We adopt most of model input datasets from the Cach′ı Reservoir flushing observations in Costa Rica (Brandt & Swenning 1999) despite the lack of detailed data on flushing. The model inputs are summarized in Table 1. The solid and liquid discharges released at the upstream boundary are assumed to be a rectangular shaped hydrograph and sedimento- graph. We define the initial concentration as clean water (C = 0) with uniform flow depth along the stretch of the river, whose slope is assumed constant. The river channel geom- etry is assumed to be a wide rectangular channel thus we consider discharge per unit width (q = Q/B). A simulation domain length of 500 km is selected so as to observe the sediment wave dynamics over a long spatial scale.
5.2 Suspended sediment wave dynamics
Figure 2 shows the longitudinal profile of suspended sediment and the hydrodynamic waves at different time steps. At the initial stage of the release the two waves are in phase (Fig. 2a) and as the waves travel downstream they start to separate (Figs. 2b,c) with the separation increas- ing further downstream and finally the two waves are completely separated (Fig. 2d). Such physical phenomenon was also observed on field investigation of sediment flushing operation of the Cachí Reservoir in Costa Rica (Brandt 2005). Figure 2 also shows that the deposition (red line and is multiplied by 20 for visualisation purpose) is observed to be enhanced as the waves separate and most of the deposition is observed at the tail of the hydrodynamic wave. At the same time concentration wave decreases at the point of deposition. This shows that the interaction between the two waves significantly controls the deposition of the suspended sediments.
5.3 Effect of wave celerity factor 5.3.1 Wave celerity factor
The relationship between the celerity factor and selected hydraulic variables (depth, dis- charge, Rouse number, and relative roughness) are analysed for five different grain sizes. Figure 3 shows the plots of the relationships of depth, discharge, Rouse number, and relative roughness with α. The calculated range of variation of α applied in the model is between 0.93 to 0.97 (shown in Fig. 3 for d50= 230 μm). There is high dependence of α on flow depth and discharge for a given sediment grain size (Figs. 3a,b). As the flow depth or discharge increases the celerity factor generally increases regardless of the grain size. The celerity factor for fine grains is higher since the Rouse number is relatively small as a result giving a more uniform
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Figure 2. Sediment and hydrodynamic waves at various time steps: relative depth (H–H0)/(Hp–H0),
relative concentration (C–C0)/(Cp–C0) and relative depth of deposition 20 * (ζ – ζ0)/(ζp – ζ0) where ζp, Hp,
and Cp= peak depth of deposition, peak flow depth, and peak concentration and ζ0, H0, and C0= mini-
mum depth of deposition, base flow depth, and base concentration respectively.
concentration profile. For increasing Rouse number the celerity factor decreases regardless of the sediment grain size (Fig. 3c). The relationship between relative bed roughness and the celerity factor (Fig. 3d) is similar to the case of Rouse number such that as the relative bed roughness increases the celerity factor decreases regardless of the grain size. We also investi- gated the computed celerity factor for two different description of the reference height (zr).
We found that the ranges of variation of the computed celerity factor α with depth and dis- charge for the different grain sizes remained the same for zr= 2d50 and zr= 3d90. Thus, defining
the reference height (zr) as 2d50 (e.g. Zyserman & Fredsoe 1994) or as 3d90 (e.g. Van Rijn 1984) does not affect the estimated value of α.
