Fluid Dynamics

, Volume 29, Issue 4, pp 549–555 | Cite as

Nonlinear interaction of surface waves in a basin covered with broken ice

  • A. E. Bukatov
Article
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Abstract

The nonlinear interaction of periodic traveling waves of the first and second harmonics in a constant-depth uniform fluid covered with broken ice is considered. Uniform asymptotic expansions up to third-order values for the velocity potential of the fluid and the elevation of the basin surface are found by means of the multivariable expansion procedure. The dependence of the wave perturbations on the thickness of the ice and the interacting-harmonic characteristics is analyzed.

Keywords

Fluid Dynamics Surface Wave Asymptotic Expansion Nonlinear Interaction Velocity Potential 

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References

  1. 1.
    D. E. Kheisin,Ice Sheet Dynamics [in Russian], Gidrometeoizdat, Leningrad (1967).Google Scholar
  2. 2.
    A. E. Bukatov, “Effect of ice cover on unsteady waves,” in:Marine Hydrophysical Research, No. 4 [in Russian], Sebastopol (1970), p. 64.Google Scholar
  3. 3.
    A.E. Bukatov and L. V. Cherkesov, “Effect of ice cover on wave motions,” in:Marine Hydrophysical Research, No. 2 [in Russian], Sebastopol (1971), p. 113.Google Scholar
  4. 4.
    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
  5. 5.
    A. E. Bukatov and O. M. Bukatova, “Surface waves of finite amplitude in a basin with broken ice,”Izv. Ros. Akad. Nauk, Fiz. Atmos. Okeana,29, 421 (1993).Google Scholar
  6. 6.
    E. R. Paunder,Physics of Ice [Russian translation], Mir, Nauka (1967).Google Scholar
  7. 7.
    V. V. Bogorodskii and V. N. Gavrilo,Ice. Physical Properties, Modern Methods of Glaciology [in Russian], Gidrometeoizdat, Leningrad (1980).Google Scholar
  8. 8.
    L. A. Timokhov and D. E. Kheisin,Sea Ice Dynamics: Mathematical models [in Russian], Gidrometeoizdat, Leningrad (1987).Google Scholar
  9. 9.
    G. G. Stokes, “On the theory of oscillatory waves,”Math. and Phys. Papers 1, Cambridge (1880), p. 197.Google Scholar
  10. 10.
    J. J. Stoker,Water Waves, New York (1959).Google Scholar
  11. 11.
    G. F. Carrier, “Gravity waves on water of variable depth,”J. Fluid Mech.,24, 641 (1966).ADSMATHMathSciNetGoogle Scholar
  12. 12.
    S. V. Nesterov, Finite-amplitude wave generation by a moving system of pressures,”Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana,4, 1123 (1968).Google Scholar
  13. 13.
    G. B. Whitham,Linear and Nonlinear Waves, Wiley-Interscience, New York (1974).Google Scholar
  14. 14.
    Yu. Z. Aleshkov,Theory of Waves on Surface of a Heavy Liquid [in Russian], Leningrad State University, Leningrad (1981).Google Scholar
  15. 15.
    A. H. Nayfeh,Perturbation Methods [Russian translation], Mir, Moscow (1976).Google Scholar
  16. 16.
    P. H. Stone, “The meridional structure of baroclinic waves,”J. Atmos. Sci.,26, 376 (1969).ADSGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. E. Bukatov

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