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In this paper we derive a new morphological model, with an extended version of the sediment transport model for the mean step length (the average distance travelled by sediment particles), in which this mean step length depends on the mean bed shear stress. This model makes the step length increase with increasing flow, in line with previous experimental results. To account for suspension and the large-scale turbulent structures in rivers, the step length also depends explicitly on water depth. This approach enabled modelling of the transition from dunes to the upper-stage plane bed. It was shown that by increasing the step length, the lag between shear stress and bed load transport rate increases, and the dunes eventually become smoother and lower, until finally the dunes wash out. The newly adopted model approach is tested successfully with a synthetic data set from the literature, where plane bed conditions are indeed reached in the model, similar to the results of a more advanced model. It is shown that with increasing discharge, the flow increases, which leads to higher step length and to the washing out of the dunes. Although the present model still overestimates the dune height for river cases, the potential of the model concept for river dune dynamics, including the transition to upper-stage plane bed, is shown. The model results indicate that, if a transition to upper-stage plane bed occurs in a realistic river scenario, a reduction of the water depth of approximately 0.5 m can occur.

Modelling Regime Changes of Dunes to Upper-Stage Plane Bed in Flumes and in Rivers