Depth-integrated modeling of suspended sediment transport

We derive a depth-averaged model of suspended sediment transport. The development of the analysis leads us to revisit the asymptotic approach originally developed by Galappatti [1983], more recently generalized by Wang [1992] and widely employed in commercial codes. We show that Galappatti's approach is formally incorrect as it differs from the formal asymptotic expansion of the exact solution. Moreover, the correct approach rather than leading to a differential equation for the depth-averaged concentration actually provides higher order corrections for the leading order equilibrium approximation of the depth-averaged concentration. Such corrections can be expressed in terms of spatial and temporal derivatives of the leading order solution. The latter picture is demonstrated on a model problem which is easily amenable to analytical treatment. On the basis of the formal asymptotic expansion of the exact solution we are then able to derive an analytical form for the flux of suspended sediment in slowly varying flows, which is suitable to applications to a variety of morphodynamic contexts including tidal and fluvial environments. An example of potential applications of the present approach is provided by examining the problem of suspended sediment transport due to a flood wave.