Summary
The chapter focuses on the physics and modelling of the extreme water wave events called rogue waves. A particular attention is paid to their formation in presence of strong wind. Two mechanisms producing the giant waves are considered: The dispersive spatio-temporal focusing and the modulational instability. In both cases an amplification of the height and duration of the rogue wave event is observed under wind action.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. I. Banner and W.K. Melville (1976) On the separation of air flow over water waves, J. Fluid Mech. 77, 825–842.
T.B. Benjamin and J.E. Feir 1967 The desintegration of wave trains on deep water. Part 1. Theory., J. Fluid Mech. 27, 417–430.
D. Clamond and J. Grue (2002) Interaction between envelope solitons as a model for freak wave formation. Pt 1: Long-time interaction, C.R. Mecanique 330, 575–580.
D. Clamond, M. Francius, J. Grue and C. Kharif (2006) Strong interaction between envelope solitary surface gravity waves, Eur. J. Mech. B/Fluids, 25(5), 536–553.
F. Dias and C. Kharif (1999) Nonlinear gravity and capillary-gravity waves, Annu. Rev. Fluid Mech. 31, 301–346.
D.G. Dommermuth and D.K.P. Yue (1987) A high-order spectral method for the study of nonlinear gravity waves, J. Fluid Mech. 184, 267–288.
K.B. Dysthe (2001) Modelling a “Rogue Wave”-Speculations or a realistic possibility?, Rogues Waves 2000 edited by M. Olagnon and G.A. Athanassoulis (Brest, France), 255–264, 2001.
J.P. Giovanangeli, C. Kharif and E. Pelinovsky (2004) Experimental study of the wind effect on the focusing of transient wave groups, Proc. of abtracts of Rogue waves 2004, Brest.
H. Jeffreys (1925) On the formation of wave by wind, Proc. Roy. Soc. A 107, 189–206.
C. Kharif and A. Ramamonjiarisoa (1988) Deep water gravity wave instabilities at large steepness, Phys. Fluids 31, 1286–1288.
C. Kharif and E. Pelinovsky (2003) Physical mechanisms of the rogue wave phenomenon, Eur. J. Mech. B/Fluids 22, 603–634.
I.V. Lavranov (1998) The wave energy concentration at the Agulhas current off South Africa, Natural Hazards 17, 117–127.
G. Lawton (2001) Monsters of the deep (The perfect wave), New Scientist 170(2297), 28–32.
M.S. Longuet-Higgins (1985) Bifurcation in gravity waves, J. Fluid Mech. 151, 457–475.
S.R. Massel (1996) Ocean surface waves: Their physics and prediction, Word Scientific, Singapour.
J.W. McLean (1982) Instabilities of finite-amplitude water waves, J. Fluid Mech. 114, 315–330.
J.W. McLean, Y.C. Ma, D.U. Martin, P.G. Saffman and H.C. Yuen (1981) Three-dimensional instability of finite-amplitude water waves, Phys. Rev. Lett. 46, 817–820.
E. Pelinovsky, T. Talipova and C. Kharif (2000) Nonlinear dispersive mechanism of the freak wave formation in shallow water, Physica D 147(1–2), 83–94.
P. Peterson, T. Soomere, J. Engelbrecht and E. van Groesen (2003) Soliton interaction as a possible model for extreme waves, Nonlinear Processes in Geophysics 10, 503–510.
T. Soomere and J. Engelbrecht (2005) Extreme elevations and slopes of interacting solitons in shallow water, Wave Motion 41, 179–192.
C. Skandrani, C. Kharif and J. Poitevin (1996) Nonlinear evolution of water surface waves: The frequency downshifting phenomenon, Contemp. Math. 200, 157–171.
A. Slunyaev, C. Kharif, E. Pelinovsky and T. Talipova (2002) Nonlinear wave focusing on water of finite depth, Physica D 173(1–2),77–96.
R. Smith (1976) Giant waves, J. Fluid Mech. 77, 417–431.
H.U. Sverdrup and W.H. Munk (1947) Wind, sea, and swell; theory of relations for forecasting, U.S. Navy Hydrographic Office, H.O. 601.
J. Touboul, J.P. Giovanangeli, C. Kharif and E. Pelinovsky (2006) Freak waves under the action of wind: Experiments and simulations, Eur. J. Mech. B/Fluids 25, 662–676.
B.S. White and B. Fornberg (1998) On the chance of freak waves at the sea, J. Fluid Mech. 255, 113–138.
G.B. Whitham (1965) A general approach to linear and non-linear dispersive waves using a Lagrangian, J. Fluid Mech. 22, 273–283.
G.B. Whitham (1967) Nonlinear dispersion of water waves, J. Fluid Mech. 27, 399–412.
C.H. Wu and A. Yao (2004) Laboratory measurements of limiting freak waves on currents, J. Geophys. Res. 109, C12002, 1–18.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kharif, C. (2007). On the modelling of huge water waves called rogue waves. In: Kundu, A. (eds) Tsunami and Nonlinear Waves. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71256-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-71256-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71255-8
Online ISBN: 978-3-540-71256-5
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)