Morphodynamics of river bed variation with variable bedload step length

Abstract. Here we consider the 1-D morphodynamics of an erodible bed subject to bedload transport. Fluvial bed elevation variation is typically modeled by the Exner equation, which, in its classical form, expresses mass conservation in terms of the divergence of the bedload sediment flux. An entrainment form of the Exner equation can be written as an alternative description of the same bedload processes, by introducing the notions of an entrainment rate into bedload and of a particle step length, and assuming a certain probability distribution for the step length. This entrainment form implies some degree of nonlocality, which is absent from the standard flux form, so that these two express…