Dynamics of resonant low-frequency waves over a schematized fringing coral reef

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Abstract

Low-lying islands are highly vulnerable to wave-induced flooding, with low-frequency waves (frequency <0.04Hz) being one of the main drivers. The impact of these inundations can increase due to wave resonance over coral reefs, which
has been observed in the range of low-frequency waves. This study aims to
understand the reef resonance phenomenon along with processes that could limit its resonant amplification over wave height and wave run-up.

A numerical experiment was carried out based on a 1D SWASH numerical model.
A cross-shore profile of a schematized fringing coral reef was built, and resonance was forced over this bathymetry for the first two resonant modes and two water depths. The offshore forcing was designed as a simplified wave climate, with small amplitude regular low-frequency waves.

Resonance was found to occur in a bandwidth of periods for each resonant mode, generating two resonant amplification peaks (one for each resonant mode). The periods leading to the maximum resonant amplification inside each resonant bandwidth are the modeled resonant periods, which were found to be longer than the theoretical resonant periods (based on reef flat width and water depth). The resonant amplification over wave height and run-up were found to be more significant for the fundamental mode than for the first mode, decreasing for both resonant modes when increasing the water depth. Moreover, for the wave conditions modeled in this experiment, the relative resonant amplification was found to be stronger for smaller wave heights than larger wave heights.

Reef wave resonance presented a build-up behavior, needing a minimum number of waves to reach a maximum resonant amplification, which varied depending on the wave period, wave height, and water depth. Resonant amplification was found to increase for a larger amount of trapped wave energy over the reef and lower friction dissipation. Frictional dissipation was found to be the most effective process to counteract wave resonant amplification. Thus, increasing coral reef bottom friction is essential for enhancing low-lying island coastal safety.