An integral treatment of friction during a swash uprush

The effects of bed friction are modelled for the flow near the moving shoreline during the uprush phase of a swash event by extending the Pohlhausen method used by Whitham (1955) to a sloping bed. The tip of the swash near the moving shoreline is treated in an integral sense as a region of uniform velocity, being acted on by the forces of friction, gravity, and the pressure force induced by the frictionless flow behind the swash tip. The bed shear stress is parameterized by using the quadratic dependence on velocity. The theory is compared to data of the shoreline velocity and position in the swash of breaking solitary waves, and the friction coefficient is determined from direct measurements of bed shear stress. The theoretical predictions are in good agreement with the laboratory results in terms of time history of the shoreline velocity and position, as well as the run-up.