Skip to main content
SpringerLink
Log in

Uniform and Nonuniform Asymptotics of Far Surface Fields from a Flashed Localized Source

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The problem of surface-wave far-field generation from a localized source that flashed in a heavy liquid of finite depth is investigated. Integral representations of the solution are constructed that describe the structure of wave surface disturbances. The characteristics of the excited wave fields far from the source of disturbances are studied. Uniform and nonuniform asymptotic solutions are constructed that are expressed in terms of the Airy function and its derivative, which make it possible to describe the far fields of surface perturbations both near and far from the wave front.

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

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. Wehausen, J.V. and Laitone, E.V., Surface waves, in Handbuch der Physik, Springer, 1960, vol. 9, pp. 446–778.

    Google Scholar 

  2. Cherchesov, L.V., Poverkhnostnye i vnutrennie volny (Surface and Internal Waves), Kiev: Naukova Dumka, 1973.

  3. Aleshkov, Yu.Z., Teoriya voln na poverkhnosti tyazheloi zhidkosti (Theory of Waves on the Surface of a Heavy Liquid), Leningrad: Leningrad Gos. Univ., 1981.

  4. Lighthill, J., Waves in Fluids, Cambridge: Univ. Press, 2001.

    MATH  Google Scholar 

  5. Shamin, R.V., Vychislitel’nye eksperimenty v modelirovanii poverkhnostnykh voln v okeane (Computational Experiments in Modeling of the Surface Waves in the Ocean), Moscow: Nauka, 2008.

  6. Bulatov, V.V. and Vladimirov, Yu.V., Volny v stratifitsirovannykh sredakh (Waves in Stratified Media), Moscow: Nauka, 2015.

  7. Mei, C.C., Stiassnie, M., and Yue, D.K.-P., Theory and Applications of Ocean Surface Waves, London: World Sci. Publ., 2017, vol. 42.

    MATH  Google Scholar 

  8. The Ocean in Motion, Velarde, M.G., Tarakanov, R.Yu., and Marchenko, A.V., Eds., Amsterdam: Springer AG, 2018.

    Google Scholar 

  9. Kharif, C., Pelinovsky, E., and Slynyaev, A., Rogue Waves in the Ocean, Berlin: Springer, 2009.

    MATH  Google Scholar 

  10. Shamin, R.V., Matematicheskie voprosy voln-ubiits (Mathematical Modelling of Rogue Waves), Moscow: Lenand, 2016.

  11. Belyaev, M.Y., Desinov, L.V., Kumakshev, S.A., Sekerzh-Zen’kovich, S.H., and Krikalev, S.K., Identification of a system of oceanic waves based on space imagery, J. Comput. Syst. Sci. Int., 2009, no. 1, pp. 110–120.

  12. Belyaev, M.Y., Vinogradov, P.V., Desinov, L.V., Kumakshev, S.A., and Sekerzh-Zen’kovich, S., Identification of a source of oceanic ring waves near Darwin’s Island based on space photos, J. Comput. Syst. Sci. Int., 2011, no. 1, pp. 67–80.

  13. Chen, X.-B. and Wu, G.X., On singular and highly oscillatory properties of the green function for ship motions, J. Fluid Mech., 2001, vol. 445, pp. 77–91.

    Article  ADS  MathSciNet  Google Scholar 

  14. Zakharov, V.E., Dyachenko, A.I., and Vasilyev, O.A., New method for numerical simulations of a nonstationary potential flow of incompressible fluid with a free surface, Eur. J. Mech., 2002, vol. 21, pp. 283–291.

    Article  MathSciNet  Google Scholar 

  15. Dobrokhotov, S.Yu., Grushin, V.V., Sergeev, S.A., and Tirozzi, B., Asymptotic theory of linear water waves in a domain with non-uniform bottom with rapidly oscillating sections, Russ. J. Math. Phys., 2016, vol. 23, pp. 455–475.

    Article  MathSciNet  Google Scholar 

  16. Bulatov, V.V., Vladimirov, Yu.V., and Vladimirov, I.Yu., Far fields of the surface disturbances produced by a pulsating source in an infinite-depth fluid, Fluid Dyn., 2017, vol. 52, no. 5, pp. 617–623.

    Article  ADS  MathSciNet  Google Scholar 

  17. Svirkunov, P.N. and Kalashnik, M.V., Phase patterns of dispersive waves from moving localized sources, Phys. Usp., 2014, vol. 57, pp. 80–91.

    Article  ADS  Google Scholar 

  18. Watson, G.N., A Treatise on the Theory of Bessel Functions, Reprint of the 2nd ed., Cambridge: Cambridge Univ. Press, 1995.

  19. Grikurov, V.É., Caustic overlap in a surface waveguide and a generalization of the ray method, Radiophys. Quantum Electron., 1980, vol. 23, no. 9, pp. 690–695.

    Article  ADS  MathSciNet  Google Scholar 

  20. Froman, N. and Froman, P., Physical Problems Solved by the Phase-Integral Method, Cambridge: Cambridge Univ. Press, 2002.

    Book  Google Scholar 

  21. Kravtsov, Yu. and Orlov, Yu., Caustics, Catastrophes and Wave Fields, Berlin: Springer, 1999.

    Book  Google Scholar 

  22. Borovikov, V.A., Uniform Stationary Phase Method, London: Institution of Electrical Engineers, 1994.

Download references

Funding

This work was supported by state orders (V.V. Bulatov and Yu.V. Vladimirov, by project no. AAAA-A20-120011690131-7, and I.Yu. Vladimirov, by project no. 0128-2021-0002) and partially supported by the Russian Foundation for Basic Research (project no. 20-01-00111A).

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    V. V. Bulatov & Yu. V. Vladimirov

  2. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia

    I. Yu. Vladimirov

Authors
  1. V. V. Bulatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. V. Vladimirov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Yu. Vladimirov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. V. Bulatov, Yu. V. Vladimirov or I. Yu. Vladimirov.

Additional information

Translated by E. Oborin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bulatov, V.V., Vladimirov, Y.V. & Vladimirov, I.Y. Uniform and Nonuniform Asymptotics of Far Surface Fields from a Flashed Localized Source. Fluid Dyn 56, 975–980 (2021). https://doi.org/10.1134/S001546282107003X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S001546282107003X

Keywords:

Search

Navigation