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3D modeling of transient bed changes in a sine generated meandering laboratory channel

ABSTRACT A three dimensional numerical model is presented to calculate the sediment transport rate and the corresponding transient bed changes in sine-generated meandering laboratory channels. Transient flow pattern as well as bed movements in simple bended laboratory channels have been successfully modeled with 2D and 3D numerical models before. However, when it comes to the successive formation of meander bends, the spatial propagation of the helical flow and its effect on the bed deformation is not fully understood yet. It is strongly depending on the deflection angle ? of the meander bend and the width to depth ratio of the channel. In addition to this geometric characteristic, bed forms were prevailing in the experiments. The present study showed how a three dimensional numerical model is able to calculate the flow field and the sediment transport in a sine-generated laboratory channel with two consecutive meander bends and occurring bed forms.

Water flow and sediment transport in meandering river is of high interest in the field of river engineer-ing. The major local erosion in river bends under steady or unsteady flow conditions is causing huge problems to the riverine structures. Prediction of the time-dependent bed changes and the lateral bed load transport with the corresponding lateral migration with the help of computer programs is becoming more and more popular. The major problem herein is the fact that the flow field in river bends is highly three-dimensional. The flow is dominated by trans-verse 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 in-ner part. Here they tend to deposit due to the reduced velocity and shear stress, forming a so called point bar. This effect is highly depending on the geometry of the channel, e.g. deflection angle of the bends or number of consecutive bends, and also on the width to depth ratio of the channel. With the increasing computer power over the last 15 years, it is now pos-sible to carry out fully 3D computations for such cases. Demuren & Rodi (1986) used a three dimen-sional model where the turbulence was predicted by the k-? model, to calculate the flow and the transport of a neutral tracer in a meandering channel. Re-cently, Wilson et al (2003) computed the fully de-veloped three dimensional velocity distributions in a meandering channel over a fixed natural bed and showed good agreement with measurements. Ruether & Olsen (2005) computed the bed changes over time in a sharply bended 90° channel with spe-cial respect to steep transversal slopes. Wu et al (2000) computed the flow in a 180° bend including suspended and bed load transport. Zeng et al (2005) computed the bed changes in a 180° bend, too. All of the results showed good agreement with measured data. Bed forms did not occur in any of the previous studies. The present study focused on the simulation of the bed changes in a laboratory channel with sine-generated consequent bends, deflection angle ? = 70°, and prevailing bed roughness caused of bed forms, like dunes and ripples.

The laboratory data used in the present study were taken from da Silva & Tarek (2006b). Movable bed experiments were carried out in a sine generated channel. The 0.8 m wide flume was filled with sand of the size of D50 = 0.65 mm of about 0.2 m and steady, uniform flow was established. The sediments were relatively well sorted with a ratio of D60 to D10 of 1.89. The measured data for two experimental runs were then compared to the numerical simula-tion. The two different experiments were denoted Run 1 und Run 5 where the bed changes were meas-ured after 60 min and 170 min for Run 1 and 5, re-spectively.

As it can be seen from table 1, the most significant difference of the two experiments is the width to depth ration of 10.67 and 18.18, respectively. For both experiments, the hydraulic conditions are listed in table 1. Figure 1 shows the experimental setup. The flow is top to bottom. (In the following Figures the flow is from left to right.) According to the different hydraulic setups, two different bed patterns were observed. The bed de-formation in Run 1, depicted in Figure 3 can be de-scribed in the following way: The locations of the deepest erosion were determined to be in the two cross over parts of the flume. Point bars developed at the inner side of each of the apex, growing with the increasing downstream coordinate. The magni-tude of the bed changes over time was in the range of -0.12 m and +0.4 m. In addition one can see that the location of the maximum erosion and deposition in each of the bends were not located in the same cross section. The bed deformation in Run 5 is depicted in Fig-ure 5. The areas of maximum erosion are located at the outside end of each of the bends with a maxi-mum bed change of -0.12 m. Similar to Run 1, the characteristic point bars developed and grow with the downstream, increasing coordinate. Where as the scour in the most downstream cross section was with -0.08 m less deep than the scours further upstream. In opposite to Run 1, the location of the maximum erosion and deposition were found to be in the same cross section, just slightly downstream of the apex. Figure 2 shows the location of the cross section being compared. Cross section 11 and 15 are located right after the first bend and cross section 26 and 30 right after the second bend.

Fig. 1: Experimental setup (daSilva & Tarek, 2006)

3.1 Results and discussion
3.1.1 Simulation results of Run 1

Since the hydraulic performance of the present model was tested intensively in meandering chan-nels (Wilson et al., 2003), the present study was focusing on the performance of predicting bed de-formation only. Two different laboratory setups were simulated. The hydraulic conditions of each experiment are de-scribed in chapter 2. The results are presented herein. Comparing the plan view of Run 1, depicted in Figure 2 for the experiments and in Figure 3 for the simulation, one can see the overall agreement with the measured data. The first two bends are characterized by a typical point bar at the apex, accompanied by a small scour in the center of the channel. The maximum scour was located further downstream, almost at the cross over, on the outside of the channel. Looking at simulated bed changes in the first two bends, one can see that the bed defor-mation was predicted well. The location of the maximum scours and bar positions matched. How-ever there was some disagreement in the pattern of the last bend. In the experiment, the scour was lo-cated far more at the outside of the bend as in the previous two bends. This characteristic was not found in the results of the numerical run. So far there is no physical explanation for this longitudinal asymmetric bed development (da Silva, 2006a). The bed pattern seen in the plan view can also be shown in a longitudinal view. One can see that the position of the maxima match well, but the absolute magnitude of the scours is slightly overestimated.

Fig. 2: Bed changes in Run#1 (daSilva & Tarek, 2006)

Calculated bed changes in Run#1

3.1.2 Simulation results of Run 5
The plan views of the bed changes from the ex-perimental and from the numerical model are de-picted in the figures 4 and 5, respectively. As well as for the results in Run 1 one can see that the overall pattern matched. The magnitude of the bed changes also matched. However, the scouring in the longitu-dinal direction was over estimated. The scour spread too far downstream.
One can see that the positions of the maxima are calculated to be at the same locations as in the physical model. For Run 5, in the sediment transport capacity formula, the default value of z = 0.053 was changed to z = 0.009. This means that the sediment transport capacity had to be reduced to get reasonable results.

Fig. 4: Bed changes in Run#5 (daSilva & Tarek, 2006)

Fig. 5: Calculated bed changes in Run#5

The transient bed changes of a meandering labo-ratory channel with two different width to depth ra-tios have been successfully modeled. The calculated bed changes are in good agreement with the meas-urements for both cases. The numerical model was enhanced with a roughness approach taking into ac-count the presence of bed forms. The results were very sensitive to the formulas for bed form height and bed roughness. The roughness approach seemed to be strongly connected to the development stage of a bed form and therefore to the sediment transport capacity. In the opinion of the authors there is more research needed for the universal implementation of a roughness approach taking bed form roughness into account. Furthermore, a wider range of the width to depth ratio should be tested in order to vali-date the present results. It seems that the width to depth ratio has a larger influence on the bed pattern in meandering channels as it is believed in literature today. To make any reliable conclusion, the model should be tested on data from experiments with dif-ferent deflection angles Q , too.

The authors would like to thank Dr. A.M. da Silva who was so kind to distribute the data used in this study and giving fruitful advices for a successful modeling of the data. In addition, the first author likes to thank the Norwegian Research Council for their support through the BeMatA Program.

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