On the Changes in Phase Speed of One Train of Water Waves in the Presence of Another

  • S. J. Hogan
  • Idith Gruman
  • M. Stiassnie


We present calculations of the change in phase speed of one train of water waves in the presence of another. We use a general method, based on Zakharov’s (1968) integral equation. In the important case of gravity-capillary waves, we present the correct form of the Zakharov kernel. This is used to find the expressions for the changes in phase-speed. These results are then checked using a perturbation method based on that of Longuet-Higgins and Phillips (1962). Agreement to 6 significant digits has been obtained between the calculations based on these two distinct methods. Full numerical results in the form of polar diagrams over a wide range of wavelengths, away from conditions of triad resonance, are provided.


Surface Tension Gravity Wave Water Wave Wave Train Phase Speed 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • S. J. Hogan
    • 1
  • Idith Gruman
    • 2
  • M. Stiassnie
    • 3
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Department of Civil EngineeringTechnion HaifaIsrael
  3. 3.School of MathematicsUniversity of BristolBristolUK

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