Parameterization of the modeling variables in velocity analytical solutions of open-channel flows with double-layered vegetation

  • P. SinghEmail author
  • H. R. Rahimi
  • X. Tang
Original Article


This paper presents a descriptive analysis of the double layer vegetation flow and the application of different empirical models for velocity distribution in vegetation flow. To establish the models, extensive experiments are carried out using plastic dowels of differential heights, configurations and densities. The previous models based on empiricism and momentum balance are applied here and found to work satisfactorily. However, it is found out that the boundary conditions play a significant role to capture inflection over vegetation level. Furthermore, the most important factor for capturing the inflection above zero plane displacement is to understand the intermediate boundary conditions and their superposition rather than extremum conditions. Therefore a new model for mixing length over the short vegetation height has been suggested. The results from the velocity distributions, turbulence intensity and vorticity of the experimental data are used to derive a new relationship for mixing length under certain assumptions. For establishing the proposed model other researchers’ data are considered and finally corroborated for the validation set, which suggests that the proposed model agrees reasonably well with the measured data.


Boundary layer Vegetative flow Double-layered Mixing length Von-Karman street 



The authors would like to thank the Nanjing Hydraulic Research Institute and their staff for their support, and also acknowledge the financial support by the Research Development Funding of XJTLU (RDF-15-01-10).


  1. 1.
    Poggi D, Porporato A, Ridolfi L, Albertson JD, Katul GG (2004) The effect of vegetation density on canopy sub-layer turbulence. Bound Lay Meteorol 111(3):565–587CrossRefGoogle Scholar
  2. 2.
    Kouwen N, Unny TE, Hill HM (1969) Flow retardance in vegetated channels. J Hydraul Div ASCE 95(IR2):329–342Google Scholar
  3. 3.
    Klopstra D, Barneveld HJ, Van Noortwijk JM, Van Velzen EH (1997) Analytical model for hydraulic roughness of submerged vegetation. In: Proceeding of 27th congress of IAHR, theme A, San Francisco, ASCE, pp 775–780Google Scholar
  4. 4.
    Carollo FG, Ferro V, Termini D (2002) Flow velocity measurements in vegetated channels. J Hydraul Eng 128(7):664–673CrossRefGoogle Scholar
  5. 5.
    Ghisalberti M, Nepf HM (2002) Mixing layers and coherent structures in vegetated aquatic flows. J Geophys Res 107(C2):3-1–3-11CrossRefGoogle Scholar
  6. 6.
    Nepf H, Ghisalberti M, White B, Murphy E (2007) Retention time and dispersion associated with submerged aquatic canopies. Water Resour Res 43:W04422CrossRefGoogle Scholar
  7. 7.
    Yang W, Choi S (2010) A two-layer approach for depth-limited open channel flows with submerged vegetation [J]. J Hydraul Res 48(4):466–475CrossRefGoogle Scholar
  8. 8.
    Katul G, Poggi D, Ridolfi L (2011) A flow resistance model for assessing the impact of vegetation on flood routing mechanics. Water Resour Res 47(8):W08533CrossRefGoogle Scholar
  9. 9.
    Nepf HM (2012) Hydrodynamics of vegetated channels. J Hydraul Res 50(3):262–279CrossRefGoogle Scholar
  10. 10.
    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, Sept. 8–13, Chengdu, ChinaGoogle Scholar
  11. 11.
    Nikora N, Nikora V, O’Donoghue T (2013) Velocity profiles in vegetated open-channel flows: combined effects of multiple mechanisms. J Hydraul Eng 139(10):1021–1032CrossRefGoogle Scholar
  12. 12.
    Huai W, Wang W, Hu Y, Zeng Y, Yang Z (2014) Analytical model of the mean velocity distribution in an open channel with double-layered rigid vegetation. Adv Water Resour 69:106–113CrossRefGoogle Scholar
  13. 13.
    Tang X (2018) Methods for predicting vertical velocity distributions in open channel flows with submerged rigid vegetation. In: Proceedings of 21st IAHR-APD congress, Sept. 2–5, vol 1, pp 567–576. Yogyakarta, IndonesiaGoogle Scholar
  14. 14.
    Huai W, Hu Y, Zeng Y, Han J (2012) Velocity distribution for open channel flows with suspended vegetation. Adv Water Resour 49:56–61CrossRefGoogle Scholar
  15. 15.
    Tang H, Tian Z, Yan J, Yuan S (2014) Determining drag coefficients and their application in modelling of turbulent flow with submerged vegetation. Adv Water Resour 69:134–145CrossRefGoogle Scholar
  16. 16.
    Tang X (2018) A mixing-length-scale based analytical model for predicting velocity profiles of open channel flows with submerged rigid vegetation. Water Environ J. Google Scholar
  17. 17.
    Liu D, Diplas P, Fairbanks JD, Hodges CC (2008) An experimental study of flow through rigid vegetation. J Geophys Res 113:F04015. Google Scholar
  18. 18.
    Liu D, Diplas P, Hodges CC, Fairbanks JD (2010) Hydrodynamics of flow through double layer rigid vegetation. Geomorphology 116(3–4):286–296CrossRefGoogle Scholar
  19. 19.
    Raupach MR, Finnigan JJ, Brunet Y (1996) Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Bound Lay Meteorol 78(3–4):351–382CrossRefGoogle Scholar
  20. 20.
    Nepf H, Ghisalberti M, White B, Murphy E (2007) Retention time and dispersion associated with submerged aquatic canopies. Water Resour Res 43:W04422. CrossRefGoogle Scholar
  21. 21.
    Nepf HM, Vivoni ER (2000) Flow structure in depth-limited, vegetated flow. J Geophys Res 105(C12):28547–28557CrossRefGoogle Scholar
  22. 22.
    López F, García MH (2001) Mean flow and turbulence structure of open-channel flow through non-emergent vegetation. J Hydraul Eng 127(5):392–402CrossRefGoogle Scholar
  23. 23.
    Ghisalberti M, Nepf HM (2004) The limited growth of vegetated shear layers. Water Resour Res 40(7):W07502CrossRefGoogle Scholar
  24. 24.
    Huai WX, Chen ZB, Han J, Zhang LX, Zeng YH (2009) Mathematical model for the flow with submerged and emerged rigid vegetation. J Hydrodyn 21(5):722–729CrossRefGoogle Scholar
  25. 25.
    MATLAB version R2018a [Computer software]. MathWorks, Natick, MAGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of EngineeringXi’an Jiaotong-Liverpool UniversitySuzhouChina

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