Skip to main content
SpringerLink
Log in

Freak Waves Phenomenon: Physical Mechanisms and Modelling

  • Chapter
Waves in Geophysical Fluids

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 489))

Abstract

The main physical mechanisms responsible for the formation of huge waves known as freak waves are described and analyzed. Data of observations in the marine environment as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. The mathematical definition of these huge waves is based on statistical parameters, namely the significant height. As linear models of freak waves the following mechanisms are considered: Wave-current interaction and dispersion enhancement of transient wave packets. When the nonlinearity of the water waves is introduced, these mechanisms remain valid but should be modified and new mechanisms such as modulational instability and soliton-collisions become good candidates to explain the freak wave occurrence. Specific numerical simulations were performed within the framework of classical nonlinear evolution equations: The Nonlinear Schrödinger equation, the Davey-Stewartson system, the Korteweg-de Vries equation, the Kadomtsev-Petviashvili equation, the Zakharov equation and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of freak wave phenomenon.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • M.J. Ablowitz, CM. Schober and B.M. Herbst (1993). Numerical chaos, roundoff errors, and homoclinic manifolds. Phys. Rev. Lett. Vol. 71(17), 2683–7.

    Article  Google Scholar 

  • M.J. Ablowitz, J. Hammack, D. Henderson and CM. Schober (2000). Modulated periodic Stokes waves in deep water. Phys. Rev. Lett. Vol. 84(5), 887–90.

    Article  Google Scholar 

  • M.J. Ablowitz, J. Hammack, D. Henderson and CM. Schober (2001). Long-time dynamics of the modulational instability of deep water waves. Physica D Vol. 152–153, 416–33.

    Article  MathSciNet  Google Scholar 

  • I.E. Alber (1978). The effects of randomness on the stability of two-dimensional surface wavetrain. Proc. Roy. Soc. Lond. A Vol. 363, 525–46.

    MATH  MathSciNet  Google Scholar 

  • LE. Alber and P.G. Saffman (1978). Stability of random nonlinear water waves with finite bandwidth spectra, In TRW Defense and Space Syst. Gr. Rep. No 31326-6035-RU-OObv.

    Google Scholar 

  • D. Anker and N.C Freeman (1978). On the soliton solutions of the Davey-Stewartson equation for long wave. Proc. Roy. Soc. London A Vol. 360, 529–40.

    Article  MATH  MathSciNet  Google Scholar 

  • S.Y. Annenkov and S.I. Badulin (2001). Multi-wave resonances and formation of high-amplitude waves in the ocean. In Rogues Waves 2000. Ed. by M. Olagnon and G.A. Athanassoulis, Brest, 205–13.

    Google Scholar 

  • W.J.D. Bateman, C Swan and P.H. Taylor (2001). On the efficient numerical simulation of directionally spread surface water waves. J. Comp. Phys. Vol. 174, 277–301.

    Article  MATH  MathSciNet  Google Scholar 

  • W.J.D. Bateman, C Swan and P.H. Taylor (2003). On the calculation of the water particle kinematics arising in a directionally spread wavefield. J. Comp. Phys. Vol. 186, 70–90.

    Article  MATH  Google Scholar 

  • T.B. Benjamin (1967). Instability of periodic wave trains in nonlinear dispersive systems. Proc. Roy. Soc. Lond. A Vol. 299, 59–75.

    Google Scholar 

  • T.B. Benjamin and J.E. Feir (1967). The desintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. Vol. 27, 417–30.

    Article  MATH  Google Scholar 

  • C. Brandini and S. Grilli (2001). Evolution of three-dimensional unsteady wave modulations. Rogues Waves, Brest 2000. Ed. by M. Olagnon and G.A. Athanassoulis, 275–82.

    Google Scholar 

  • P.P. Bretherton and J.R. Garrett (1969). Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. London A Vol. 302, 529–54.

    Google Scholar 

  • U. Brinch-Nielsen and I.G. Jonsson (1986). Fourth-order evolution equations and stability analysis for Stokes waves on arbitrary water depth. Wave Motion. Vol. 8, 455–72.

