WAVE REFLECTION FROM A GENTLY SLOPING BEACH

The linear reflection of an obliquely incident gravity wave of frequency o) from a gently sloping beach of shoreline slope cr and characteristic length l is determined for a 1 (i)H/g. An asymptotic (cr jO), 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 = cr/[l— 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| i?| = exp [— nar~%g~1(2po)3)t]i where v is the kinematic viscosity. These predictions are in qualitative agreement with the experimental results of Mahony & PRITCHARD (1980). © 1990, Cambridge University Press. All rights reserved.