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Edge waves: a long-wave theory for oceans of finite depth

Published online by Cambridge University Press:  29 March 2006

R. Grimshaw
R. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Victoria 3052, Australia
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Abstract

Edge waves travelling along a straight coastline are examined in the case when the water depth approaches a constant value at large distances from the coast. Only the fundamental mode is examined in the limit as the ratio of the water depth at infinity to the edge-wave wavelength tends to zero. Two comparison theorems are used to obtain upper and lower bounds for the dispersion relation. A long-wave approximation procedure is used to obtain the leading terms in the dispersion relation for a wide class of bottom topographies. The results obtained are compared with an exact result for the case when the bottom topography is a rectangular step.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 4 , 27 February 1974 , pp. 775 - 791
Copyright
© 1974 Cambridge University Press

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References

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