A Well-posed Model for Mixed-Sediment River Morphodynamics

Abstract

The mixed-size character of sediment is a necessary property to ex- plain physical phenomena such as downstream fining or the presence of armor layers. The active layer model was developed to model mixed-size sediment in river morphodynamics. This model assumes that the topmost part of the bed, the active layer, has no vertical stratification and interacts with the flow. The substrate, below the active layer, only interacts with the active layer in case of aggradation or degradation. The active layer model has been used in morphody- namic modelling for more than four decades but under certain conditions it may become mathematically ill-posed. When a model becomes ill-posed, the solu- tion presents unphysical oscillations and its predictive capabilities are lost. We present two alternatives to the active layer model. The first one retains the basic concepts and guarantees well-posedness by means of an additional parameter controlling the celerity of mixed-size sediment processes. The second solution yields a well-posed model by means of considering the sediment transport rate as a stochastic process rather than to adapt instantaneously to the flow. Both models provide reasonable results when compared to measured data from a lab- oratory experiment conducted under conditions in which the active layer model is ill-posed.