    Article  MATH  MathSciNet  Google Scholar 

  • M.G. Brown and A. Jensen (2001). Experiments on focusing unidirectional water waves. J. Geophys. Res. Vol. 106(C8), 16917–28.

    Article  Google Scholar 

  • A. Calini and C.M. Schober (2002). Homoclinic chaos increases the likelihood of rogue wave formation. Phys. Lett. A Vol. 298, 335–49.

    Google Scholar 

  • D. Clamond and J. Grue (2001). A fast method for fully nonlinear water wave computations. J. Fluid Mech. Vol. 398, 45–60.

    Article  MathSciNet  Google Scholar 

  • 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 Vol. 330, 575–80.

    Article  MATH  Google Scholar 

  • D. Clamond, M. Francius, J. Grue and C. Kharif (2006). Strong interaction between envelope solitary surface gravity waves. Eur. J. Mech. B/Fluids Vol. 5.

    Google Scholar 

  • G. Clauss (2002). Dramas of the sea: Episodic waves and their impact on offshore structures. Appl. Ocean Res. Vol. 24, 147–61.

    Article  Google Scholar 

  • G. Contento, R. Codigha and F. D’Este (2001). Nonlinear effects in 2D transient nonbreaking waves in a closed flume. Appl. Ocean Res. Vol. 23, 3–13.

    Article  Google Scholar 

  • W. Craig and C. Sulem (1993). Numerical simulation of gravity waves. J. Comput. Phys. Vol. 108, 73–83.

    Article  MATH  MathSciNet  Google Scholar 

  • D.R. Crawford, P.G. saffman and H.C. Yuen (1980). Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves. Wave Motion Vol. 2, 1–16.

    Article  MATH  MathSciNet  Google Scholar 

  • F. Dias and C. Kharif (1999). Nonhnear gravity and capillary-gravity waves. Annu. Rev. Fluid Mech. Vol. 31, 301–46.

    Article  MathSciNet  Google Scholar 

  • J.W. Dold (1992). An efficient surface-integral algorithm applied to unsteady gravity waves. J. Comp. Phys. Vol. 103, 90–115.

    Article  MATH  MathSciNet  Google Scholar 

  • D.G. Dommermuth and D.K.P. Yue (1987). A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. Vol. 184, 267–88.

    Article  MATH  Google Scholar 

  • A.I. Dyachenko and V.E. Zakharov (2005). Modulational instability of Stokes wave → freak wave. J.E.T.P. Vol. 81(6), 318–22.

    Google Scholar 

  • K.B. Dysthe (1979). Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. Roy. Soc. London A Vol. 369, 105–14.

    MATH  Google Scholar 

  • K.B. Dysthe (2001). Modelling a “Rogue Wave”-Speculations or a realistic possibility? Rogues Waves, Brest 2000. Ed. by M. Olagnon and G.A. Athanassoulis, 255–64.

    Google Scholar 

  • K.B. Dysthe (2001). Refraction of gravity waves by weak current gradients. J. Fluid Mech. Vol. 442, 157–59.

    Article  MATH  MathSciNet  Google Scholar 

  • K.B. Dysthe and K. Trulsen (1999). Note on breather type solutions of the NLS as a model for freak waves. Phys. Scripta Vol. T82, 48–52.

    Article  Google Scholar 

  • K.B. Dysthe, K. Trulsen, H.E. Krogstad and H. Socquet-Juglard (2003). Evolution of a narrow-band spectrum of random surface gravity waves. J. Fluid Mech. Vol. 478, 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  • J.P. Giovanangeh, C. Kharif and E. Pehnovsky (2004a). An experimental study on the effect of wind on the generation of freak waves, In Proc. of 1st European Geophysical Union 6, Natural Hazards, Abstract number EGU-A-07436, Nice 2004.

    Google Scholar 

  • J.P. Giovanangeh, C. Kharif and E. Pelinovsky (2004b). Experimental study of the wind effect on the focusing of transient wave groups. Proc. Rogue waves 2004, Brest.

