Spatiotemporal numerical modeling of wave overtopping flow over dike crests and landward slopes

Wave overtopping can cause severe erosion on the crest and landward slope of a dike. Accurate erosion prediction requires resolving the spatiotemporal evolution of overtopping flow, which remains insufficiently understood. This study investigates the behavior of overtopping flow along the crest and landward slope using a new, efficient numerical model based on the Steep-Slope Shallow Water Equations. The model was validated against measurements from field experiments using a wave overtopping simulator. The model was applied to a typical dike geometry (B _c = 5 m; tan(α) = 1V:3H), where the overtopping flow is imposed at the waterside crest line based on a schematization using empirical equations from literature and insights from small-scale overtopping experiments. The spatiotemporal evolution of the flow was analyzed along the crest and landward slope for different overtopping volumes. The flow was observed to stretch in time along both the crest and slope while the wavefront steepens, causing the peak flow thickness (h _peak) to decrease significantly. The peak flow velocity (u _peak) decreases along the crest but initially accelerates on the slope due to gravitational forcing. As the flow becomes progressively thinner and faster downslope, frictional forcing increases, reducing the acceleration. Eventually, gravitational and frictional forces balance, causing u _peak to decelerate and then decrease. Overall, the model captures key spatiotemporal dynamics such as flow stretching, wavefront steepening, and deceleration of u _peak on long slopes, which are absent in time-independent analytical models. It offers a computationally efficient approach that provides a practical middle ground between simplified analytical methods and full CFD simulations.