Applicability of kinematic, diffusion and quasi-steady wave models to shallow mud flows

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.