    Google Scholar 

  • D.M. Graham (2000) NOAA vessel swamped by rogue wave. Oceanspace 284.

    Google Scholar 

  • J. Grue and E. Palm (1985). Wave radiation and wave diffraction from a submerged body in a uniform current. J. Fluid Mech. Vol. 151, 257–78.

    Article  Google Scholar 

  • J. Grue and E. Palm (1986). The influence of a uniform current on slowly varying forces and displacements. Appl. Ocean Res. Vol. 8(4), 232–39.

    Article  Google Scholar 

  • S. Haver and O.J. Andersen (2000). Freak waves: Rare realizations of a typical population or typical realizations of a rare population? Proc. of 10th IS OPE Conference, 123–30.

    Google Scholar 

  • K.L. Henderson, D.H. Peregrine and J.W. Dold (1999). Unsteady water wave modulations: Fully nonlinear solutions and comparison with the nonlinear Schrödinger equation. Wave Motion Vol. 29, 341–61.

    Article  MATH  MathSciNet  Google Scholar 

  • B.M. Herbst and M.J. Ablowitz (1989). Numerically induced chaos in the nonhnear Schrödinger equation. Phys. Rev. Lett. Vol. 62(18), 2065–8.

    Article  MathSciNet  Google Scholar 

  • A.L. Islas and C.M. Schober (2005). Predicting rogue waves in random oceanic sea states. Phys. Fluids Vol. 17, 031701-1-4.

    Google Scholar 

  • P.A.E.M. Janssen (2003). Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. Vol. 33, 863–84.

    Article  MathSciNet  Google Scholar 

  • H. Jeffreys (1925). On the formation of wave by wind. Proc. Roy. Soc. A Vol. 107, 189–206.

    Article  Google Scholar 

  • T.B. Johannessen and C. Swan (1997). Nonlinear transient water waves-Pt. 1. A numerical method of computation with comparisons to 2D laboratory data. Appl. Ocean Res. Vol. 19, 293–308.

    Article  Google Scholar 

  • T.B. Johannessen and C. Swan (2001). A laboratory study of the focusing of transient and directionally spread surface water waves. Proc. Roy. Soc. Lond. A Vol. 457, 971–1006.

    MATH  Google Scholar 

  • T.B. Johannessen and C. Swan (2003). On the nonlinear dynamics of wave groups produced by the focusing of surface-water waves. Proc. Roy. Soc. Lond. A Vol. 459, 1021–52.

    MATH  MathSciNet  Google Scholar 

  • C. Kharif (1990). Some aspects of the kinematics of short waves over longer gravity waves on deep water. In Water Wave kinematics. Ed. by A. Torum and O.T. Gudmestad, Kluwer Academic, Dordrecht, 265–79.

    Google Scholar 

  • C. Kharif, E. Pelinovsky and T. Talipova (2000). Formation de vagues géantes en eau pen profonde. C. R. Acad. Sci. Paris, Ser. lib Vol. 328(11), 801–7.

    MATH  Google Scholar 

  • C. Kharif, E. Pelinovsky, T. Talipova and A. Slunyaev (2001). Focusing of nonlinear wave groups in deep water. J.E.T.P. Lett. Vol. 73(4), 170–5.

    Article  Google Scholar 

  • C. Kharif and E. Pelinovsky (2003). Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B/Fluids Vol. 22, 603–34.

    Article  MATH  MathSciNet  Google Scholar 

  • C. Kharif, J.P. Giovanangeh, J. Touboul and E. Pelinovsky (2005). Influence of the Jeffreys’ sheltering mechanism on rogue waves. Workshop on Rogue Waves, Dec. 2005, Edinburgh.

    Google Scholar 

  • E. Kit, L. Shemer, E. Pelinovsky, T. Talipova, O. Eitan and H. Jiao (2000). Nonlinear wave group evolution in shallow water. J. Waterways Port. Coast. Ocean Engng. Vol. 126(5), 221–8.

    Article  Google Scholar 

  • E. Kit and L. Shemer (2002). Spatial versions of the Zakharov and Dysthe equations for deep-water gravity waves. J. Fluid Mech. Vol. 450, 201–5.

    Article  MATH  MathSciNet  Google Scholar 

  • V.P. Krasitskii (1994). On reduced equations in the Hamilitonian theory of weakly nonlinear surface waves. J. Fluid Mech. Vol. 272, 1–30.

    Article  MATH  MathSciNet  Google Scholar 

  • I.V. Lavrenov (1998a). Mathematical modeling of the wind waves in spatially inhomogeneous Ocean. Hydrometeozdat, St Petersburg.

    Google Scholar 

  • I.V. Lavrenov (1998b). The wave energy concentration at the Agulhas current off South Africa. Natural Hazards Vol. 17, 117–27.

    Article  Google Scholar 

  • G. Lawton (2001). Monsters of the deep (The perfect wave). New Scientist Vol. 170(2297), 28–32.

    Google Scholar 

  • M.J. Lighthill (1965). Contributions to the theory of waves in nonlinear dispersive systems. J. Inst. Math. Appl. 1, 269–306.

    Article  MathSciNet  Google Scholar 

  • E. Lo and C.C. Mei (1985). A numerical study of water-wave modulation based on a high-order nonlinear Schrödinger equation. J. Fluid Mech. Vol. 150, 395–416.

    Article  MATH  Google Scholar 

  • M.S. Longuet-Higgins and R.W. Stewart (1961). The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. Vol. 10, 529–49.

    Article  MATH  MathSciNet  Google Scholar 

  • M.S. Longuet-Higgins and R.W. Stewart (1964). Radiation stress in water waves; a physical discussion, with applications. Deep Sea Res. Vol. 11, 529–62.

    Google Scholar 

  • M.S. Longuet-Higgins (1986). Eulerian and Lagrangian aspects of surface waves. J. Fluid Mech. Vol. 173, 683–707.

    Article  MathSciNet  Google Scholar 

  • J.K. Mallory (1974). Abnormal waves in the south-east coast of South Africa. Int. Hydrog. Rev. Vol. 51, 99–129.

    Google Scholar 

  • S.R. Massel (1996). Ocean surface waves: Their physics and prediction. Word Scientific, Singapore.

    Google Scholar 

  • J.W. Miles (1977). Resonantly interacting solitary waves. J. Fluid Mech. Vol. 79, 171–9.

    Article  MATH  MathSciNet  Google Scholar 

  • N. Mori and Y. Yasuda (2001). Effects of high-order nonlinear interactions on unidirectional wave trains. Rogues Waves, Brest 2000. Ed. by M. Olagnon and G.A. Athangissoulis, 229–44.

    Google Scholar 

  • N. Mori, P.C. Liu and Y. Yasuda (2002). Analysis of freak wave measurements in the sea of Japan. Ocean Engrg. Vol. 29, 1399–414.

    Article  Google Scholar 

  • K. Onkuma and M. Wadati (1983). The Kadomstev-Petviashvili equation, the trace method and the soliton resonance. J. Phys. Soc. Japan Vol. 52, 749–60.

    Article  Google Scholar 

  • M. Onorato, A.R. Osborne, M. Serio and T. Damiani (2001). Occurrence of freak waves from envelope equations in random ocean wave simulations. Rogues Waves 2000 edited by M. Olagnon and G.A. Athanassoulis (Brest, France), 181–91.

    Google Scholar 

  • M. Onorato, A.R. Osborne, M. Serio and S. Bertone (2001). Freak waves in random oceanic sea states. Phys. Rev. Lett. Vol. 86(25), 5831–4.

    Article  Google Scholar 

  • M. Onorato, A.R. Osborne and M. Serio (2002). Extreme wave events in directional, random oceanic sea states. Phys. Fluids Vol. 14(4), L25–8.

