Skip to main content
SpringerLink
Log in

Steepness and spectrum of a nonlinearly deformed wave on shallow waters

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

The process of nonlinear deformation of a surface wave on shallow waters is investigated. The main attention is given to the relationship between the wave Fourier spectrum and the steepness of wave front slope. It is shown that an unambiguous relationship couples these quantities in the case of an initially sinusoidal wave, which allows estimation of the spectral composition of the wave field from the observed wave steepness.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Stoker, Water waves (New York, 1957; Inostrannaya Literatura, Moscow, 1959).

    Google Scholar 

  2. N. E. Vol’tsinger, K. A. Klevannyi, and E. N. Pelinovsky, Longwave Dynamics in the Coastal Zone (Gidrometeoizdat, Leningrad, 1989) [in Russian].

    Google Scholar 

  3. A. S. Arsen’ev and N. K. Shelkovnikov, Dynamics of Sea-Water Long Waves (Mosk. Gos. Univ., Moscow, 1991) [in Russian].

    Google Scholar 

  4. E. N. Pelinovsky, Nonlinear Dynamics of Tsunami Waves (IPF Akad. Nauk SSSR, Gor’ki, 1982) [in Russian].

    Google Scholar 

  5. E. N. Pelinovsky and E. N. Troshina, “Propagation of Long Waves in Straits,” Morsk. Gidrofiz. Issled., No. 1, 47–52 (1993).

  6. Y. Tsuji, T. Yanuma, I. Murata, and C. Fujiwara, “Tsunami Ascending in Rivers As an Undular Bore,” Natural Hazards Pelinovsky E., Talipova T., Kozelkov A., 4, 257–266 (1991).

    Article  Google Scholar 

  7. Y. H. Wu and J.-W. Tian, “Mathematical Analysis of Long-Wave Breaking on Open Channels with Bottom Friction,” Ocean Eng. 26, 187–201 (2000).

    Article  Google Scholar 

  8. J.-G. Caputo and Y. A. Stepanyants, “Bore Formation, Evolution and Disintegration into Solitons in Shallow Inhomogeneous Channels,” Nonlinear Processes Geophys. 10, 407–424 (2003).

    Google Scholar 

  9. N. Zahibo, E. Pelinovsky, T. Talipova, et al., “Analytical and Numerical Study of Nonlinear Effects at Tsunami Modelling,” Appl. Math. Comput. 174, 795–809 (2006).

    Article  Google Scholar 

  10. O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Nauka, Moscow, 1975; Consultants Bureau, New York, 1977).

    Google Scholar 

  11. S. N. Gurbatov, A. N. Malakhov, and A. I. Saichev, Nonlinear Random Waves in Nondispersion Media (Nauka, Moscow, 1990).

    Google Scholar 

  12. E. N. Pelinovsky, “Spectral Analysis of Simple Waves,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 19, 373–383 (1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nizhni Novgorod State Technical University, ul. Minina 24, Nizhni Novgorod, 603600, Russia

    I. I. Didenkulova, A. A. Kurkin & E. N. Pelinovsky

  2. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhni Novgorod, 603950, Russia

    I. I. Didenkulova & E. N. Pelinovsky

  3. University of Antilles, Pointe-à-Pitre, 97159, France

    N. Zahibo

Authors
  1. I. I. Didenkulova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Zahibo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. A. Kurkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. N. Pelinovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © I.I. Didenkulova, N. Zahibo, A.A. Kurkin, E.N. Pelinovsky, 2006, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2006, Vol. 42, No. 6, pp. 839–842.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Didenkulova, I.I., Zahibo, N., Kurkin, A.A. et al. Steepness and spectrum of a nonlinearly deformed wave on shallow waters. Izv. Atmos. Ocean. Phys. 42, 773–776 (2006). https://doi.org/10.1134/S0001433806060119

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433806060119

Keywords

Search

Navigation