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Wave reflection from a gently sloping beach

Published online by Cambridge University Press:  26 April 2006

John Miles
John Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California. San Diego, La Jolla, CA 92093, USA
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Abstract

The linear reflection of an obliquely incident gravity wave of frequency ω from a gently sloping beach of shoreline slope σ and characteristic length l is determined for σ [Lt ] 1 [Lt ] ω2l/g. An asymptotic (σ↓0), inviscid approximation that is uniformly valid in the shallow-water domain is matched to Keller's (1958) geometrical-optics approximation for non-shallow water. An exact solution is obtained for the profile h = σl[1−exp (−x/l)] in the shallow-water domain and used to test the asymptotic approximation. The absence of viscosity implies perfect reflection. A model that incorporates both small viscosity and small capillarity predicts a fixed contact line and the reflection coefficient |R| = exp [−πσ−2g−1(2νω3)½], where ν is the kinematic viscosity. These predictions are in qualitative agreement with the experimental results of Mahony & Pritchard (1980).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 59 - 66
Copyright
© 1990 Cambridge University Press

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