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Resonant amplification of gravity waves over a circular sill

Published online by Cambridge University Press:  21 April 2006

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

The trapping of gravity waves over a circular sill, originally studied by Longuet-Higgins (1967), is re-examined in the limit δ ≡ dl/d ↓ 0 with λ ≡ σ2d/g = O(1), where d1 is the depth over the sill, d the outer depth, and a the angular frequency of the incident wave. Explicit results are obtained for the resonance curves. These results are in qualitative agreement with the corresponding shallow-water approximations (Λ [Lt ] 1) of Longuet-Higgins, which have been questioned by Renardy (1983). A remarkably simple result is obtained for the mean-square response to a broadband, randomly phased incident wave.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 167 , June 1986 , pp. 169 - 179
Copyright
© 1986 Cambridge University Press

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References

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