Skip to main content
Log in

Theory of two-dimensional nonlinear waves in liquid covered by ice

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The aim is to develop a method of Hamiltonian formalism for the waves in the liquid beneath an ice sheet and on that basis to construct a systematic nonlinear theory. Attention is concentrated on the investigation of the essentially two-dimensional effects whose properties depend to a large extent on the stresses in the ice.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. A. E. Bukatov, “The effect of a longitudinally compressed elastic plate on the unsteady wave motion of a homogeneous liquid,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 68 (1980).

    Google Scholar 

  2. A. E. Bukatov and L. V. Cherkesov, “Effect of ice cover on the development of internal waves due to periodic disturbances,” in: Marine Hydrophysical Research, No. 4 (75) [in Russian], Sevastopol' (1976), p. 5.

    Google Scholar 

  3. D. E. Kheisin, Ice Sheet Dynamics [in Russian], Gidrometeoizdat, Leningrad (1967).

    Google Scholar 

  4. A. V. Marchenko and N. R. Sibgatullin, “Resonant wave interaction in a heavy liquid beneath an elastic plate,” Vestn. Mosk Univ. Mat. Mekh., Ser. 1, No. 4, 94 (1986).

    Google Scholar 

  5. A. V. Marchenko and N. R. Sibgatullin, “Wave packet evolution with three-wave interaction in a heavy liquid beneath an ice sheet,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 57 (1987).

    Google Scholar 

  6. A. V. Marchenko, “Resonant wave excitation in a heavy liquid beneath a viscoelastic plate,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3 (1991).

  7. A. T. Il'ichev and A. V. Marchenko, “Propagation of long nonlinear waves in a heavy liquid covered with ice,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 88 (1989).

    Google Scholar 

  8. A. V. Marchenko, “Long waves in a shallow liquid covered with ice,” Prikl. Mat. Mekh.,52, 230 (1988).

    Google Scholar 

  9. V. V. Bogorodskii and V. P. Gavrilo, Ice. Physical Properties. Modern Methods of Glaciology [in Russian], Gidrometeoizdat, Leningrad (1980).

    Google Scholar 

  10. V. E. Zakharov, “Stability of periodic finite-amplitude waves on the surface of a deep liquid,” Zh.Prikl. Mekh. Tekh. Fiz., No. 2, 86 (1968).

    Google Scholar 

  11. V. E. Zakharov, “Hamiltonian formalism for waves in nonlinear media with dispersion,” Izv. Vyssh. Uchebn. Zaved. Radiofiz.,17, 431 (1974).

    Google Scholar 

  12. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Maths., Vol. 4), Philadelphia (1981).

  13. V. E. Zakharov and V. S. Synakh, “Nature of the singularity in self-focusing,” Zh. Eksp. Teor. Fiz.,68, 940 (1975).

    Google Scholar 

  14. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett.15, 1005 (1965).

    Google Scholar 

  15. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave packets in linear and nonlinear media (method of moments),” Izv. Vyssh. Uchebn. Zaved. Radiofiz.,14, 1353 (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 125–133, July–August, 1991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marchenko, A.V., Shrira, V.I. Theory of two-dimensional nonlinear waves in liquid covered by ice. Fluid Dyn 26, 580–587 (1991). https://doi.org/10.1007/BF01050321

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01050321

Keywords

Navigation