We investigate swash on an erodible beach using the one-dimensional shallow-water equations fully coupled to a bed-evolution (Exner) equation. In particular, the dam-break/bore-collapse initial condition of Shen & Meyer (J. Fluid Mech., vol. 16, 1963, pp. 113–125) and Peregrine & Williams (J. Fluid Mech., vol. 440, 2001, pp. 391–399) is investigated using a numerical model based on the method of characteristics. A sediment-transport formula (cubic in velocity u: Au3) is used here; this belongs to a family of sediment-transport formulae for which Pritchard & Hogg (Coastal Engng, vol. 52, 2005, pp. 1–23) showed that net sediment transport under the Shen & Meyer (1963) bore collapse is offshore throughout the swash zone when a non-erodible bed is considered. It is found that full coupling with the beach, although still resulting in the net offshore transport of sediment throughout the swash zone, leads to a large reduction in the net offshore transport of sediment from the beach face. This is particularly true for the upper third of the swash zone. Moreover, in contradistinction to swash flows over non-erodible beds, flows over erodible beaches are unique to the bed mobility and porosity under consideration; this has very important implications for run-up predictions. The conclusion is that it is essential to consider full coupling of water and bed motions (i.e. full morphodynamics) in order to understand and predict sediment transport in the swash, regardless of other physical effects (e.g. turbulence, infiltration, pre-suspended sediment, etc.).
An experimental study on sediment transport and bed evolution under different swash zone morphological conditions