    Article  MathSciNet  Google Scholar 

  • M. Onorato, D. Ambrosi, A.R. Osborne and M. Serio (2003). Interaction of two quasimonochromatic waves in shallow water. Phys. Fluids Vol. 15, 3871.

    Article  MathSciNet  Google Scholar 

  • A.R. Osborne, M. Onorato and M. Serio (2000). The nonhnear dynamics of rogue waves and holes in deep-water gravity wave train. Phys. Lett. A Vol. 275, 386–93.

    Article  MATH  MathSciNet  Google Scholar 

  • E. Pelinovsky (1996). Hydrodynamics of tsunami waves. Applied Physics Institute Press, Niznhy Novgorod, 1996.

    Google Scholar 

  • E. Pelinovsky, T. Talipova and C. Kharif (2000). Nonlinear dispersive mechanism of the freak wave formation in shallow water. Physica D Vol. 147(1–2), 83–94.

    Article  MATH  Google Scholar 

  • D.H. Peregrine (1983). Wave jumps and caustics in the propagation of finite-amplitude water waves. J. Fluid Mech. Vol. 136, 435–52.

    Article  MATH  MathSciNet  Google Scholar 

  • D.H. Peregrine and R. Smith (1979). Nonlinear effects upon waves near caustics. Philos. Trans. Roy. Soc. London A Vol. 29210, 341–70.

    Article  MATH  Google Scholar 

  • P. Peterson, T. Soomere, J. Engelbrecht and E. van Groesen (2003). Soliton interaction as a possible model for extreme waves. Nonlinear Processes in Geophysics Vol. 10, 503–10.

    Google Scholar 

  • S.E. Sand, N.E. Hansen, P. Klinting, O.T. Gudmestad and M.J. Steindorff (1990). Freak wave kinematics. In Water Wave kinematics. Ed. by A. Torum and O.T. Gudmestad, Kluwer Academic, Dordrecht, 535–49.

    Google Scholar 

  • R.N. Sanderson (1974). The unusual waves off south east Africa. Marine Observer Vol. 44,180–3.

    Google Scholar 

  • J. Satsuma (1976). N-soliton solution of the two-dimensional Korteweg-de Vries equation. J. Phys. Soc. Japan Vol. 40, 286–90.

    Article  MathSciNet  Google Scholar 

  • J. Satsuma and N. Yajima (1974). Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media. Suppl. Prog. Theor. Phys. Vol. 55, 284–306.

    MathSciNet  Google Scholar 

  • L. Shemer, E. Kit, H. Jiao, O. Eitan (1998). Experiments on nonhnear wave groups in intermediate water depth. J. Waterways Port. Coast. Ocean Engng. Vol. 124, 320–7.

    Article  Google Scholar 

  • A. Slunyaev, C. Kharif, E. Pelinovsky and T. Talipova (2002). Nonlinear wave focusing on water of finite depth. Physica D Vol. 173(1–2), 77–96.

    Article  MATH  MathSciNet  Google Scholar 

  • R. Smith (1976). Giant waves. J. Fluid Mech. Vol. 77, 417–31.

    Article  MATH  MathSciNet  Google Scholar 

  • H. Socquet-Juglard, K.B. Dysthe, K. Trulsen and H.E. Krogstad (2005). Probability distributions of surface gravity waves during spectral changes, J. Fluid Mech. Vol. 542, 195–216.

    Article  MATH  MathSciNet  Google Scholar 

  • T. Soomere and J. Engelbrecht (2005). Extreme elevations and slopes of interacting solitons in shallow water. Wave Motion Vol. 41, 179–92.

    Article  MathSciNet  Google Scholar 

  • C.T. Stansberg (2001). Random waves in the laboratory-what is expected for the extremes?. In M. Olagon and G.A. Athanassoulis (Eds.), Rogue Waves 2000 (Brest, France), 289–301.

    Google Scholar 

  • M. Stassnie and L. Shemer (1984). On modifications of the Zakharov equation for surface gravity waves. J. Fluid Mech. Vol. 143, 47–67.

    Article  MathSciNet  Google Scholar 

  • H. Sturm (1974). Giant waves. Ocean Vol. 2(3), 98–101.

    MathSciNet  Google Scholar 

  • 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. y

    Google Scholar 

  • M.A. Tayfun (1980). Narrow-band nonlinear sea waves. J. Geophys. Res. Vol. 85, 1548–52.

    Google Scholar 

  • M.A. Tayfun, R.A. Dalrymple and C.Y. Yang (1976). Random wave-current interactions in water of varying depth Ocean Engng. 3, 403–20.

    Google Scholar 

  • K. Trulsen (2001). Simulating the spatial evolution of a measured time series of a freak wave. Rogues Waves, Brest 2000. Ed. by M. Olagnon and G.A. Athanassoulis, 265–74.

    Google Scholar 

  • K. Trulsen and K.B. Dysthe (1996). A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion Vol. 24, 281–9.

    Article  MATH  MathSciNet  Google Scholar 

  • K. Trulsen and K.B. Dysthe (1997). Freak waves-a three-dimensional wave simulation. Proc. 21st Symposium on Naval Hydrodynamics, 550–6.

    Google Scholar 

  • K. Trulsen, I. Khakhandler, K.B. Dysthe and M.G. Velarde (2000). On weakly nonlinear modulation of waves on deep water. Phys. Fluids Vol. 12, 2432–7.

    Article  MathSciNet  Google Scholar 

  • B.J. West, K.A. Brueckner and R.S. Janda. A method of studying nonlinear random field of surface gravity waves by direct numerical simulation. J. Geophys. Res. Vol. 92,C 11, 11803–24.

    Google Scholar 

  • B.S. White and B. Fornberg (1998). On the chance of freak waves at the sea. J. Fluid Mech. Vol. 255, 113–38.

    Article  MathSciNet  Google Scholar 

  • G.B. Whitham (1965). A general approach to linear and non-linear dispersive waves using a Lagrangian. J. Fluid Mech. Vol. 22, 273–83.

    Article  MathSciNet  Google Scholar 

  • G.B. Whitham (1967). Nonlinear dispersion of water waves J. Fluid Mech. Vol. 27, 399–412.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Willebrand (1975). Energy transport in a nonlinear and inhomogeneous random gravity wave field. J. Fluid Mech. Vol. 70, 113–26.

    Article  MATH  Google Scholar 

  • C.H. Wu and A. Yao (2004). Laboratory measurements of limiting freak waves on currents. J. Geophys. Res. Vol. 109,C12002, 1–18.

    Google Scholar 

  • V.E. Zakharov (1966). Instability of waves in nonlinear dispersive media. J.E.T.P. Vol. 51, 1107–14.

    Google Scholar 

  • V.E. Zakharov (1968). Stability of periodic waves of finite amplitude on the surface of deep water. J. Appl. Mech. Tech. Phys. Vol. 9, 190–94.

    Article  Google Scholar 

  • V.E. Zakharov, A.I. Dyachenko and O. Vasilyev (2002). New method for numerical simulation of nonstationary potential flow of incompressible fluid with a free surface. Eur. J. Mech.B/Fluids Vol. 21, 283–91.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Recherche sur les phénomènes Hors Equilibre, Marseille, France

    Christian Kharif

  2. Institute of Applied Physics, Niznhy Novgorod, Russia

    Efim Pelinovsky

Authors
  1. Christian Kharif
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Efim Pelinovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Oslo, Norway

    John Grue  & Karsten Trulsen  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2006 CISM, Udine

About this chapter

Cite this chapter

Kharif, C., Pelinovsky, E. (2006). Freak Waves Phenomenon: Physical Mechanisms and Modelling. In: Grue, J., Trulsen, K. (eds) Waves in Geophysical Fluids. CISM International Centre for Mechanical Sciences, vol 489. Springer, Vienna. https://doi.org/10.1007/978-3-211-69356-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-211-69356-8_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-37460-3

  • Online ISBN: 978-3-211-69356-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation