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Kelvin waves on oceanic boundaries

Published online by Cambridge University Press:  29 March 2006

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

The primitive Kelvin wave (on a rotating, semi-infinite, plane sheet of water of uniform depth bounded by a vertical wall) is corrected for the effects of the Earth's curvature, the reduction in depth over the continental shelf, and bends in the coastline. The results are of interest for coastal propagation of the tides; numerical examples are given for the California coastline. It is found that the Earth's curvature reduces the wave speed south of Cape Mendocmo by 8–10% (the possible range for other coastlines is roughly ± 15%) and that the continental shelf reduces the wave speed by 2−8%. The off-shore mass transport (which vanishes identically for the primitive Kelvin wave) induced by curvature and/or the shelf also is calculated. The analysis of Packham & Williams (1968) for diffraction of a Kelvin wave by a corner is extended to obtain explicit results for the phase of the transmission coefficient. It is found that a sustained change in the direction of the coastline may induce a phase shift of the order of an hour (1·3 hours for the bend at Cape Mendocino), but that small distortions of the coastline without a sustained change in direction have negligible effects on the transmitted Kelvin wave at tidal frequencies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 1 , 12 September 1972 , pp. 113 - 127
Copyright
© 1972 Cambridge University Press

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