Suspended sediment concentration profiles in nonuniform flows: Is the classical perturbative approach suitable for depth-averaged closures?

[1] Several contributions have been proposed in the past decades with the aim to set up a reliable quantification of suspended sediment transport on the basis of depth-averaged closure relationships for the concentration profiles. However, a definitive answer to the problem in unsteady and nonuniform conditions has not been found yet. In this paper, we compare a semianalytical solution, based on a formally correct classical perturbative approach relying on small values of characteristic parameters, with the results of a numerical model. The aim is to understand to which extent the simplified solution is able to reproduce the most important features of the complete solution. In particular, we analyze the behavior of vertical concentration profiles, depth-averaged concentrations, and suspended sediment transport rates when temporal and spatial variations are imposed to the system. The comparison between the complete model and the perturbative approximation, pursued also with the aid of fully analytical solutions obtained in the case of constant eddy diffusivity, shows that the simplified solution is affected by some limits that are intrinsically related to the perturbative formulation itself. The main shortcoming of the perturbation approach lies in its failure to reproduce the inertia of the sedimentation process. This results in an amplification of the system response to high-frequency external forcing, while the complete solution actually predicts a strong damping. Thus applying the perturbative model to real cases should be carefully considered when the perturbation parameter is not sufficiently small, as a rigorous application of the perturbation approach would require.