Some effects of surface tension on water waves at a wall.
The work presented here mainly concerns the effects of surface tension on steep
gravity waves. These are investigated by extending a numerical program to include
surface tension. The work has been influenced by contact with coastal engineers,
and as a result the third chapter is devoted to the study of waves near a wall,
in particular on shallow water. The two themes are brought together in the final
substantial chapter which has significant implications for the extrapolation of results
from small scale experiments to prototype scale.
Chapter 1 introduces capillary waves. In chapter 2, results from the potential
flow solver for nonlinear almost steady waves are compared with the theoretical
work of Longuet-Higgins (1963,1995) and experiments Perlin, Ting & Lin (1993)
and found generally to be in agreement. Some differences between our numerical
results and the work of these authors are highlighted and explained.
Chapter 3 relates to coastal engineering applications and considers a different
type of surface wave, the gravity waves found in front of coastal structures. The
study focuses on the hydrodynamic parameters on the bed under such waves. In
particular, trends as the water depth is decreased and the failure of linear theory on
Study of the interaction of such waves with coastal structures is continued in
chapter 4. The flow of water due to the overtopping of a vertical wall by waves is
modelled. Results for overtopping volume per wave are in general agreement with
experimental data on overtopping rates. The model is used to investigate the effect
of different shapes for bed geometry in front of the wall.
The preceding chapters are brought together in the final sections. The inclusion
of surface tension allows us to perform overtopping calculations for the small scale
waves often used in wave experiments. We find that surface tension can significantly
affect the overtopping volumes and run-up heights