Hurricane is a common natural disaster. In natural hurricanes, irregular waves will shoal with decreasing depth when moving toward the beach. Once the wave height depth ratio exceeds a critical value, waves will break and generate a bore in the surf zone. Breaking waves will continue to propagate onshore and scour coastal zones. Breaking wave induced run-up can significantly risk infrastructure in coastal areas. For instance, run-up height can cause coastal flooding. Moreover, the momentum flux transported onshore can also exert forces on beaches and coastal structures. Therefore, properly simulating this process is a supplement of in-situ field measurement and is of great importance for coastal structure design. Previous studies have already shown the potential in numerically simulating the wave run-up in lab length scales and in short time scales (less than half hour).In my study, long time (1h) wave run-up will be simulated on larger scale domains .
Numerical run-up results are compared with Stockdon’s formula  and two percent exceedance run-up elevation is used for comparison. The result shows that two dimensional run-up height is always higher than Stockdon’s formula because two dimensional simulation doesn’t consider directional spreading angle . In three dimensional cases, directional spreading plays an important role in mitigating run-up height. Result shows that run-up heights calculated by Stockdon’s formula are very close to numerical results when directional spreading angle . Furthermore, my study calculates 0.5% exceedance dimensionless momentum flux, noting its variation with different surf simulation numbers , dimensionless elevation and directional spreading angle. Result shows that the extreme momentum flux decreases with increasing elevation. Furthermore, given a location, waves with bigger Iribarren number will generate a higher momentum flux. However, momentum flux cannot be expressed as a simple function of aforementioned parameters. By further investigation, a simple model is established to approximate 0.5% momentum flux.