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Long waves on a beach

Published online by Cambridge University Press:  28 March 2006

D. H. Peregrine
D. H. Peregrine
Affiliation:
Department of Mathematics, University of Bristol
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Abstract

Equations of motion are derived for long waves in water of varying depth. The equations are for small amplitude waves, but do include non-linear terms. They correspond to the Boussinesq equations for water of constant depth. Solutions have been calculated numerically for a solitary wave on a beach of uniform slope. These solutions include a reflected wave, which is also derived analytically by using the linearized long-wave equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 4 , 20 March 1967 , pp. 815 - 827
Copyright
© 1967 Cambridge University Press

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