A simple numerical model for the damage of corals by Tsunami

Recent studies suggested that damage of corals by the 2004 Indian Ocean tsunami may have been related to the characteristics of corals (shape, size, and fixed strength to the sea floor), coastal profiles, and tsunami wave properties. However, no systematic study has yet clarified the relationships among these factors. To provide basic knowledge of tsunami effects on coral reefs and to aid in the future evaluations of coral damage by tsunami, we describe the variation of tsunami inundation patterns depending on the incident wave properties and coastal profiles based on a cross-sectional numerical model. We assume the period and amplitude of the incident wave (sine wave) as 30 min and 3 m, respectively. Five coastal profiles of a reef with different slope inclinations (1/100, 1/50, 1/20, 1/10, and 1/5) are used in this calculation. Our results indicate that there is a significant difference in the tsunami inundation pattern depending on whether the first arrival is a crest-start wave (crest propagates first) or trough-start wave (trough propagates first). The maximum current velocity of the trough-start wave is higher than that of the crest-start wave for each slope inclination. In the case of a crest-start wave, the point where the maximum current velocity in the computational region is generated occurs on land. In contrast, the point occurs offshore in the case of a trough-start wave, because of the receding seawater. Moreover, the point shifts toward deeper areas at gentler slopes. Under the assumption that wave amplitude and period are the same, our findings indicate that the damage to corals would be greater in an area where a trough-start wave arrives first rather than a crest-start wave. Moreover, within the region where a trough-start wave arrives first, greater damage to corals would be expected even in deeper areas in case of a gentle slope rather than a steep slope.