Skip to main content
SpringerLink
Log in

Secondary flow coefficient of overbank flow

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

Abstract

This paper presents a 2D analytical solution for the transverse velocity distribution in compound open channels based on the Shiono and Knight method (SKM), in which the secondary flow coefficient (K-value) is introduced to take into account the effect of the secondary flow. The modeling results agree well with the experimental results from the Science and Engineering Research Council-Flood Channel Facility (SERC-FCF). Based on the SERC-FCF, the effects of geography on the secondary flow coefficient and the reason for such effects are analyzed. The modeling results show that the intensity of the secondary flow is related to the geometry of the section of the compound channel, and the sign of the K-value is related to the rotating direction of the secondary flow cell. This study provides a scientific reference to the selection of the K-value.

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. Yang, K., Cao, S., and Knight, D. W. Flow patterns in compound channels with vegetated floodplains. Journal of Hydraulic Engineering 133(2), 148–159 (2007)

    Article  Google Scholar 

  2. Zhang, M., Shen, Y., and Wu, X. 3D numerical simulation on overbank flows in compound channels (in Chinese). Journal of Hydroelectric Engineering 25(5), 31–36 (2006)

    Google Scholar 

  3. Huai, W., Chen, W., and Tong, H. 3D numerical simulation on overbank steady open channel flows in compound channels (in Chinese). Advances in Water Science 14(1), 15–19 (2003)

    Google Scholar 

  4. Krishnappan, B. G. and Lau, Y. L. Turbulence modeling of floodplain flows. Journal of Hydraulic Engineering 112(4), 251–266 (1986)

    Article  Google Scholar 

  5. 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 

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

    Article  Google Scholar 

  7. Huai, W., Xu, Z., Yang, Z., and Zeng, Y. Two dimensional analytical solution for a partially vegetated compound channel flow. Applied Mathematics and Mechanics (English Edition) 29(8), 1077–1084 (2008) DOI 10.1007/s10483-008-0811-y

    Article  MATH  Google Scholar 

  8. Xu, W. Study on computational method of overbank flow in channels with compound cross section (in Chinese). Journal of Hydraulic Engineering (6), 21–26 (2001)

  9. Yang, Z. H. and Gao, W. Two dimensional analytical solution for overbank flows with interaction between the main channel and floodplain (in Chinese). Journal of Sichuan University (Engineering Science Edition) 41(5), 42–46 (2001)

    MathSciNet  Google Scholar 

  10. Castanedo, S., Medina, R., and Mendez, F. J. Models for the turbulent diffusion terms of shallow water equations. Journal of Hydraulic Engineering 131(3), 217–223 (2005)

    Article  Google Scholar 

  11. Abbott, M. B. and Price, W. A. Coastal, Estuarial, and Harbour Engineers’ Reference Book, Taylor & Francis, London/New York (1994)

    Google Scholar 

  12. Shome, M. L. and Steffler, P. M. Lateral flow exchange in transient compound channel flow. Journal of Hydraulic Engineering 124(1), 77–80 (1998)

    Article  Google Scholar 

  13. Stelling, G. S., Wiersma, A. K., and Willemse, J. Practical aspects of accurate tidal computations. Journal of Hydraulic Engineering 112(9), 802–817 (1986)

    Article  Google Scholar 

  14. Blumberg, A. F. and Mellor, G. L. A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Coastal Ocean Models (ed. Heaps, N. S.), American Geophysical Union, Washington, DC, 1–16 (1987)

    Google Scholar 

  15. Roig, L. C. and King, I. P. Continuum model for flows in emergent marsh vegetation. Estuarine and Coastal Modeling, Proceedings of the 2nd International Conference (eds. Spaulding, M. L., Bedford, K., Blumberg, A., Cheng, R., and Swanson, C.), ASCE, New York, 268–279 (1992)

    Google Scholar 

  16. Hu, S. and Kot, S. C. Numerical model of tides in Pearl River estuary with moving boundary. Journal of Hydraulic Engineering 123(1), 21–29 (1997)

    Article  Google Scholar 

  17. Benque, J. P., Cunge, J. A., Feuillet, J., Hauguel, A., and Holly, F. M., Jr. New method for tidal current computation. Journal of the Waterway Port Coastal and Ocean Division 108(3), 396–417 (1982)

    Google Scholar 

  18. Darby, S. E. and Thorne, C. R. Predicting stage-discharge curves in channels with bank vegetation. Journal of Hydraulic Engineering 122(10), 583–586 (1996)

    Article  Google Scholar 

  19. Balzano, A. Evaluation of methods for numerical simulation of wetting and drying in shallow water flow models. Coastal Engineering 34(1–2), 83–107 (1998)

    Article  Google Scholar 

  20. Huai, W., Gao, M., Zeng, Y., 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 

  21. Tang, X. and Knight, D. W. A general model of lateral depth-averaged velocity distributions for open channel flows. Advances in Water Resources 31(5), 846–857 (2008)

    Article  Google Scholar 

  22. Knight, D. W., Omran, M., and Tang, X. Modeling depth-averaged velocity and boundary shear in trapezoidal channels with secondary flows. Journal of Hydraulic Engineering 133(1), 39–47 (2007)

    Article  Google Scholar 

  23. McGahey, C. A Practical Approach to Estimating the Flow Capacity of Rivers Application and Analysis, Ph. D. dissertation, Open University, Milton Keynes, UK (2006)

    Google Scholar 

  24. Ikeda, S. Self-formed straight channels in sandy beds. Journal of the Hydraulics Division 107(4), 389–406 (1981)

    Google Scholar 

  25. Chlebek, J. and Knight, D. W. A new perspective on sidewall correction procedures, based on SKM modelling. Proceedings of the International Conference on Fluvial Hydraulics (eds. Ferreira, R. M. L., Alves, E. C. T. L., Leal, J. G. A. B., and Cardosa, A. H.), Taylor & Francis, London/NewYork, 135–144 (2006)

    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

    Zhong-hua Yang  (杨中华), Wei Gao  (高 伟) & Wen-xin Huai  (槐文信)

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

    You can also search for this author in PubMed Google Scholar

  2. Wei Gao  (高 伟)
    View author publications

    You can also search for this author in PubMed Google Scholar

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

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhong-hua Yang  (杨中华).

Additional information

Communicated by Shi-qiang DAI

Project supported by the National Natural Science Foundation of China (No. 50749031) and the Doctoral Fund of the Ministry of Education of China (No. 20070486022)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, Zh., Gao, W. & Huai, Wx. Secondary flow coefficient of overbank flow. Appl. Math. Mech.-Engl. Ed. 31, 709–718 (2010). https://doi.org/10.1007/s10483-010-1305-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-010-1305-9

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation