Advertisement

JETP Letters

, Volume 97, Issue 4, pp 188–193 | Cite as

On the modulation instability of surface waves on a large-scale shear flow

  • V. P. Ruban
Plasma, Hydro- and Gas Dynamics

Abstract

The problem of the modulation instability of a weakly nonlinear quasi-monochromatic wave on the surface of deep water in the presence of a steady-state collinear large-scale inhomogeneous flow (e.g., of a jet type) has been considered. In a certain range of (obtuse) angles of incidence of the wave with respect to the flow direction, the steepness of the refracted wave increases considerably, which contributes to the enhancement of nonlinear effects, including the formation of so-called rogue waves. The corresponding nonlinear Schrödinger equation with variable coefficients suitable for the analysis of the modulation instability has been derived.

Keywords

Surface Wave JETP Letter Modulation Instability Rogue Wave Peregrine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Kharif and E. Pelinovsky, Eur. J. Mech. B: Fluids 22, 603 (2003).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    E. Pelinovsky and C. Kharif, Eur. J. Mech. B: Fluids 25, 535 (2006).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    N. Akhmediev and E. Pelinovsky, Eur. Phys. J.: Spec. Top. 185, 1 (2010).CrossRefGoogle Scholar
  4. 4.
  5. 5.
    V. E. Zakharov, J. Appl. Mech. Tech. Phys. 9, 190 (1968).ADSCrossRefGoogle Scholar
  6. 6.
    T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).ADSzbMATHCrossRefGoogle Scholar
  7. 7.
    V. E. Zakharov, A. I. Dyachenko, and O. A. Vasilyev, Eur. J. Mech. B: Fluids 21, 283 (2002).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    A. I. Dyachenko and V. E. Zakharov, JETP Lett. 81, 255 (2005).ADSCrossRefGoogle Scholar
  9. 9.
    V. E. Zakharov, A. I. Dyachenko, and O. A. Prokofiev, Eur. J. Mech. B: Fluids 25, 677 (2006).MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10.
    V. P. Ruban, Phys. Rev. Lett. 99, 044502 (2007).ADSCrossRefGoogle Scholar
  11. 11.
    N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, Theor. Math. Phys. 72, 809 (1987).MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).ADSzbMATHCrossRefGoogle Scholar
  13. 13.
    M. Erkintalo, K. Hammani, B. Kibler, et al., Phys. Rev. Lett. 107, 253901 (2011).ADSCrossRefGoogle Scholar
  14. 14.
    D. H. Peregrine, Adv. Appl. Mech. 16, 9 (1976).zbMATHCrossRefGoogle Scholar
  15. 15.
    B. S. White and B. Fornberg, J. Fluid Mech. 355, 113 (1998).MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    I. V. Lavrenov and A. V. Porubov, Eur. J. Mech. B: Fluids 25, 574 (2006).MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 17.
    T. T. Janssen and T. H. C. Herbers, J. Phys. Oceanogr. 39, 1948 (2009).ADSCrossRefGoogle Scholar
  18. 18.
    A. Toffoli, L. Cavaleri, A. V. Babanin, et al., Nature Hazards Earth Syst. Sci. 11, 895 (2011).ADSCrossRefGoogle Scholar
  19. 19.
    F. P. Bretherton and C. J. R. Garrett, Proc. R. Soc. London A 302, 529 (1968).ADSCrossRefGoogle Scholar
  20. 20.
    F.-M. Turpin, C. Benmoussa, and C. C. Mei, J. Fluid Mech. 132, 1 (1983).MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 21.
    M. Gerber, J. Fluid Mech. 176, 311 (1987).ADSzbMATHCrossRefGoogle Scholar
  22. 22.
    J. R. Stocker and D. H. Peregrine, J. Fluid Mech. 399, 335 (1999).MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. 23.
    K. B. Hjelmervik and K. Trulsen, J. Fluid Mech. 637, 267 (2009).MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. 24.
    V. P. Ruban, JETP Lett. 95, 486 (2012).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations