Simplified Wave Models Applicability to Shallow Mud Flows Modeled as Power-Law Fluids

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 quasi-steady 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.