Abstract
This paper examines the scattering of a train of small-amplitude harmonic surface waves on water by one-dimensional topography, using the mild-slope equation. The associated boundary value problem is converted into a pair of integral equations whose solutions are approximated by variational techniques, which also supply error bounds. Excellent approximations to the reflection and transmission coefficients and to the free surface shape are produced with only 2- or 3-dimensional trial spaces, by choosing these spaces to be problem dependent. The bed profiles considered include localised humps and taluds which join two horizontal planes at different depths.
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