Skip to main content
SpringerLink
Log in

Analytical solutions for transverse distributions of stream-wise velocity in turbulent flow in rectangular channel with partial vegetation

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The theory of poroelasticity is introduced to study the hydraulic properties of the steady uniform turbulent flow in a partially vegetated rectangular channel. Plants are assumed as immovable media. The resistance caused by vegetation is expressed by the theory of poroelasticity. Considering the influence of a secondary flow, the momentum equation can be simplified. The momentum equation is nondimensionalized to obtain a smooth solution for the lateral distribution of the longitudinal velocity. To verify the model, an acoustic Doppler velocimeter (ADV) is used to measure the velocity field in a rectangular open channel partially with emergent artificial rigid vegetation. Comparisons between the measured data and the computed results show that the method can predict the transverse distributions of stream-wise velocities in turbulent flows in a rectangular channel with partial vegetation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cowna, W. L. Estimating hydraulic roughness coefficients. Agriculture Engineering, 37(7), 473–475 (1956)

    Google Scholar 

  2. Kouwen, N. and Unny, T. E. Flexible roughness in open channels. Journal of the Hydraulics Division, 99(5), 713–728 (1973)

    Google Scholar 

  3. Bennett, S. J., Pirim, T., and Barkdoll, B. D. Using simulated emergent vegetation to alter stream flow direction within a straight experimental channel. Geomorphology, 44(1–2), 115–126 (2002)

    Article  Google Scholar 

  4. Liu, C. and Shen, Y. M. Flow structure and sediment transport with impacts of aquatic vegetation. Journal of Hydrodynamics, Series B, 20(4), 461–468 (2008)

    Article  Google Scholar 

  5. Shimizu, Y., Tsujimoto, T., Nakagawa, H., and Kitamura, T. Experimental study on flow over rigid vegetation simulated by cylinders with equi-spacing (in Japanese). Proceedings of the Japan Society of Civil Engineers, 438, 31–40 (1991)

    Google Scholar 

  6. Stone, B. M. and Shen, H. T. Hydraulic resistance of flow in channels with cylindrical roughness. Journal of Hydraulic Engineering, 128(5), 500–506 (2002)

    Article  Google Scholar 

  7. Tsujimoto, T. and Kitamura, T. Experimental Study on Open-Channel Flow with Vegetated Zone along Side Wall, KHL Progressive Report, Hydraulic Laboratory, Kanazawa University, Japan, 21–35 (1992)

    Google Scholar 

  8. Wang, C., Zhu, P., Wang, P. F., and Zhang, W. M. Effects of aquatic vegetation on flow in the Nansi Lake and its flow velocity modeling. Journal of Hydrodynamics, Series B, 18(6), 640–648 (2006)

    Article  Google Scholar 

  9. Wu, F. C., Shen, H. W., and Chou, Y. J. Variation of roughness coefficients for unsubmerged and submerged vegetation. Journal of Hydraulic Engineering, 125(9), 934–942 (1999)

    Article  Google Scholar 

  10. Yang, K. J., Liu, X. N., Cao, S. Y., and Zhang, Z. X. Turbulence characteristics of overbank flow in compound river channel with vegetated floodplain (in Chinese). Journal of Hydraulic Engineering, 36(10), 1263–1268 (2005)

    Google Scholar 

  11. Shiono, K. and Knight, D. W. Turbulent open channel flows with variable depth across the channel. Journal of Fluid Mechanics, 222(5), 617–646 (1991)

    Article  Google Scholar 

  12. Huai, W. X., Gao, M., Zeng, Y. H., and Li, D. Two-dimensional analytical solution for compound channel flows with vegetated floodplains. Applied Mathematics and Mechanics (English Edition), 30(9), 1121–1130 (2009) DOI 10.1007/s10483-009-0906-z

    Article  MATH  Google Scholar 

  13. Rameshwaran, P. and Shiono, K. Quasi two-dimensional model for straight overbank flows through emergent vegetation on floodplains. Journal of Hydraulic Research, 45(3), 302–315 (2007)

    Article  Google Scholar 

  14. Tang, X. N. and Knight, D. W. Lateral distributions of streamwise velocity in compound channels with partially vegetated floodplains. Science in China, Series E: Technological Sciences, 52(11), 3357–3362 (2009)

    Article  MATH  Google Scholar 

  15. Hsieh, P. C. and Shiu, Y. S. Analytical solutions for water flow passing over a vegetal area. Advances in Water Resources, 29(9), 1257–1266 (2006)

    Article  Google Scholar 

  16. Biot, M. A. Theory of propagation of elastic waves in a fluid saturated porous solid, I: low-frequency range. Journal of the Acoustical Society of America, 28(2), 168–178 (1956)

    Article  MathSciNet  Google Scholar 

  17. Ervine, D. A., Babaeyan-Koopaei, K., and Sellin, R. H. J. Two-dimensional solution for straight and meandering overbank flows. Journal of Hydraulic Engineering, 126(9), 653–669 (2000)

    Article  Google Scholar 

  18. Abril, J. B. and Knight, D. W. Stage-discharge prediction for rivers in flood applying a depthaveraged mode. Journal of Hydraulic Research, 42(6), 616–629 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, P. R. China

    Wen-xin Huai  (槐文信), Chuan Geng  (耿 川), Yu-hong Zeng  (曾玉红) & Zhong-hua Yang  (杨中华)

Authors
  1. Wen-xin Huai  (槐文信)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuan Geng  (耿 川)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu-hong Zeng  (曾玉红)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhong-hua Yang  (杨中华)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen-xin Huai  (槐文信).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10972163 and 51079102) and the Fundamental Research Funds for the Central Universities (No. 2104001)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huai, Wx., Geng, C., Zeng, Yh. et al. Analytical solutions for transverse distributions of stream-wise velocity in turbulent flow in rectangular channel with partial vegetation. Appl. Math. Mech.-Engl. Ed. 32, 459–468 (2011). https://doi.org/10.1007/s10483-011-1430-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-011-1430-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation