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Note on a parametrically excited, trapped cross-wave

Published online by Cambridge University Press:  20 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, California 92093
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Abstract

The cubic Schrödinger equation, which governs the complex amplitude of a cross-wave that is subharmonically excited by a symmetric wavemaker in a deep wave tank (Jones 1984), is solved for prescribed boundary conditions at the wavemaker and a null condition at infinity. This solution (which is a limiting case of a one-parameter family of cnoidal waves) typically describes a trapped wave that decays exponentially in a semi-infinite tank, although it may be fitted to a tank of finite length for a particular combination of parameters. It is closely related to the solution for trapped waves excited through vertical oscillation of a long channel (Wu, Keolian & Rudnick 1984).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 151 , February 1985 , pp. 391 - 394
Copyright
© 1985 Cambridge University Press

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References

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