Overtopping a truncated planar beach

Run-up on a truncated impermeable beach is analysed theoretically and experimentally to find the volume of fluid, associated with a single wave event, that flows over the end of the beach. The theoretical calculations investigate the motion using the shallow-water equations and the fluid is allowed to flow freely over the end of the beach. Two models of wave events are considered: dam-break initial conditions, in which fluid collapses from rest to run-up and overtop the beach, and a waveform that models swash associated with the collapse of a long solitary bore. The calculations are made using quasi-analytical techniques, following the hodograph transformation of the governing equations. They yield predictions for the volume of fluid per unit width that overtops the beach, primarily as a function of the dimensionless length of the beach. These predictions are often far in excess of previous theoretical calculations. New experimental results are also reported in which the overtopping volumes due to flows initiated from dam-break conditions are studied for a range of reservoir lengths and heights and for a range of lengths and inclinations of the beach. Without the need for any empirically fitted parameters, good agreement is found between the experimental measurements and the theoretical predictions in regimes for which the effects of drag are negligible.