Analytical Model For Stage-Discharge Estimation In Meandering Compound Channels With Submerged Flexible Vegetation
A natural river often forms as a meandering channel to maintain a balance between bed erosion and sediment deposition. On both sides of a river, floodplains are an ideal habitat for vegetation because they are close to a water source and are not inundated during the majority of the year.
When floods occur, floodplains with vegetation are inundated, which can help the main channel carry flow downstream. However, the presence of submerged floodplain vegetation leads to an increase in resistance on the floodplains and decreases the floodplain conveyance capacity and channel conveyance capacity relative to a channel with non-vegetated floodplains. Therefore, stage-discharge relationships in smooth and vegetated compound channels are different due to the extra drag force caused by floodplain vegetation.
Previous studies have proposed various methods of estimating the stage-discharge relationship in meandering compound channels. For example, the divided panel method and the conventional Manning’s equation have been combined to improve the accuracy of discharge prediction (Greenhill and Sellin, 1993). A predictive equation for the conveyance capacity was proposed using dimensionless analysis and used to accurately estimate discharges in channels with various bed slopes, sinuosities and water depths (Shiono et al., 1999). However, a valid model does not yet exist to predict the stage-discharge relationship in a meandering channel with submerged flexible vegetation, which serves as the motivation for this study.
The goal of this study is to propose an analytical model to estimate the stage-discharge relationship in a meandering compound channel with dense, submerged, flexible vegetation. A governing equation in curvilinear coordinates is derived from the momentum equation and flow continuity equation. The relationship between the mean velocity within the canopy and the depth-averaged velocity is proposed based on the method of Nepf and Ghisalberti (2008). The lateral shear stresses were demonstrated to be sufficiently small such that they were ignored in the governing equation. Finally, the analytical solution with a simple structure was proposed.
The data from two flume experiments and one field study were used to verify the predictive capability of the proposed model. First, the proposed model was verified using the measurements from MartínVide et al. (2008). The channel bed was covered with gravel. These bed conditions were equivalent to those of the riverbed covered by an armored layer, which is a typical scenario in natural rivers. Second, this model was further verified using the experimental data from Shiono et al. (2009). The channel bed consisted of fine sand and was modified based on the flow condition, which is similar to the bed condition of the downstream Yangtze River, China. The proposed model was shown to accurately predict subarea discharges and total discharge with a mean relative error of 2%.
In the field, the height of vegetation on floodplains is different. Thus, the field data from the River Blackwater, UK (Sun et al. 2010) were used to further verify the model, which involves a natural river with both submerged and emergent grass on the floodplains. The predicted discharges agree well with flood recordings.
In summary, our model is capable of accurately predicting both subarea discharges and total discharge in a meandering compound channel with dense, submerged, flexible vegetation on floodplains at high flow conditions. This model could be a powerful tool for hydraulic engineers and river managers, who care about the stage-discharge in a natural river.
These findings are described in the article entitled Analytical model for stage-discharge estimation in meandering compound channels with submerged flexible vegetation, recently published in the journal Advances in Water Resources. This work was conducted by Yuqi Shan from Chengdu University of Information Technology, and Xingnian Liu, Kejun Yang, and Chao Liu from Sichuan University.
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