Propagation and interaction of non-linear surface and internal waves in a two-layer fluid


This paper focuses on the study of linear and non-linear surface and internal waves, in a complete setting, using a two-layer model of a stratified fluid. The respective Korteweg-de Vries evolutionary equations have been obtained, analysed, and compared with the ‘rigid lid’ model data. Boussinesq-type equations have been derived for the interacting modes pertaining to one type and to different types. It is shown that in addition to the known mechanisms of interaction between internal and surface waves, interaction between long non-linear baroclinic modes and barotropic modes, propagating in the same direction, is likely in such a system.

This is a preview of subscription content, access via your institution.


  1. 1.

    Osborne, A. and Burch, T. Internal solitons in the Andaman Sea.Science (1980)208, 451–460.

    Google Scholar 

  2. 2.

    Blatov, A. S. and Ivanov, V. A.Hydrology and Hydrodynamics of the Black Sea Shelf Zone, Kiev: Naukova Dumka (1992).

    Google Scholar 

  3. 3.

    Vlasenko, V. I. Modelling of the generation of non-linear baroclinic tides in the northwestern tropical Atlantic.Izv. Ros. Akad. Nauk, Fiz. Atmos. Okeana (1992)28, 310–318.

    Google Scholar 

  4. 4.

    Le Blond, P. and Mysek, L.Oceanic Waves, Moscow. Mir (1981).

    Google Scholar 

  5. 5.

    Pelinovsky, E. N.Non-linear Dynamics of Tsunami Waves. Gorky: IPF Akad. Nauk SSSR (1982).

    Google Scholar 

  6. 6.

    Cherkesov, L. V., Ivanov, V. A. and Khartiev, S. M.Introduction to Hydrodynamics and Wave Theory. St. Peterburg: Gidrometeoizdat (1992).

    Google Scholar 

  7. 7.

    Miropol'sky, Yu. Z.Dynamics of Internal Gravity Waves in the Ocean. Leningrad: Gidrometeoizdat (1981).

    Google Scholar 

  8. 8.

    Stepanyants, Yu. A., Sturova, I. V. and Teodorovich, E. V. Linear theory for the generation of internal and surface waves.Itogi Nauki Tekh., Ser. Mekh. Zhid. Gaza (1987)21, 93–179.

    Google Scholar 

  9. 9.

    Lee, C. Y. and Beardsley, C. The generation of long non-linear internal waves in a weakly-stratified shear flow.J. Geophys. Res. (1974)79, 453–458.

    Google Scholar 

  10. 10.

    Witham, J.Linear and Non-linear Waves. Moscow: Mir (1977).

    Google Scholar 

  11. 11.

    Phillips, O. M. On the interaction between internal and surface waves.Izv. Akad. Nauk, Fiz. Atmos. Okeana (1973)9, 954–961.

    Google Scholar 

  12. 12.

    Gardett, A. and Hughes, B. On the interaction of surface and internal waves.J. Fluid Mech. (1972)52, 179–191.

    Google Scholar 

  13. 13.

    Volyak, K. I. and Semenov, A. Yu. Interaction between surface and internal waves.Tr. IOF Akad. Nauk SSSR (1983)18, 3–32.

    Google Scholar 

  14. 14.

    Ma, Y. C. and Redekopp, L. G. Some solutions pertaining to the resonant interaction of long and short waves.Phys. Fluids (1979)10, 1872–1876.

    Google Scholar 

  15. 15.

    Gear, J. A. and Grimshaw, R. Weak and strong interactions between internal solitary waves.Stud. Appl. Math. (1983)10, 235–258.

    Google Scholar 

  16. 16.

    Gear, J. A. Strong interactions between solitary waves belonging to different wave modes.Stud. Appl. Math. (1985)72, 95–124.

    Google Scholar 

  17. 17.

    Liu, A. K., Pereira, N. R. and Ko, D. R. Weakly interacting internal solitary waves in neighbouring pycnoclines.J. Fluid. Mech. (1982)122, 187–194.

    Google Scholar 

  18. 18.

    Corpell, A. and Banergy, P. P. Heuristic approach to non-linear wave equations with dispersion and to soliton-type solutions.IEEE (1984)72, 6–30.

    Google Scholar 

  19. 19.

    Korsunsky, S. V. Non-linear waves in current-conducting disperging media. Doctoral thesis, summary. Riga (1991).

  20. 20.

    Stepanyants, Yu. A. On the theory of internal bores in shallow basins.Morsk. Gidrofiz. Zh. (1990)2, 19–23.

    Google Scholar 

  21. 21.

    Ablowitz, M. and Sigur, H.Solitons and the Method of Inverse Problem. Moscow: Mir (1987).

    Google Scholar 

Download references


Additional information

Translated by Vladimir A. Puchkin.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Korsunsky, S.V. Propagation and interaction of non-linear surface and internal waves in a two-layer fluid. Phys. Oceanogr. 6, 331–341 (1995).

Download citation


  • Climate Change
  • Evolutionary Equation
  • Surface Wave
  • Model Data
  • Environmental Physic