Journal article Open Access
Evans F. Osaisai
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.