A Simple Model of Sediment Transport in the Nearshore Zone

In this paper we examine a simple model of sediment transport, induced by the breaking waves in the surf zone. Essentially the bottom is allowed to move in response to the divergence of a sediment flux, in turn determined by the breaking waves. The effect of this extra term on the previous solutions for set-up, longshore currents and rip currents is then determined. It is found that the solutions for the mean flow are now unsteady on a slow timescale determined by a certain sediment transport parameter. There is a change in beach slope in the rip currents controlled by the sediment transport. The system of equations now forms a three-by-three nonlinear hyperbolic system of equations. These we solve approximately, using a simple wave solution based on the simple wave speed corresponding to the small sediment transport parameter. However, this solution will always breakdown after a long time, so we show that by adding another term proportional to the beach slope into the expression for the sediment flux, we can obtain a steady-state solution.