Advertisement

JETP Letters

, Volume 99, Issue 12, pp 685–688 | Cite as

On simplified simulation of nonlinear waves on flows

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

Abstract

Several new mathematical models yielding qualitatively correct description of the dynamics of nonlinear sea waves on inhomogeneous flows have been proposed. These models are characterized by a more or less approximated form of the four-wave interaction coefficient as compared to the standard Zakharov equation. The new systems are quite efficient for numerical calculations, although poor in taking into account the details of nonlinearity. The propagation of waves on a jet counterflow, which serves as a waveguide and prevents nonlinear defocusing of waves in the transverse direction, thus creating favorable conditions for the development of modulation instability and the formation of rogue waves, has been simulated as an example.

Keywords

JETP Letter Nonlinear Wave Modulation Instability Rogue Wave Diagonal Part 
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).CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    K. Dysthe, H. E. Krogstad, and P. Müller, Ann. Rev. Fluid Mech. 40, 287 (2008).CrossRefADSGoogle Scholar
  3. 3.
    M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    V. E. Zakharov, J. Appl. Mech. Tech. Phys. 9, 190 (1968).CrossRefADSGoogle Scholar
  5. 5.
    T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).CrossRefzbMATHADSGoogle Scholar
  6. 6.
    V. E. Zakharov, A. I. Dyachenko, and O. A. Vasilyev, Eur. J. Mech. B: Fluids 21, 283 (2002).CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    A. I. Dyachenko and V. E. Zakharov, JETP Lett. 81, 255 (2005).CrossRefADSGoogle Scholar
  8. 8.
    V. E. Zakharov, A. I. Dyachenko, and O. A. Prokofiev, Eur. J. Mech. B: Fluids 25, 677 (2006).CrossRefzbMATHMathSciNetADSGoogle Scholar
  9. 9.
    V. P. Ruban, Phys. Rev. Lett. 99, 044502 (2007).CrossRefADSGoogle Scholar
  10. 10.
    V. P. Ruban, JETP Lett. 94, 177 (2011).CrossRefADSGoogle Scholar
  11. 11.
    D. H. Peregrine, Adv. Appl. Mech. 16, 9 (1976).CrossRefzbMATHGoogle Scholar
  12. 12.
    B. S. White and B. Fornberg, J. Fluid Mech. 355, 113 (1998).CrossRefzbMATHMathSciNetADSGoogle Scholar
  13. 13.
    I. V. Lavrenov and A. V. Porubov, Eur. J. Mech. B: Fluids 25, 574 (2006).CrossRefzbMATHMathSciNetADSGoogle Scholar
  14. 14.
    V. P. Ruban, JETP Lett. 95, 486 (2012).CrossRefADSGoogle Scholar
  15. 15.
    V. P. Ruban, JETP Lett. 97, 188 (2013).CrossRefADSGoogle Scholar
  16. 16.
    V. I. Shrira and A. V. Slunyaev, J. Fluid Mech. 738, 65 (2014).CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    V. I. Shrira and A. V. Slunyaev, Phys. Rev. E 89, 041002(R) (2014).CrossRefADSGoogle Scholar
  18. 18.
    F. P. Bretherton and C. J. R. Garrett, Proc. R. Soc. London A 302, 529 (1968).CrossRefADSGoogle Scholar
  19. 19.
    V. E. Zakharov, Eur. J. Mech. B: Fluids 18, 327 (1999).CrossRefzbMATHMathSciNetADSGoogle Scholar
  20. 20.
    A. I. Dyachenko and V. E. Zakharov, JETP Lett. 93, 701 (2011).CrossRefADSGoogle Scholar
  21. 21.
    A. J. Majda, D. W. McLaughlin, and E. G. Tabak, J. Nonlin. Sci. 6, 9 (1997).CrossRefMathSciNetGoogle Scholar
  22. 22.
    A. Pushkarev and V. E. Zakharov, Physica D 248, 55 (2013).CrossRefzbMATHMathSciNetADSGoogle Scholar
  23. 23.
    V. P. Ruban, Phys. Rev. E 80, 065302(R) (2009).CrossRefADSGoogle Scholar
  24. 24.

Copyright information

© Pleiades Publishing, Inc. 2014

Authors and Affiliations

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

Personalised recommendations