Physical Oceanography

, Volume 7, Issue 3, pp 159–166 | Cite as

Spectral evolution of surface waves in a deep sea due to the effect of wave-wave interactions

  • V. A. Kalmykov
Thermohydrodynamics of the Ocean
  • 54 Downloads

Abstract

The wave-wave kinetic equation for surface gravity waves in a deep sea is solved numerically, using the Runge-Kutta technique. Spectral evolution of waves resulted only from their being non-linear, with no wave generation and decaying taking place. To perform computations the JONSWAP-type frequency spectra and a variety of angular wave spectra were used. The angular spectrum of waves turned out to be stable. The frequency spectrum differed from the JONSWAP spectrum in that it had a high-frequency part, which was not similar to the Phillips spectrum. The form of the high-frequency spectral slope was determined as a result of spectral evolution and proved to have the form of the ‘−6’ law.

Keywords

Gravity Wave Wave Spectrum Wind Wave Angular Spectrum Spectral Maximum 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fox, M. J. On the non-linear transfer of the energy in the peak of a gravity wave spectrum.Proc-R. Soc., Ser. A (1976)348, 467–483.Google Scholar
  2. 2.
    Hasselmann, K. On the non-linear energy transfer in a gravity wave spectrum. Part 1. General theory.J. Fluid Mech. (1961)12, 481–500.CrossRefGoogle Scholar
  3. 3.
    Hasselmann, K. On the non-linear energy transfer in a gravity wave spectrum. Part 2. Conservation theorems, wave-particle analogy: irreversibility.J. Fluid Mech. (1963)15, 273–281.CrossRefGoogle Scholar
  4. 4.
    Hasselmann, K. On the non-linear energy transfer in a gravity wave spectrum. Part 3. Evaluation of the energy flux and swell-sea interaction for a Neumann spectrum.J. Fluid Mech. (1963)15, 385–398.CrossRefGoogle Scholar
  5. 5.
    Longuett-Higgins, M. S. On the non-linear transfer of energy in the peak of a gravity wave spectrum: a simplified model.Proc-R. Soc., Ser. A (1976)347, 311–328.Google Scholar
  6. 6.
    Masuda, A. Non-linear energy transfer between wind waves.J. Phys. Oceanogr. (1980)10, 2082–2093.CrossRefGoogle Scholar
  7. 7.
    Herterich, K. and Hasselmann, K. A similarity relation of the non-linear energy transfer in a finite-depth gravity wave spectrum.J. Fluid Mech. (1980)97, 215–224.CrossRefGoogle Scholar
  8. 8.
    Hasselmann, S. and Hasselmann, K. Computation and parameterizations of the non-linear energy transfer in a gravity wave spectrum. Part 1. A new method for efficient computations of the exact non-linear transfer integral.J. Phys. Oceanogr. (1985)15, 1369–1377.CrossRefGoogle Scholar
  9. 9.
    The SWAMP Group.Ocean Wave Modelling. New York: Plenum Press (1985).Google Scholar
  10. 10.
    Polnikov, V. G. Numerical solution of the kinetic equation for surface gravity waves.Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana (1990)26, 168–176.Google Scholar
  11. 11.
    Resio, D. and Perrie, W. A numerical study of non-linear energy fluxes to wave-wave interactions. Part 1. Methodology and basic results.J. Fluid Mech. (1991)223, 603–629.CrossRefGoogle Scholar
  12. 12.
    Lavrenov, I. V. Weakly non-linear wave spectrum evolution in shallow water.Jzv. Akad. Nauk SSSR, Fiz. Atmos. Okeana (1991)27, 1372–1378.Google Scholar
  13. 13.
    Kalmykov, V. A. Numerical computation of the non-linear energy transfer in a surface wind wave spectrum by five-wave resonance interactions.Dokl. Akad. Nauk Ukr. (1993)8, 101–104.Google Scholar
  14. 14.
    Zakharov, V. E. and Smilga, A. V. About quasi-one-dimensional spectra in the weak turbulence.ZHETF (1981)81, 1318–1326.Google Scholar
  15. 15.
    Zaslavsky, M. M. About the approximation of a kinetic equation for a wind wave spectrum.Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana (1989)25, 402–410.Google Scholar
  16. 16.
    Iroshmikov, R. S. The possible development of a non-isotropic wind wave spectrum by weakly non-linear interactions.Dokl. Akad. Nauk SSSR (1985)280, 1321–1325.Google Scholar
  17. 17.
    Tsimring, L. Sh. The evolution of a narrow angular wind wave spectrum as a result of non-linear wind-wave interaction.Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana (1989)25, 411–420.Google Scholar
  18. 18.
    Zakharov, V. E. and Shrira, V. I. About the formation of an angular spectrum of wind waves.ZHETF (1990)98, 1941–1958.Google Scholar
  19. 19.
    Krasitsky, V. P. The five-wave kinetic equation for surface gravity waves.Phys. Oceanogr. (1994)5, 413–421.CrossRefGoogle Scholar
  20. 20.
    Phillips, O. M.Dynamics of the Upper Ocean Layer. Leningrad: Gidrometeoizdat (1980).Google Scholar
  21. 21.
    Efimov, V. V. and Polnikov, V. G.Numerical Modelling of Wind Waves. Kiev: Naukova Dumka (1991).Google Scholar

Copyright information

© VSP 1996

Authors and Affiliations

  • V. A. Kalmykov

There are no affiliations available

Personalised recommendations