Morphodynamic model of Lower Yellow River: flux or entrainment form for sediment mass conservation?
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Abstract. Sediment mass conservation is a key factor that constrains river morphodynamic processes. In most models of river morphodynamics, sediment mass conservation is described by the Exner equation, which may take various forms depending on the problem in question. One of the most widely used forms of the Exner equation is the flux-based formulation, in which the conservation of bed material is related to the streamwise gradient of the sediment transport rate. An alternate form of the Exner equation, however, is the entrainment-based formulation, in which the conservation of bed material is related to the difference between the entrainment rate of bed sediment into suspension and the deposition rate of suspended sediment onto the bed. In the flux form, sediment transport is regarded to be in local equilibrium (i.e., sediment transport rate locally equals sediment transport capacity). However, the entrainment form does not require this constraint: the sediment transport rate may lag in space and time behind the changing flow conditions. In modeling the fine-grained Lower Yellow River, it is usual to treat sediment conservation in terms of an entrainment (nonequilibrium) form rather than a flux (equilibrium) form, in consideration of the condition that fine-grained sediment may be entrained at one place but deposited only at some distant location downstream. However, the differences in prediction between the two formulations have not been comprehensively studied to date. Here we study this problem by comparing the results of flux-based and entrainment-based morphodynamics under conditions typical of the Lower Yellow River, but simplified for clarity of comparison. We used sediment transport equations specifically designed for the Lower Yellow River. We find that in a treatment of a 200km reach using a single characteristic bed sediment size, there is little difference between the two forms since the corresponding adaptation length is relatively small. However, a consideration of sediment mixtures shows that the two forms give very different patterns of grain sorting: clear kinematic waves occur in the flux form but are diffused out in the entrainment form. Both numerical simulation and mathematical analysis show that the morphodynamic processes predicted by the entrainment form are sensitive to sediment fall velocity.
