Abstract:
In this thesis the diffraction of water waves passing through a gap in a breakwater is investigated experimentally, using close range photogrammetry, and numerically, using finite and infinite elements. The author was particularly interested in validating specific breakwater gap diffraction diagrams given in popular coastal engineering design manuals. Breakwater gap configurations with the following gap width to wave length ratios (B/L ratios) were analysed, both experimentally and numerically, namely: B/L = 1,64; 1,41; 1,2; 1; 0,75; 0,5. These configurations are symmetrical, i.e. both breakwater arms lie on the same straight line. An asymmetrical B/L = 1,64 breakwater gap configuration was also analysed. Previous experimental breakwater gap diffraction investigations are reviewed leading to the conclusion that the reported results are inconclusive due to (1) the relatively poor accuracy with which the wave heights were measured and (2) secondary basin effects which were superimposed upon and thus distorted the pure diffraction phenomena. In the experimental breakwater gap configurations investigated by the author, splitter plates were used to eliminate the reflection problems on the seaward side of the breakwaters, whilst a novel photogrammetric wave height measurement technique was used to measure accurately the wave heights in the entire basin, before they could be distorted by reflecting waves, basin resonance effects, etc. This "infinite basin technique" was used to simulate experimentally and measure the diffraction of a continuous wave train entering an infinite basin via a gap in an approximate totally absorbing breakwater. A number of different photogrammetric wave height measurement techniques based on analogue procedures, the theory of projective transformations, and the theory of the deformed reference plane, are investigated and developed. It was found that the technique based on the projective transformation theory, and in which the plates are analysed using a stereo-comparator linked to a microcomputer, is the most accurate. Using this technique it was found that, with the cameras situated approximately 5 m above the water surface, the wave heights in the basin can be measured with an accuracy of better than 2 mm. The above method, in conjunction with the infinite basin technique, was used to analyse the experimental breakwater gap configurations. The basic linear wave theory is described leading to the derivation of the Helmholtz diffraction equation. The classical diffraction theories for the semi-infinite breakwater and breakwater gap configurations are reviewed and compared. The Better-off refraction - diffraction equation is then briefly derived. A review of previous numerical refraction - diffraction investigations, and also of modern numerical methods for water wave diffraction and refraction-diffraction, is given. This review led to the adoption of the finite and infinite element program "WAVE", developed at the University College of Swansea, to model numerically the experimental breakwater gap configurations. The use of the "WAVE" program to model breakwater gap wave diffraction is novel and certain conceptual problems had to be overcome. Finally, the experimental and numerical diffraction diagrams obtained were compared to analytical diagrams where these were available. The correlation between the finite element and analytical results is excellent. When comparing the experimental and finite element results the general conclusions are : 1) in regions outside the shadow zones the linear diffraction theory is conservative except close to small gaps (B/L ≤ 1); and 2) within the shadow zones the linear theory is not conservative and one will have to allow for non-linear effects such as radiating second-order waves generated at the breakwater tips, and increased wave orthogonal spreading near the gap centre line and subsequent orthogonal bunching in the shadow zones caused by wave steepness differences along the crests. Other conclusions drawn are : 1) the photogrammetric techniques described are the best available for the experimental simulation and analysis of infinite domain diffraction and refraction - diffraction problems; and 2) the finite and infinite element program "WAVE" is a very useful tool for the prediction of wave heights in large harbour basins.
Reference:
Pos, J. 1984. A study of breakwater gap wave diffraction using close range photogrammetry and finite and infinite elements. University of Cape Town.