Modeling the effect of dune sorting on the river long profile

River dunes, which occur in low slope sand bed and sand-gravel bed rivers, generally show a downward coarsening pattern due to grain flows down their avalanche lee faces. These grain flows cause coarse particles to preferentially deposit at lower elevations of the lee face, while fines show a preference for its upper elevations. Before considering the effect of this dune sorting mechanism on the river long profile, let us first have a look at some general trends along the river profile. Tributaries increasing the river's water discharge in streamwise direction also cause a streamwise increase in flow depth. As under subcritical conditions mean dune height generally increases with increasing flow depth, the dune height shows a streamwise increase, as well. This means that also the standard deviation of bedform height increases in streamwise direction, as in earlier work it was found that the standard deviation of bedform height linearly increases with an increasing mean value of bedform height. As a result of this streamwise increase in standard deviation of dune height, the above-mentioned dune sorting then results in a loss of coarse particles to the lower elevations of the bed that are less and even rarely exposed to the flow. This loss of coarse particles to lower elevations thus increases the rate of fining in streamwise direction. As finer material is more easily transported downstream than coarser material, a smaller bed slope is required to transport the same amount of sediment downstream. This means that dune sorting adds to river profile concavity, compared to the combined effect of abrasion, selective transport and tributaries. A Hirano-type mass conservation model is presented that deals with dune sorting. The model includes two active layers: a bedform layer representing the sediment in the bedforms and a coarse layer representing the coarse and less mobile sediment underneath migrating bedforms. The exposure of the coarse layer is governed by the rate of sediment supply from upstream. By definition the sum of the exposure of both layers equals unity. The model accounts for vertical sediment fluxes due to grain flows down the bedform lee face and the formation of a less mobile coarse layer. The model with its vertical sediment fluxes is validated against earlier flume experiments. It deals well with the transition between a plane bed and a bedform-dominated bed. Applying the model to field scale confirms that dune sorting increases river profile concavity.