The Stability of Gravity Waves on the Surface of a Flow with Non-uniform Velocity Distribution

  • H. G. M. Velthuizen
  • L. van Wijngaarden
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


The stability of gravity waves on the free surface of a fluid with nonuniform velocity distribution is affected by two mechanisms. One mechanism is analogous to what J. W. Miles discovered in relation to the generation of gravity waves by wind over the surface. The other mechanism is connected with the momentum transport from the mean flow into the wave and vice versa by viscous stresses. In this contribution the neutral stability problem associated with these mechanisms is investigated.


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  1. 1.
    Miles, J. W.: J. Fluid Mech. 8, 593 (1960).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Miles, J. W.: J. Fluid Mech. 13, 427 (1962).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Lin, C. C.: The Theory of Hydrodynamic Stability. London/New York: Cambridge Univ. Press 1955.Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1971

Authors and Affiliations

  • H. G. M. Velthuizen
    • 1
  • L. van Wijngaarden
    • 1
  1. 1.Twente Institute of TechnologyEnschedeNetherlands

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