GEP  Vol.7 No.4 , April 2019
An Improved Analytical Model for Vertical Velocity Distribution of Vegetated Channel Flows
Abstract: The existence of vegetation plays an important role to protect the ecosystem and water environment in natural rivers and wetlands, but it alters the velocity field of flow, consequently influencing the transport of pollutant and biomass. As a pre-requisite for the analysis of environmental capacity in a channel, the vertical velocity distribution of flows has attracted much research attention; however, there is yet lack of a good prediction model available. For the channel with submerged vegetation, the vertical velocity distribution in the lower vegetation layer will be different from that in the upper flow layer of non-vegetation. In this paper, after review on the most recent two-layer model proposed by Baptist et al., the author has proposed an improved two-layer analytical model by introducing a different mixing length scale (λ). The proposed model is based on the momentum equation of flow with the turbulent eddy viscosity assumed as a linear relationship with the local velocity. The proposed model is compared with the Baptist model for different datasets published in the literature, which shows that the proposed analytical model can improve the vertical velocity distribution prediction well compared with the Baptist model for a range of data. This study reveals that the λ is well related with the submergence of vegetation (H/h), as suggested by . When the constant β is taken as 3/100, the proposed model shows good agreement with a wide range of datasets studied: flow depth (H)/vegetation height (h) in 1.25 to 3.33, different vegetation densities of a in 1.1 to 18.5 m−1 (a defined as the frontal area of the vegetation per unit volume), and bed slopes in (1.38 - 4.0) × 10−3.
Cite this paper: Tang, X. (2019) An Improved Analytical Model for Vertical Velocity Distribution of Vegetated Channel Flows. Journal of Geoscience and Environment Protection, 7, 42-60. doi: 10.4236/gep.2019.74004.

[1]   Baptist, M. J., Babovic, V., Rodriguez Uthubrubu, J., Keijzer, M., Uittenbogaadr, R. E., Mynett, A., & Verwey, A. (2007). On Inducing Equations for Vegetation Resistance. Journal of Hydraulic Research, 45, 435-450.

[2]   Carollo, F. G., Ferro, V., & Termini, D. (2002). Flow Velocity measurements in Vegetated Channels. Journal of HydraulicEngineering, 128, 664-673.

[3]   Cheng, N. (2015). Single-Layer Model for Average Flow Velocity with Submerged Rigid Cylinders. Journal of HydraulicEngineering, 140, Article ID: 06015012.

[4]   Defina, A., & Bixio, A. C. (2005). Mean Flow and Turbulence in Vegetated Open Channel Flow. Water Resources Research, 41, W07006.

[5]   Dimitris, S., & Panayotis, P. (2011). Macroscopic Turbulence Models and Their Application in Turbulent Vegetated Flows. Journal of Hydraulic Engineering, 137, 315-332.

[6]   Dunn, C., Lopez, F., & Garcia, M. (1996). Mean Flow and Turbulence Structure Induced by Vegetation: Experiments. Hydraulic Engineering, Series 51, Urbana, IL: Department of Civil Eng., University of Illinois at Urbana-Champaign.

[7]   Ghisalberti, M., & Nepf, H. M. (2004). The Limited Growth of Vegetated Shear Layers. Water Resources Research, 40, w07502.

[8]   Ghisalberti, M., & Nepf, H. M. (2006). The Structure of the Shear Layer in Flows over Rigid and Flexible Canopies. Environmental Fluid Mechanics, 6, 277-301.

[9]   Hao, W. L., Zhu, C. J., & Chang, X. P. (2014). Research on Vertical Distribution of Longitudinal Velocity in the Flow with Submerged Vegetation. Journal of Heibei University of Engineering, 31, 64-67. (In Chinese)

[10]   Huai, W. X., Chen, Z., & Han, J. (2009). Mathematical Model for the Flow with Submerged and Emerged Rigid Vegetation. Journal of Hydrodynamics, 21, 722-729.

[11]   Huai, W., Wang, W., Hu, Y., Zeng, Y., & Yang, Z. (2014). Analytical Model of Mean Velocity Distribution in an Open Channel with Double-Layered Rigid Vegetation. Advances in Water Resources, 69, 106-113.

[12]   Katul, G. G., Poggi, D., & Ridolfi, L. (2011). A Flow Resistance Model for Assessing the Impact of Vegetation on Flood Routing Mechanics. Water Resources Research, 47, W08533.

[13]   Klopstra, D., Barneveld, H. J., Noortwijk, J. M., & Velzen, E. H. (1997). Analytical Model for Hydraulic Roughness of Submerged Vegetation. In Proceeding of 27th Congress of IAHR, Theme A (pp. 775-780). New-York: American Society of Civil Engineers (ASCE).

[14]   Kouwen, N., Unny, T. E., & Hill, H. M. (1969). Flow Retardance in Vegetated Channels. Journal of the Irrigation and Drainage Division, 95, 329-342.

[15]   Kubrak, E., Kubrak, J., & Rowinski, P. M. (2008). An Experimental Study of Flow through Rigid Vegetation. Hydrological Sciences Journal, 53, 905-920.

[16]   Lopez, F., & Garcia, M. H. (2001). Mean Flow and Turbulence Structure of Open-Channel Flow through Non-Emergent Vegetation. Journal of Hydraulic Engineering, 127, 392-402.

[17]   Meijer, D. G., & Van Velzen, E. H. (1999). Prototype-Scaleflume Experiments on Hydraulic Roughness of Submerged Vegetation. In 28th International IAHR Conference (1-7). Delft: IAHR.

[18]   Nepf, H. M. (2012). Flow and Transport in Regions with Aquatic Vegetation. Annual Reviews Fluid Mechanics, 44, 123-142.

