Diffusive approximation for unsteady mud flows with backwater effect

•Adoption of Diffusive Wave (DW) model for studying mud flood propagation.•Mud fluid represented through a linearized depth integrated Herschel–Bulkley model.•Individuation of DW applicability criteria in terms of flood rising time.•Significant effect of the downstream backwater is retrieved on the DW applicability.•The results provide guidelines for correctly applying the simplified DW model.

The adoption of the Diffusive Wave (DW) instead of the Full Dynamic (FD) model in the analysis of mud flood routing within the shallow-water framework may provide a significant reduction of the computational effort, and the knowledge of the conditions in which this approximation may be employed is therefore important. In this paper, the applicability of the DW approximation of a depth-integrated Herschel–Bulkley model is investigated through linear analysis. 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 mud flood must satisfy additional constraints, whose dependence on the flow depth, along with the Froude number and the rheological parameters, is deeply analyzed and discussed.