Capillary-Gravitational Waves of Finite Amplitude on the Surface of a Homogeneous Liquid

Capillary-Gravitational Waves of Finite Amplitude on the Surface of a Homogeneous Liquid The method of multiple scales is used to deduce equations for three nonlinear approximations of the capillary-gravitational disturbances of the free surface of a layer of a homogeneous liquid of constant depth. In these equations, the space-time variations of the wave profile in the expression for the velocity potential on the liquid surface are taken into account. On this basis, we construct asymptotic expansions up to the quantities of the third order of smallness for the velocity potential and elevations of the liquid surface induced by running periodic waves of finite amplitude. Furthermore, we analyze the dependences of the amplitude-phase characteristics of wave disturbances on the surface tension, depth of the liquid, and the length and steepness of waves of the first harmonic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Oceanography Springer Journals

Capillary-Gravitational Waves of Finite Amplitude on the Surface of a Homogeneous Liquid

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Publisher
Kluwer Academic Publishers-Consultants Bureau
Copyright
Copyright © 2005 by Springer Science+Business Media, Inc.
Subject
Earth Sciences; Oceanography; Remote Sensing/Photogrammetry; Atmospheric Sciences; Climate Change; Environmental Physics
ISSN
0928-5105
eISSN
0928-5105
D.O.I.
10.1007/s11110-006-0003-3
Publisher site
See Article on Publisher Site

Abstract

The method of multiple scales is used to deduce equations for three nonlinear approximations of the capillary-gravitational disturbances of the free surface of a layer of a homogeneous liquid of constant depth. In these equations, the space-time variations of the wave profile in the expression for the velocity potential on the liquid surface are taken into account. On this basis, we construct asymptotic expansions up to the quantities of the third order of smallness for the velocity potential and elevations of the liquid surface induced by running periodic waves of finite amplitude. Furthermore, we analyze the dependences of the amplitude-phase characteristics of wave disturbances on the surface tension, depth of the liquid, and the length and steepness of waves of the first harmonic.

Journal

Physical OceanographySpringer Journals

Published: Feb 10, 2006

References

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