[19]   Nepf, H. M., & Koch, E. W. (1999). Vertical Secondary Flows in Submerged Plant-Like Arrays. Limnology and Oceanography, 44, 1072-1080.

[20]   Nepf, H. M., & Vivoni, E. R. (2000). Flow Structure in Depth-Limited, Vegetated Flow. Journal of Geophysical Research, 105, 28547-28557.

[21]   Nezu, I., & Sanjou, M. (2008). Turburence Structure and Coherent Motion in Vegetated Canopy Open-Channel Flows. Journal of Hydro-Environment Research, 2, 62-90.

[22]   Nguyen, H. T. (2012). Characteristics of Hydraulic Resistance and Velocity Profile in Vegetated Open-Channel Flows (pp. 1-201). PhD Thesis, Singapore: Nanyang Technological University.

[23]   Nikora, N., Nikora, V., & O’Donoghue, T. (2013). Velocity Profiles in Vegetated Open-Channel Flows: Combined Effects of Multiple Mechanisms. Journal of Hydraulic Engineering, 139, 1021-1032.

[24]   Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D., & Katul, G. G. (2004). The Effect of Vegetation Density on Canopy Sub-Layer Turbulence. Boundary-Layer Meteorology, 111, 565-587.

[25]   Rahimi, H., Tang, X., & Wang, X. (2018). Numerical Study on Mixing Layer Vegetation in Open Channel Flow. In Proceedings of the 12th International Symposium on Ecohydraulics (ISE2018) (1-9). Tokyo, Japan.

[26]   Shimizu, Y., & Tsujimoto, T. (1994). Numerical Analysis of Turbulent Open-Channel Flow over a Vegetation Layer Using k-Turbulence Model. Journal of Hydroscience and Hydraulic Engineering, 11, 57-67.

[27]   Singh, P., Rahimi, H., & Tang, X. (2019). Parameterization of the Modeling Variables in Velocity Analytical Solutions of Open-Channel Flows with Double-Layered Vegetation. Environmental Fluid Mechanics, 19, 1-20.

[28]   Stoesser, T., Kim, S. J., & Diplas, P. (2010). Turbulent Flow through Idealized Emergent Vegetation. Journal of Hydraulic Engineering, 136, 1003-1017.

[29]   Stone, B. M., & Shen, H. T. (2002). Hydraulic Resistance of Flow in Channels with Cylindrical Roughness. Journal of Hydraulic Engineering, 128, 500-506.

[30]   Tang, X. (2017). An Improved Method for Predicting Discharge of Homogeneous Compound Channels Based on Energy Concept. Flow Measurement and Instrumentation, 57, 57-63.

[31]   Tang, X. (2018a). A Mixing-Length-Scale-Based Analytical Model for Predicting Velocity Profiles of Open Channel Flows with Submerged Rigid Vegetation. Water and Environment Journal, 32, WEJ12434.

[32]   Tang, X. (2018b). Methods for Predicting Vertical Velocity Distributions in Open Channel Flows with Submerged Rigid Vegetation. In Proceedings of 21st IAHR-APD Congress (Vol. 1, pp. 567-576). Yagyakart, Indonesia: Universitas Gadjah Mada

[33]   Tang, X. (2019a). Evaluating Two-Layer Models for Velocity Profiles in Open-Channels with Submerged Vegetation. Journal of Geoscience and Environment Protection, 7, 68-80.

[34]   Tang, X. (2019b). A New Apparent Shear Stress-Based Approach for Predicting Discharge in Uniformly Roughened Compound Channels. Flow Measurement and Instrumentation, 65, 280-287.

[35]   Tang, X., & Ali, S. (2013). Evaluation of Methods for Predicting Velocity Profiles in Open Channel Flows with Submerged Rigid Vegetation. In Proceedings of the 35th IAHR World Congress (Vol. 4, B1, pp. 1744-1755). Beijing: Tsinghua University Press.

[36]   Tang, X., & Knight, D. W. (2009). Lateral Distributions of Streamwise Velocity in Compound Channels with Partially Vegetated Flood Plains. Journal of Science in China Series E: Technological Sciences, 52, 3357-3362.

[37]   Tang, X., Knight, D. W., & Sterling, M. (2011). Analytical Model of Streamwise Velocity in Vegetated Channels. Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics, 164, 91-102.

[38]   Tang, X., Rahimi, H., Singh, P., Wei, Z., Wang, Y., Zhao, Y., & Lu, Q. (2018). Experimental Study of Open-Channel Flow with Partial Double-Layered Vegetation. In Proceedings of the 1st International Symposiumon Water Resource and Environmental Management (pp. 1-7). London: EDP Sciences,Hamilton House.

[39]   Tang, X., Sterling, M., & Knight, D. W. (2010). A General Analytical Modelfor Lateral Velocity Distributions in Vegetated Channels. In A. Dittrich, K. Koll et al. (Eds.), River Flow 2010 (Vol. 1, pp. 469-476). BrundesanstaltfurWasserbau.

[40]   Temple, D. M. (1986). Velocity Distribution Coefficients for Grass-Lined Channels. Journal of Hydraulic Engineering, 112, 193-205.

[41]   Tsujimoto, T., & Kitamur, T. (1990). Velocity Profile of Flow in Vegetated Bed Channels (pp. 43-55). KHL Progress Report 1, Hydrualic Lab., Kazavava University.

[42]   White, F. M. (1974). Viscous Fluid Flow. New York: McGraw-Hill.

[43]   Yang, W., & Choi, S. (2010). A Two-Layer Approach for Depth-Limited Open Channel Flows with Submerged Vegetation. Journal of Hydraulic Research, 48, 466-475.