Author(s): Gerald Muller

Linked Author(s): Gerald Muller

Keywords: Coastal structures. vertical sea walls; Wave effects; Breaking wave overtoppping

Abstract: The overtopping of coastal structures is an important design criterion since the overtopping water volume and spray formation can affect harbor operations. The determination of average and maximum overtopping volumes is a standard requirement for coastal structures. Overtopping is a highly non-linear dynamic phenomenon, and usually analyzed using physical or numerical models. There is only a very limited amount of theoretical work reported, relating to overtopping by reflected waves where a linear approximation for the wave profile gave good results. No theoretical model however exists for breaking wave or ‘impulsive’ overtopping. When the front of the breaking wave hits a vertical structure, a fast uprush jet is generated. The uprush velocity vup of the jet can reach a speed of six to ten times the shallow water wave velocity giving theoretical uprush heights of 18 to 50 times the water depth. This appears very high when compared with observations. At Southampton University, a model for breaking wave or 'impulsive' overtopping was developed using a linearised approach for simplicity. The theoretical approach is based on the conservation of energy and mass, and links two steady-state conditions: (1) the approaching undisturbed wave, and (2) the moment when run-up is complete, and the kinetic energy has been transformed to potential. For the analysis, the complete energy of wave crest is assumed to be focused into the uprush jet as a conservative assumption, The uprush is idealized as a triangular body of water. The overtopping volume VOT is assumed to be the volume of the uprush which extends above the top of the structure at a freeboard height Rc. VOT can then be calculated and plotted as a function of the uprush height and the freeboard. The analysis showed that the overtopping volume depends on the freeboard Rc of the structure, and on the ratio of uprush height and wave height. It is assumed that this ratio can vary, depending on the breaker shape. The overtopping volume then reaches a maximum for a defined ratio of uprush and wave height which ranges from 3 to 15 for relative freeboard heights of 1 ≤ Rc / H ≤ 3. The theoretical model developed here was compared with measurements of overtopping volumes created by single waves as reported in the literature. The theoretical predictions were found to be surprisingly close to the measured overtopping volumes. The trend of the experimental results, with overtopping volumes reducing with increasing freeboard, was also matched by the theory. The model allows to assess the effect and interaction of wave and geometric parameters on overtopping volumes. Uprush heights predicted from initial velocities given in the literature however led to unrealistically thin uprush jets.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022672

Year: 2022