Abstract
An analytical solution for the vertical profiles of the horizontal velocity of channel flow with submerged shrub-like vegetation is investigated in this paper. At first, a shape function is proposed to fit the diameter change of different types of shrub-like vegetation. Using the momentum theorem and the mixing-length turbulence model, an analytical solution for the vertical profile of the horizontal velocity within the vegetation is obtained. The velocity distribution of the whole column is determined in tandem with the logarithmic velocity profile above the vegetation. The solution is compared with experimental data in excellent agreement. The results show that the flow above the vegetation has a logarithmic velocity profile while the flow within the vegetation is impacted greatly by the shape and density of vegetation. The flows within shrub-like vegetations are non-uniform and vary inversely with the shrub diameter.
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References
Baptist M, Babovic V et al (2007) On inducing equations for vegetation resistance. J Hydraulic Res 45(4): 435–450
Darby S (1999) Effect of riparian vegetation on flow resistance and flood potential. J Hydrol Eng 125(5): 443–454. doi:10.1061/(ASCE)0733-9429
Huai W, Zeng Y, Xu Z (2009) Three-layer model for vertical velocity distribution in open channel flow with submerged rigid vegetation. Adv Water Resour 32(4): 487–492. doi:10.1016/j.advwatres.2008.11.014
Hui E, Jiang C, Pan Y (2009) Vertical velocity distribution of longitudinal flow in a vegetated channel. J Tsinghua Univ (Sci & Tech) 49(6): 818–821
Jackson P (1981) On the displacement height in the logarithmic velocity profile. J Fluid Mech 111: 15–25. doi:10.1017/S0022112081002279
Klopstra D, Barneveld HJ, Van Noortwijk JM (1997) Analytical model for hydraulic roughness of submerged vegetation. In: Managing water: coping with scarcity and abundance, Proceedings of the 27th IAHR Congress, San Francisco, pp. 775–780
Righetti M, Armanini A (2002) A flow resistance in open channel flows with sparsely distributed bushes. J Hydrol 269(1–2): 55–64. doi:10.1016/S0022-1694(02)00194-4
Thom A (1997) Momentum absorption by vegetation. Q J R Meteorl Soc 97: 414–428. doi:10.1002/qj.49709741404
Van Velzen E, Jesse P, Cornelissen P, Coops H (2003) Hydraulic resistance of vegetation in floodplains, Part 2: Background Document Version 1-2003. Ministry of Transport, Public Works and Water Management, Institute for Inland Water Management and Waste Water Treatment, report 2003.029, Lelystad, The Netherlands
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Liu, Z., Chen, Y., Zhu, D. et al. Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation. Environ Fluid Mech 12, 341–346 (2012). https://doi.org/10.1007/s10652-012-9243-6
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DOI: https://doi.org/10.1007/s10652-012-9243-6