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Resonantly interacting water waves

Published online by Cambridge University Press:  21 April 2006

Joseph B. Keller
Joseph B. Keller
Affiliation:
Departments of Mathematics and Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

Coupled nonlinear equations are derived for the amplitudes of two small-amplitude resonantly interacting gravity waves in water of non-uniform depth. Such resonance is possible only for wavelengths long compared to the depth. It is shown that the same equations are obtained from the exact Euler equations, from the nonlinear shallow water theory, and from the Boussinesq equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 191 , June 1988 , pp. 529 - 534
Copyright
© 1988 Cambridge University Press

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References

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