On the Changes in Phase Speed of One Train of Water Waves in the Presence of Another
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.
KeywordsSurface Tension Gravity Wave Water Wave Wave Train Phase Speed
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