles in intermediate and shallow water. Oceanol. Acta 4 (2), 107-115.
4. Bateman, W. J. D., Swan, C. & Taylor, P. H. 2001 On the efficient numerical simulation of directionally spread surface water waves. J. Comput. Phys. 174, 277-305.
5. Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part I: Theory. J. Fluid Mech. 27, 417-430.
6. Bitner, E. M. (now Bitner-Gregersen, E. M.) 1980 Nonlinear effects of the statistical model of shallow-water wind waves. Appl. Ocean Res. 2, 63-73.
7. Bitner-Gregersen, E. & Magnusson, A. K. 2004 Extreme events in field data and in a second order wave model. In Proc. Rogue Waves 2004, Brest, France.
8. Clamond, D., Francius, M., Grue, J. & Kharif, C. 2006 Long time interaction of envelope solitons and freak wave formations. Eur. J. Mech. B/Fluids 25, 536-553.
9. Clamond, D. & Grue, J. 2001 A fast method for fully nonlinear water-wave computations. J. Fluid Mech. 447, 337-355.
10. Denissenko, P., Lukaschuk, S. & Nazarenko, S. 2007 Gravity wave turbulence in a laboratory flume. Phys. Rev. Lett. 99, 014501.
11. Dommermuth, D. G. & Yue, D. K. 1987 A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267-288.
12. 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.
13. Ducrozet, G., Bonnefoy, D., Le Touzé, D. & Ferrant, P. 2007 3-D HOS simulations of extreme waves in open seas. Nat. Hazards Earth Syst. Sci. 7, 109-122.
14. Dysthe, K. B. 1979 Note on the modification of the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A369, 105-114.
15. Dysthe, K., Krogstad, H. E. & Müller, P. 2008 Oceanic rogue waves. Annu. Rev. Fluid Mech. 40 (1), 287-310.
16. Dysthe, K. B., Trulsen, K., Krogstad, H. & Socquet-Juglard, H. 2003 Evolution of a narrowband spectrum of random surface gravity waves. J. Fluid Mech. 478, 1-10.
17. Emery, W. J. & Thomson, R. E. 2001 Data Analysis Methods in Physical Oceanography. Elsevier Science.
18. Fochesato, C . & Dias, F. 2006 A fast method for nonlinear three-dimensional free-surface waves. Proc. R. Soc. Lond. A 462, 2715-2735.
19. Fochesato, C., Grilli, S. & Dias, F. 2007 Numerical modeling of extreme rogue waves generated by directional energy focusing. WaveMotion 26, 395-416.
20. Forristall, G. Z. 2000 Wave crests distributions: observations and second-order theory. J. Phys. Ocean. 30, 1931-1943.
21. Gibson, R. S., Swan, C. & Tromans, P. S. 2007 Fully nonlinear statistics of wave crest elevation calculated using a spectral response surface method: application to unidirectional sea states. J. Phys. Ocean. 379, 3-15.
22. Gramstad, O. & Trulsen, K. 2007 Influence of crest and group length on the occurrence of freak waves. J. Fluid Mech. 582, 463-472.
23. Gramstad, O. & Trulsen, K. 2010 Can swell increase the number of freak waves in a wind sea? J. Fluid Mech. 650, 57-79.
24. Hasselmann, K. 1962 On the non-linear energy transfer in a gravity-wave spectrum. Part 1: General theory. J. Fluid Mech. 12, 481-500.
25. 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 Office.
26. 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.
27. Janssen, P. A. E. M. 2003 Nonlinear four-wave interaction and freak waves. J. Phys. Ocean. 33 (4), 863-884.
28. Janssen, P. A. E. M. 2009 On some consequences of the canonical transformation in the Hamiltonian theory of water waves. J. Fluid Mech. 637, 1-44.
29. Kharif, C. & Pelinovsky, E. 2003 Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B/Fluids 22, 603-634.
30. Komen, G. J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, H. & Janssen, P. A. E. M. 1994 Dynamics and Modelling of Ocean Waves. Cambridge University Press.
31. Lo, E. Y. & Mei, C. C. 1987 Slow evolution of nonlinear deep-water waves in two horizontal directions: a numerical study. Wav e Motion 9, 245-259.
32. 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.
33. Longuet-Higgins, M. S. 1976 On the nonlinear transfer of energy in the peak of a gravity-wave spectrum: a simplified model. Proc. R. Soc. Lond. A 347, 311-328.
34. Lvov, Y. V., Nazarenko, S. & Pokorni, B. 2006 Discreteness and its effect on water-wave turbulence. Physica D 218, 24-35.
35. 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, C09011.
36. Mori, N. & Yasuda, T. 2002 Effects of high-order nonlinear interactions on unidirectional wave trains. Ocean Engng 29, 1233-1245.
37. Onorato, M., Cavaleri, L., Fouques, S., Gramstad, O., Janssen, P. A. E. M., Monbaliu, J., Osborne, A. R., Pakozdi, C., Serio, M., Stansberg, C. T., Toffoli, A. & Trulsen, K. 2009a Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin. J. Fluid Mech. 627, 235-257.
38. Onorato, M., Osborne, A. R. & Serio, M. 2002a Extreme wave events in directional random oceanic sea states. Phys. Fluids 14 (4), 25-28.
39. Onorato, M., Osborne, A. R. & Serio, M. 2005a On deviations from Gaussian statistics for surface gravity waves. In Rogue Waves: Proceedings of the Hawaiian Winter Workshop. University of Hawaii at Manoa, pp. 79-83.
40. Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. 2001 Freak waves in random oceanic sea states. Phys. Rev. Lett. 86 (25), 5831-5834.
41. Onorato, M., Osborne, A. R., Serio, M. & Cavaleri, L. 2005b Modulational instability and non-Gaussian statistics in experimental random water-wave trains. Phys. Fluids 17, 078101.
42. Onorato, M., Osborne, A., Serio, M., Cavaleri, L., Brandini, C. & Stansberg, C. T. 2006 Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves. Eur. J. Mech. B/Fluids 25, 586-601.
43. Onorato, M., Osborne, A. R., Serio, M., Resio, D., Puskarev, A., Zakharov, V. E. & Brandini, C 2002b Freely decaying weak turbulence for sea surface gravity waves. Phys. Rev. Lett. 89, 144501.
44. Onorato, M., Waseda, T., Toffoli, A., Cavaleri, L., Gramdstad, O., Janssen, P. A. E. M., Kinoshita T., Monbaliu, J., Mori, N., Osborne, A. R., Serio, M., Stansberg, C. T., Tamura, H. & Trulsen, K. 2009b Statistical properties of directional ocean waves: the role of the modulational instability in the formation of extreme events. Phys. Rev. Lett. 102, 114502.
45. Petrova, P, Cherneva, Z. & Guedes Soares, C. 2006 Distribution of crest heights in sea states with abnormal waves. Appl. Ocean Res. 28, 235-245.
46. Prevosto, M., Krogstad, H. E. & Robin, A. 2000 Probability distributions for maximum wave and crest heights. Coast. Engng 40, 329-360.
47. Shemer, L., Sergeeva, A. & Slunyaev, A. 2010 Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random wave field evolution: experimental validation. Phys. Fluids 22, 016601.
48. 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.
49. Stansberg, C.T. 1994 Effects from directionality and spectral bandwidth on non-linear spatial modulations of deep-water surface gravity waves. In Proceedings of the 24th International Conference on Coastal Engineering, Kobe, Japan, vol. 1, pp. 579-593.
50. Tanaka, M . 2001a A method of studying nonlinear random field of surface gravity waves by direct numerical simulations. Fluid Dyn. Res. 28, 41-60.
51. Tanaka, M . 2001b Verification of Hasselmann's energy transfer among surface gravity waves by direct numerical simulations of primitive equations. J. Fluid Mech. 444, 199-221.
52. Tanaka, M . 2007 On the role of resonant interactions in the short-term evolution of deep-water ocean spectra. J. Phys. Ocean. 37, 1022-1036.
53. Tanaka, M. & Yokoyama, N. 2004 Effects of discretization of the spectrum in water-wave turbulence. Fluid Dyn. Res. 34, 199-216.
54. Tayfun, M . A . 1980 Narrow-band nonlinear sea waves. J. Geophys. Res. 85 (C3), 1548-1552.
55. Tayfun, M. A. & Fedele, F. 2007 Wave-height distributions and nonlinear effects. Ocean Engng 34, 1631-1649.
56. Toffoli, A., Benoit, M., Onorato, M. & Bitner-Gregersen, E. M. 2009 The effect of third-order nonlinearity on statistical properties of ransom directional waves in finite depth. Nonlin. Process. Geophys. 16, 131-139.
57. Toffoli, A., Bitner-Gregersen, E., Onorato, M. & Babanin, A. V. 2008a Wave crest and trough distributions in a broad-banded directional wave field. Ocean Engng 35, 1784-1792.
58. Toffoli, A., Onorato, M., Babanin, A. V., Bitner-Gregersen, E., Osborne, A. R. & Monbaliu, J. 2007 Second-order theory and set-up in surface gravity waves: a comparison with experimental data. J. Phys. Ocean. 37, 2726-2739.
59. Toffoli, A., Onorato, M., Bitner-Gregersen, E., Osborne, A. R. & Babanin, A. V. 2008b Surface gravity waves from direct numerical simulations of the Euler equations: a comparison with second-order theory. Ocean Engng 35 (3-4), 367-379.
60. Toffoli, A., Onorato, M., Bitner-Gregersen, E. M. & Monbaliu, J. 2010 The development of a bimodal structure in ocean wave spectra. J. Geophys. Res. 115, C03006.
61. Trulsen, K. & Dysthe, K. B. 1996 A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24, 281-289.
62. Tsai, W.-T. & Yue, D. K. 1996 Computation of nonlinear free-surface flows. Annu. Rev. Fluid Mech. 28, 249-278.
63. Waseda, T., Kinoshita, T. & Tamura, H. 2009 Evolution of a random directional wave and freak wave occurrence. J. Phys. Oceanogr. 39, 621-639.
64. West, B. J., Brueckner, K. A., Jand, R. S., Milder, D. M. & Milton, R. L. 1987 A new method for surface hydrodynamics. J. Geophys. Res. 92 (C11), 11803-11824.
65. Young, I. R. 1994 On the measurement of directional wave spectra. Appl. Ocean Res. 16, 283-294.
66. Zakharov, V. 1968 Stability of period waves of finite amplitude on surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190-194.
67. Zakharov, V. E., Dyachenko, A. I. & Vasilyev, O. A. 2002 New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface. Eur. J. Mech. B/Fluids 21, 283-291.
68. Zakharov, V. E. & Shabat, P. B. 1972 Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62-69.