Use of simplified wave models in shallow unsteady flows of power law fluids

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