The challenge to pass from shallow water flows to sediment transport and bed evolution in a coupled 1D/2D model

Overview & Synopsis

Sediment transport is present in the river flows at all stages and may cause a change of the shape of the bed with consequences on the flowing conditions. The finer part of the sediments is carried by the flow in the whole water column while the coarser one stays close to the bed. Except strong variations of hydraulic parameters, the finer sediments follow the flow and are seldom deposited. In a river in which the flow can be considered as 1-D, the sediment discharge is usually limited by the capacity of the flow to carry the sediments. The simpler way to estimate this capacity uses an empirical equation that considers the median diameter (D50) although the behaviour of a mixture of sediments is known to be different. The erosion or deposition terms are estimated as the difference between the transport capacity and the actual sediment discharge. Then, the mass of sediments is distributed across the width of the bed generally taking into account the local shear stress. The model should represent these processes of mixing, fining or coarsening but also the features of the various sediment layers. In a 2-D representation of the flow and the bed, the question of distribution of the erosion and deposition is no longer a problem if the processes can be reduced to what occurs in a vertical column, The behaviour of the sediments can be described in the same way as in a 1-D model focusing on the median diameter and considering additional modelling to represent the evolution of the diameter and of such key parameters that are the critical shear stress for erosion or deposition. Then, if the sediment modelling in the 1-D and 2-D models is unified (as it is the presented software RubarBE and Rubar20TS), the coupling of such models is mathematically simple. The water flux will be accompanied by a sediment flux defined using the concentration but also the sediment diameter and its standard deviation. However, similarly to the coupling of hydrodynamic models, if getting boundary parameters from the 2-D side is easy, it is not so simple for the 1-D side. For instance, the concentration and diameter of the sediments near the bank of a river are often quite lower from the ones in the centre of the main channel.