×

Freak waves under the action of wind: experiments and simulations. (English) Zbl 1103.76013

Summary: The freak wave formation due to the dispersive focusing mechanism is investigated experimentally without wind and in the presence of wind. An asymmetric behaviour between the focusing and defocusing stages is found when the wind is blowing over the mechanically generated gravity wave group. This feature corresponds physically to the sustenance of the freak wave mechanism on longer periods of time. Furthermore, we observe a weak amplification of the freak wave and a shift in the downstream direction of the point where the waves merge. The experimental results suggest that the Jeffreys’ sheltering mechanism could play a key role in the coherence of the group of the freak wave. Hence, the Jeffreys’ sheltering theory is introduced in a fully nonlinear model. The results of the numerical simulations confirm that the duration of the freak wave event increases with the wind velocity.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76-05 Experimental work for problems pertaining to fluid mechanics
Full Text: DOI

References:

[1] Lawton, G., Monsters of the deep (the perfect wave), New Scientist, 170, 2297, 28-32 (2001)
[2] Mallory, J. K., Abnormal waves on the South-East Africa, Int. Hydrog. Rev., 51, 89-129 (1974)
[3] Lavrenov, I. V., The wave energy concentration at the Agulhas current of South Africa, Natural Hazards, 17, 1998, 117-127 (1974)
[4] Pelinovsky, E.; Talipova, T.; Kharif, C., Nonlinear-dispersive mechanism of the freak wave formation in shallow water, Physica D, 147, 83-94 (2000) · Zbl 0978.76014
[5] Slunyaev, A.; Kharif, C.; Pelinovsky, E.; Talipova, T., Nonlinear wave focusing on water of finite depth, Physica D, 173, 77-97 (2002) · Zbl 1047.76010
[6] Trulsen, K.; Dysthe, K. B., Freak waves - A three-dimensional wave simulation, (Proc. 21st Symp. on Naval Hydrodynamics (1997), National Academy Press), 550-560
[7] Osborne, A. R.; Onorato, M.; Serio, M., The nonlinear dynamics of rogue waves and holes in deep water gravity wave train, Phys. Lett. A, 275, 386-393 (2000) · Zbl 1115.76315
[8] Clamond, D.; Grue, J., Interaction between envelop solitons as a model for freak wave formation, C. R. Mecanique, 330, 575-580 (2002) · Zbl 1177.76055
[9] Kharif, C.; Pelinovsky, E., Physical mechanisms of the rogue wave phenomenon, Eur. J. Mech. B Fluids, 22, 603-634 (2003) · Zbl 1058.76017
[10] Socquet-Juglard, H.; Dysthe, K.; Trulsen, K.; Krogstad, H., Probability distributions of surface gravity waves during spectral changes, J. Fluid Mech., 542, 195-216 (2005) · Zbl 1165.76317
[11] Whitham, G. B., Linear and Non Linear Waves (1974), Willey & Sons: Willey & Sons New York · Zbl 0373.76001
[12] Balk, A. M., The suppression of short waves by a train of long waves, J. Fluid Mech., 315, 139-150 (1996) · Zbl 0869.76009
[13] J.P. Giovanangeli, C. Kharif, E. Pelinovsky, Experimental study of the wind effect on the focusing of transient wave group, in: Rogue Waves Proceedings, Rogue Waves (Brest, 2004); J.P. Giovanangeli, C. Kharif, E. Pelinovsky, Experimental study of the wind effect on the focusing of transient wave group, in: Rogue Waves Proceedings, Rogue Waves (Brest, 2004)
[14] Miles, J., Surface wave generation: a viscoelastic model, J. Fluid Mech., 322, 131-145 (1996) · Zbl 0881.76008
[15] Jeffreys, H., On the formation of water waves by wind, Proc. Roy. Soc. London Ser. A, 107, 189-206 (1925) · JFM 51.0673.04
[16] Jeffreys, H., On the formation of water waves by wind, Proc. Roy. Soc. London Ser. A, 110, 241-247 (1926) · JFM 52.0876.06
[17] Reul, N.; Branger, H.; Giovanangeli, J. P., Air flow separation over unsteady breaking waves, Phys. Fluids, 11, 1959-1961 (1999) · Zbl 1147.76480
[18] Banner, M. L., The influence of wave breaking on the surface pressure distribution in wind-wave interactions, J. Fluid Mech., 211, 463-495 (1990)
[19] M. Greco, A two-dimensional study of green water loading, PhD thesis, Dept. Marine Hydrodynamics, NTNU, Norway, 2001; M. Greco, A two-dimensional study of green water loading, PhD thesis, Dept. Marine Hydrodynamics, NTNU, Norway, 2001
[20] T. Vinje, P. Brevig, Breaking waves on finite depth: a numerical study, Ship Res. Inst. Norway, R-118-81, 1981; T. Vinje, P. Brevig, Breaking waves on finite depth: a numerical study, Ship Res. Inst. Norway, R-118-81, 1981
[21] Dommermuth, D.; Yue, D.; Lin, W.; Rapp, R.; Chan, E.; Melville, W., Deep-water plunging breakers: a comparison between potential theory and experiments, J. Fluid Mech., 189, 423-442 (1988) · Zbl 0642.76020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.