Diffusive approximation for unsteady mud flows with backwater effect

In the analysis of flood routing within the shallow-water framework the adoption of the Diffusive Wave (DW) instead of the Full Dynamic (FD) model may provide a significant reduction of the computational effort, but it is important to understand the conditions in which this approximation may be employed. In this paper, the applicability range of the DW model is investigated through linear analysis of a depth-integrated Herschel-Bulkley model. Assuming as the initial condition a steady hypocritical decelerated flow, induced by downstream backwater, the propagation characteristics of a small perturbation predicted by the DW and FD models are compared. The results show that the spatial variation on the initial profile may preclude the application of DW model with a prescribed accuracy. Whenever the method is applicable, the rising time of the flood must satisfy additional constraints, whose dependence on the flow depth, along with the Froude number and the rheological parameters, are deeply analyzed and discussed.