5.3.2 Sediment concentration wave dynamics
Figure 4 shows the longitudinal profile of suspended sediment and the hydrodynamic waves at different time steps for two cases where the first is when the sediment wave celerity is cor- rected and the second is with the regular assumption that the sediment wave travels with average flow velocity (α = 1). In the latter case (shown in Fig. 4 in broken lines) there is less deposition comparatively since the wave separation is less enhanced. The region and length of deposition is also relatively different. There is less deposition when α = 1 as a result the local concentration becomes higher than the one corrected by the celerity factor. This agrees well with two-dimensional (2-D) model study of Huybrechts et al. (2010). We evaluated the
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mass balance at the end of simulation for the two cases: with and without the celerity factor. We observed that the proportion of boundary inputs of sediments that deposit were 10% and 7% and remain in suspension are 90% and 92% without and with celerity factor respectively. But we recognize that these figures may not lead us to a general conclusion as the computed percentages depend on the length of the domain as well as the duration of simulation. It is observed (Figs. 4c,d) that without celerity factor the suspended load is over predicted com- pared to the case with α < 1. Huybrechts et al. (2010) implemented the celerity factor in 2-D model and compared simulated suspended load with the result of three-dimensional (3-D) model simulation and they obtained acceptable agreement with observed one when the celer- ity factor is considered. The effect of the celerity factor is also more evident and higher on the suspended load than on the concentration since the estimation of the suspended sediment load is directly related to the celerity factor. Over all, the sediment wave celerity affects the deposition of the fine sediments and its proper implementation is expected to improve the modelling of the deposition and transport of suspended sediments.
5.3.3 Sediment concentration and load behaviour
Figures 5a,b show the longitudinal pattern of modelled sediment concentration and loads respectively at t = 20 hr of the simulation with and without celerity factor when there is no bed exchange (E − D = 0). When the celerity factor is applied there is increment of sediment concentration, above the amount of concentration applied at the boundary, at the tail of concentration wave and at the tail of the hydrodynamic wave. When the celerity factor is not applied (α = 1) such local increase in concentration is not evident at all. As shown in Equa- tion 9, the last term of the equation contributes to this behaviour in concentration. But this term as well as the celerity factor could be very relevant in modelling suspended sediment Figure 3. The relationship celerity factor with depth (H), discharge (q), Rouse number (Ro), and relative roughness ( *)
r .
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transport. On the other hand, as shown in Figure 5b the sediment load shows a decrease at its front with its peak lower than the case of α = 1. Figures 6a,b show the time evolution of sediment load and concentration at two downstream stations (x = 90 km, and 300 km from release point). With the celerity factor sediment load wave shows some decrease at its front and at the front of the hydrodynamic wave (Fig. 6a) though it agrees well with that of α = 1 at the tail of the hydrodynamic wave. The effect of the celerity factor on the local increment of sediment concentration is evident only on the rising limb of the hydrodynamic wave. When the two waves are fully separated (Fig. 6b) the local increment vanishes. Overall, the local sediment concentration increase due to the celerity factor does not increase the sediment load.
Figure 4. Sediment and hydrodynamic wave dynamics at various time steps with and without celerity factor: relative depth (H), relative concentration (C), and relative sediment load (Qs) (Qs− Qs0)/(Qsp− Qs0)
where Qsp and Qs0= peak and base sediment loads respectively.
Figure 5. Sediment concentration (a) and sediment load (b) at t = 20 hr with and without celerity factor when there is no bed exchange.
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172 6 CONCLUSIONS
We studied how the interaction between the waves of suspended sediments and liquid discharge is controlled by the sediment wave celerity during reservoir sediment flushing operation. The effect of the sediment wave celerity on wave interaction and depositional proc- esses has been investigated at larger spatial scale. Preliminary results of this study shows that the wave celerity controls the wave interaction significantly and thus the traditional assump- tion of representing sediment wave celerity as equal to the average flow velocity may lead to under-prediction of sediment deposition. We observed that the celerity factor enhances the wave separation and more deposition can be expected. We also investigated the dependence of the celerity factor on flow depth, discharge, Rouse number and relative roughness. There is generally an increasing trend in celerity factor with depth and discharge, while a decreasing trend is observed with Rouse number and relative roughness. The results presented in this study are based on the assumption that there is no sediment supply from the bed and only sediments supplied from the upstream are entrained and transported. The effect of changes of bed slope and channel geometry and dimensions were not taken in to account in this first analysis. The model also assumed the suspended sediments transported are uniform in grain size.
ACKNOWLEDGEMENTS
This work has been carried out within the SMART Joint Doctorate (Science for the Manage- ment of Rivers and their Tidal systems) funded with the support of the Erasmus Mundus programme of the European Union.
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