Journal of Fluid Mechanics

Long waves on a beach

D. H.  Peregrine a1
a1 Department of Mathematics, University of Bristol

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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.

(Published Online March 28 2006)
(Received May 31 1966)

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