Abstract:

In this paper, the FUNWAVE-TVD (fully nonlinear wave model with total variation diminishing) numerical model based on the two-dimensional horizontal Boussinesq equations was used to simulate the wave propagation and run-up near a three-dimensional barrier reef. Firstly, the model was verified by existing physical experiments. Subsequently, the effects of different reef widths, gap widths and gap locations on wave transformation and run-up around the three-dimensional barrier reef were analyzed. The results show that the existence of reefs can effectively reduce the impact of solitary waves. As the width of the reef increases, wave height decreases more rapidly, and wave run-up around the whole island drops continuously. The values of run-up near the leeward side are very small and exhibit some variability. The run-up decline due to reefs around the central island coastline decreases as the reef width increases. As the gap width increases, the extend of wave height increase in the lagoon near the gap increases. The influence of the gap width on the run-up is evident within a certain range on the windward side of the central island. As the gap width increases, the run-up on the windward side of the central island increases in this area, and the maximum run-up shifts from bimodal to unimodal. Outside this range, wave run-up is almost unaffected by the gap width. As the angle between the direction of the incident wave and the gap increases, the extent of wave height increase in the lagoon near the gap decreases. Moreover, the change of the gap location only affects the run-up in the region close to the gap of the central island, and this affected region shifts towards the back of the gap as the angle between the direction of the incident wave and the gap increases.

Key words: Boussinesq equation, solitary waves, wave run-up, barrier reef