In the paper a linear stability analysis of a one-dimensional morphodynamical model is presented. The local equilibrium assumption on the solid discharge is removed and a dynamical description of the bed-load transport is employed. Both unsteady and quasi-steady flow models are analysed and discussed. The results reveal the existence, at moderate Froude number values, of perturbations related to bed elevation instability, migrating in the upstream direction both in quasi-steady and full unsteady models.
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