Reflection and transmission of surface water waves by undulating bottom topography

Abstract

The objective of this thesis is to investigate the scattering of a train of small amplitude harmonic surface water waves by small undulation of a sea-bed for both normal and oblique incidence. In this study of scattering, mixed boundary value problems are set up for the determi- nation of a velocity potential where the governing partial differential equation happens to be Laplace's equation in two dimensions for normal incidence and in three dimensions for oblique incidence within the fluid with a mixed boundary condition on the free surface and a condition on the bottom boundary. As the fluid domain extends to infinity, a far-field condition or an infinity condition arises to ensure uniqueness of the problem. Applying a perturbation analysis, which involves a small parameter Epsilon present in the representation of the small undulation of the sea-bed, directly to the boundary value problem the original problem is reduced to a simpler boundary value problem for the first order correction of the potential..