TY - JOUR

T1 - On the changes in phase speed of one train of water waves in the presence of another

AU - Hogan, S. J.

AU - Gruman, Idith

AU - Stiassnie, M.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - 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. It is shown that the change in phase speed of each wavetrain is directly proportional to the square of the amplitude of the other. This generalizes the work of Longuet-Higgins & Phillips (1962) who considered gravity waves only.
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 & 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.

AB - 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. It is shown that the change in phase speed of each wavetrain is directly proportional to the square of the amplitude of the other. This generalizes the work of Longuet-Higgins & Phillips (1962) who considered gravity waves only.
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 & 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.

UR - http://www.scopus.com/inward/record.url?scp=0004932326&partnerID=8YFLogxK

U2 - 10.1017/S0022112088001806

DO - 10.1017/S0022112088001806

M3 - Article (Academic Journal)

AN - SCOPUS:0004932326

VL - 192

SP - 97

EP - 114

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -