Fluid Dynamics

, Volume 22, Issue 6, pp 893–901 | Cite as

Asymptotic analysis of the unsteady problem of waves in a two-layer flow

  • A. A. Korobkin


The problem investigated is the unsteady problem of the internal waves generated in a two-layer flow by a certain periodic perturbation which leads to small deviations from the basic flow. A method of constructing an approximate solution uniformly valid throughout the region of variation of the variables and the parameters of the problem is indicated. It is confirmed that for large times and near-resonance parameters the motion of the fluid is described by the mixed problem for a cubic Schrödinger equation. Certain qualitative properties of the solution of this nonlinear problem are noted.


Small Deviation Approximate Solution Large Time Internal Wave Nonlinear Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    L. Debnath and S. Rosenblat, “The ultimate approach to the steady state in the generation of waves on a running stream,” Q. J. Mech. Appl. Math.,22, 221 (1969).Google Scholar
  2. 2.
    T. R. Akylas, “On the excitation of nonlinear water waves by a moving pressure distribution oscillating at resonant frequency,” Phys. Fluids,27, 2803 (1984).Google Scholar
  3. 3.
    G. Dagan and T. Miloh, “Free-surface flow past oscillating singularities at resonant frequency,” J. Fluid Mech.,120, 139 (1982).Google Scholar
  4. 4.
    I. V. Sturova, “Generation of internal waves in a stratified fluid,” in: Nonlinear Problems of the Theory of Surface and Internal Waves [in Russian], Nauka, Novosibirsk (1985), p. 200.Google Scholar
  5. 5.
    H. J. Haussling and R. M. Coleman, “Finite-difference computations using boundary-fitted coordinates for free-surface potential flows generated by submerged bodies,” Proc. 2nd Intern. Conf. on Numerical Ship Hydrodynamics, University of California, Berkeley (1977), p. 221.Google Scholar
  6. 6.
    R. H. J. Crimshaw and D. I. Pullin, “Stability of finite-amplitude interfacial waves,” J. Fluid Mech.,160, 297 (1985).Google Scholar
  7. 7.
    A. A. Korobkin, “Linear approximation in the problem of internal waves in a two-layer flow,” in: Continuum Dynamics, Vol. 81 [in Russian], Institute of Hydrodynamics, Siberian Branch of the USSR Academy of Sciences, Novosibirsk (1987), p. 78.Google Scholar
  8. 8.
    V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1976).Google Scholar
  9. 9.
    A. V. Zhiber and A. B. Shabat, “Cauchy problem for the nonlinear Schrödinger equation,” Differents. Uravneniya.,6, 137 (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • A. A. Korobkin
    • 1
  1. 1.Novosibirsk

Personalised recommendations