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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.

Simplified wave models - such as kinematic, diffusion and quasi-steady - are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows, and especially for flood routing. While their use may guarantee a significant reduction of the computational effort, it is mandatory to define the conditions in which they may be confidently applied. The present paper investigates the applicability conditions of the kinematic, diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids. The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress, such as clay or kaolin suspensions, which are frequently encountered in Chinese rivers. In the framework of a linear analysis, the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one. Based on this comparison, applicability criteria for the different wave approximations for mud flood of power-law fluids are derived. The presented results provide guidelines for selecting the appropriate approximation for a given flow problem, and therefore they may represent a useful tool for engineering predictions.

Unsteady shallow-layer flows may be described through full dynamic models or using simplified momentum equations, based on kinematic, diffusion, and quasi-steady approximations, which guarantee a reduction of the computational effort. This paper aims to investigate through linear analysis the applicability range of simplified shallow-wave models with special concern to unsteady flows of mud. Considering a three-equation depth-integrated Herschel-Bulkley model, the applicability of the approximated wave models is discussed comparing the propagation characteristics of a small perturbation of an initial steady uniform flow as predicted by the simplified models with those of the full dynamic model. Based on this comparison, applicability criteria for the different wave approximations for mud flows of Herschel-Bulkley fluids, which account for the effects of the rheological parameters, are derived. The results show that accounting for the fluid rheology is mandatory for the choice of an appropriate simplified model. DOI: 10.1061/(ASCE)HE.1943-5584.0000881. © 2014 American Society of Civil Engineers.

For unsteady flow problems, such as propagation of flood waves in open channels, simplified models, know as kinematic, diffusion and quasi-steady, are widely used instead of solving the full dynamic model. In order to correctly use these models, it is mandatory to define the conditions in which they may be applied. The present paper investigate the applicability conditions of the kinematic, diffusion and quasi-steady dynamic shallow wave models for mud flows, modeled as a power law fluid. In the framework of a linear analysis, the applicability ranges are defined by comparing the propagation characteristics of a sinusoidal perturbation to the initial steady uniform flow predicted by the simplified models with those of the full dynamic one. The present results provide guidelines for selecting an appropriate approximation for modeling unsteady power law fluid flow problems and they may represent a useful tool for engineering predictions.

The commonly used approach for modelling unsteady river morphological processes considers Saint Venant-Exner equations, with local equilibrium condition for the solid discharge evaluation. Despite its widespread application, some physical behaviors related to sediment dynamics are not presented by the above model. Recently, some different morphological models have been proposed, in order to overcome these limitations. In this paper a two-phase morphological model is presented. The model eigenstructure is analysed and its hyperolic nature is shown. Simulations of laboratory documented test-cases are finally carried out, enlightenin the potentialities of the proposed model.