Prediction of Water Setup and Wave Crest Heights on Submerged Coral Reefs with Steep Slopes

Submerged coral reefs develop unique topographic profiles over time. Moving landward from the offshore, they are recognized by a very steep slope with a transition at the algal ridge or reef crest to a large, gentle, or concave region attached to the shore. The water depth of the reef flat is relatively small and often exposed during low tides, in the range of a few to tens meters. The mechanism of wave transformation from offshore to the reef crest and reef flat is complicated. The main distinction in the wave propagation in these geometric profiles is caused by a sudden change of reef topography, from hundreds of meters in deep water depth to a few meters of shallow flat shelves. When waves propagate from deep water to reefs with steep foreshore, the mean sea level (MSL) will significantly increase and be associated with the increased wave crest elevation. Predicting the wave propagation, water setup, and wave crest elevation is crucial in analyzing and designing structures on nearby islands, such as determining the scale of wave height effects, overtopping discharge, etc. This paper predicts the water setup and the increase of wave crests above MSL based on a physical model in a wave flume. The remarkable result shows that the water surface elevation above water level can even reach approximately a wave height offshore due to the resonant phenomenon of wave amplitudes at the shoreline…