ABSTRACT A three dimensional numerical model is introduced which is able to calculate the sediment transport rate and the according bed changes over time in river bends. The model was tested against data from laboratory experiments. Several detailed studies of the lateral bed load movement on side slopes were investi-gated to find the appropriate formulas describing the physical phenomena of sediment transport in alluvial channel bends. Considering a stability analysis of a sediment particle on a side slope, and introducing an ap-propriate algorithm which takes the characteristic movement of sediments in river bends into account, the cal-culated velocities as well as the bed level changes over time showed a good agreement with the measure-ments.

Introduction Sediment transport in river bends is of highest interest in the field of sedimentation engineering. The lateral bed load transport and corresponding lateral migration of rivers is one of the major unknown herein. Many research studies have been carried out to investigate particle movement on side slopes in channel bends. The flow in river bends is dominated by transverse secondary currents. The sediments are eroded by the accelerated flow at the outer part of the bend and transported by the secondary currents to the inner part. Here they tend to deposit due to the reduced velocity and shear stress, forming a so called point bar. Additionally, bed load particles tend to move down slope in response to gravity. This force is acting contrary to the force from the secon-dary currents, and keeps the river bed in an equilib-rium condition.

Bed Load Transport in River Bends Sediment transport in river bends is mainly influenced by the complex flow structure. To understand morphodynamics in river bends and consequently to derive formulas for sediment transport on side slopes, a number of researchers (van Bendegom 1947; Engelund 1974; Kikkawa et al. 1976; Ikeda et al. 1982 a, b; Olesen 1987; Kovacs & Parker 1994) has done investigations in this field. The main re-sults are the following. The sediment particle on a side slope has a lower critical shear stress compared to those on the flat bed. Furthermore it is observed that the sediment particle being transported on a transversal slope is not following the direction of the near bed velocity as it would on a flat bed. To reproduce the sediment transport in channel bends, it was necessary to find reasonable models from the literature. Investigations on an incipient motion criteria of particles on side slopes leads to a formula calculating a factor k which is reducing the critical shear stress of sediments resulting in an effective shear stress for particles on side slopes (Brookes 1963). The factor K is a function of the sediments’ friction angle of repose, the transversal slope and the direction of the near bed velocity.
The characteristic mechanism how the sediments are transported in channel bends is described by an equation derived by Engelund (1981). It is a further development of a formula by Engelund (1974) which was based on a static consideration of the forces acting on a grain on side slopes. The improvements are done by introducing a modified shields parameter which is derived empirically considering the skin friction of the sediments.
The model leads to an angle of the sediment transport related to the direction of the near bed velocity, being a function of both the transversal slope and the shields parameter related to the skin friction. At the initial stage of the scour and deposition process in a channel bend, where the bed is still flat, a bed load particle will move along the same direction as the flow at the bed which is skewed inward due to the effect of the secondary flow. However, as the deformation of the bed develops, the path of the particles does not longer follow the direction of the flow at the bed due to the effect of gravity. Dependent on the side slope of the bed geometry the bed load is transported more in the direction of the outer part of the channel bend.

Results The Figure above illustrates the contour map of the bed level changes of the numerical calculations after the full simulation time. The bed changes were calculated with the default sediment transport algorithm. Herein, the sediment transport direction is in accordance with the direction of the near bed flow velocity. Considering the Figure above one can see that the maximum values of the calculated bed changes are matching the measured ones from the physical model. However the locations of the maxima in bed changes are shifted towards the downstream direction of about 10°. The maximum scour and the minimum water depth are at a bend angle of about 70° and 40°, respectively. More over the plane dimensions of the point bar deposit at the inner side of the bend are too small compared to the measured values. These deviations could be interpreted as an over estimation of the sediment transport in longitudinal direction. Most likely this is due to the fact that the lateral sediment transport in this simulation was too small.

The Figure above shows the contour map of the bed level changes with the zero reference to the initial flat bed, with the modified bed load transport algorithm ac-cording to the model after Engelund Looking at the bed changes one can see that these results are much closer to the measurements than that without the enhanced sediment transport algo-rithm. In this case, both the range of the bed eleva-tion and the location of the maximum values are matching the results from the physical model. The plane dimensions of the scour and deposition are also fitting better the observed values.

Conclusion A three dimensional model is presented which is ca-pable to calculate the flow field and the sediment transport in a channel bend of 90°. The model uses formulas based on a stability analysis for sediment particle on a side slope, and introduces an appropri-ate algorithm which takes the characteristic move-ment of sediments in river bends into account. The calculated velocities as well as the bed level changes over time showed good agreement to measurements from a physical model study.