WAVE SCATTERING OVER UNEVEN DEPTH USING THE MILD-SLOPE EQUATION

This paper examines the scattering of a train of small-amplitude harmo nic surface waves on water by one-dimensional topography, using the mi ld-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 appr oximations to the reflection and transmission coefficients and to the free surface shape are produced with only 2- or 3-dimensional trial sp aces, by choosing these spaces to be problem dependent. The bed profil es considered include localised humps and taluds which join two horizo ntal planes at different depths.