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Nonlinear Kelvin and continental-shelf waves

Published online by Cambridge University Press:  29 March 2006

Ronald Smith
Ronald Smith
Affiliation:
Fluid Mechanics Research Institute, University of Essex
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Abstract

Equations are derived for the variation along a straight coastline of Kelvin and continental-shelf waves. It is assumed that the effects of nonlinearity and dispersion are of the same order in a small parameter ε defined by the equation ε2 = f2=L2/gH, in which f is the Coriolis parameter, L the shelf width and H the water depth beyond the shelf. Kelvin waves are found to satisfy the Korteweg–de Vries equation, while continental-shelf waves satisfy a closely related equation. An approximate rule is derived for the variation along a real coastline of the maximum wave height for fully developed nonlinear Kelvin waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 2 , 28 March 1972 , pp. 379 - 391
Copyright
© 1972 Cambridge University Press

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