Reflection and transmission of surface water waves by undulating bottom topography

No Thumbnail Available
Journal Title
Journal ISSN
Volume Title
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..
Supervisor: S. N. Bora