Journal of Fluid Mechanics


Overtopping a truncated planar beach


a1 Centre for Environmental and Geophysical Flows, School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK

a2 School of Civil Engineering, University of Queensland, Brisbane, QLD 4072, Australia

a3 Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK


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.

(Received November 26 2009)

(Revised August 02 2010)

(Accepted August 11 2010)

(Online publication November 16 2010)

Key words:

  • coastal engineering;
  • hydraulic control;
  • shallow water flows


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