Nonlinear Kelvin and continental-shelf waves
- 14 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 52 (2), 379-391
- https://doi.org/10.1017/s002211207200148x
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.Keywords
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