Dune formation in gradually widening channels as a morphodynamic process seeking equilibrium between flow and sediment transport: Insights from numerical studies

Gravel-bed rivers exhibit diverse topographies that offer critical habitats and ecosystem services. Previous studies indicated that the geometric effect of channel width variations can significantly influence the morphodynamic processes of gravel-bed rivers. In particular, flume experiments revealed that at the wide sections, riffle topographies build by migrating fronts of bedload sediment. Also, in a gradually widening segment of the upper Xindian River (Taiwan), we observed the migration of a dune-like bedform driven by flood events. However, how the channel widening triggers the dune formation and development of the migrating front are not well known. In this study, we use the Delft3D model to simulate the morphodynamic processes of linearly widening rectangular channels 300 m in length, with the model setting mimicking the prototype Xindian River. The channels have plane bed of a slope 0.002, with constant inflows of water and sediment. A series of simulations were performed to test sensitivity, with the width expansion ratesranging from 0.02 to 0.18 m/m, grain sizes and flowrates giving Shields numbers between 0.11 and 0.22, all correspond to full transport modes. Based on the simulations, we identify two stages of morphodynamic development: (1) geometry-dominated, and (2) topography-dominated stages. At stage 1, flow entering from the upstream narrow cross-section is strongly affected by channel expansion, resulting in the transverse components of velocity and sediment transport, and thus depositions along the sidewalls. Longitudinally, the increase of channel width reduces the velocity and bed shear stress along the centerline, leading to deposition in the central area. These transverse and longitudinal deposits together evolve as a crescent-shaped dune near the entrance. As the dune migrates downstream it continues to grow, and eventually a steep lee face would develop, which defines stage 2. The stoss-lee topography causes a sudden rise in the water surface and thus sudden drops in the velocity and bed shear stress. Over 90% of bedload sediment would deposit on the lee face, forming a migrating front of deformation that aligns with the prograding lee face. Maps of spatial flow concentration reveal that such development of dune is a morphodynamic process that seeks an equilibrium between flow and sediment transport in response to the perturbation of channel widening. At stage 1, the transverse flows toward the sidewalls are redistributed by the side deposits, while the highly concentrated longitudinal flow near the centerline is redistributed by the central deposit, both seek to uniformize the concentration of flow over a cross-section. The migrating front observed at stage 2 represents the cross-section where the uniformity of flow concentration is reestablished. Results further reveal that, once stage 2 is reached, increasing or decreasing the flowrate only aggrades or degrades the stoss slope to seek a new equilibrium between flow and sediment transport, while the migrating front keeps pace with the prograding lee face, as evidenced by its track during the rising or falling limbs of the flood hydrograph in the Xindian River.