Optimal Estimation of Secondary Flow Coefficient in Compound Channels with Vegetated Floodplains

نوع مقاله : مقاله کامل (پژوهشی)


1 استادیار گروه مهندسی عمران، دانشگاه صنعتی سیرجان، سیرجان

2 مهندسی کامپیوتر، دانشگاه صنعتی سیرجان


This study adopted the Shiono-Knight model (SKM) to estimate the lateral distribution of the depth-averaged velocity within rectangular and trapezoidal compound channels with emergent vegetation in floodplains. To implement the SKM, it was required to estimate the eddy viscosity coefficient, friction coefficient, and secondary flow coefficient. The present study estimated the friction coefficient using the Colebrook–White equation modified by Rameshwaran and Shiono for vegetated beds. An analysis of eddy viscosity models across compound channels indicated that the model was not sensitive to the eddy viscosity coefficient; thus, the eddy viscosity coefficient could be assumed constant across the channel. However, the negligence of the secondary flow in the model would lead to a significant error, and it was required to calibrate the secondary flow coefficient. Thus, this study used a genetic algorithm (GA) to develop equations for the secondary flow coefficient for different sections of the compound channel under two different approaches: (1) the approach of Abril and Knight (2004), who proposed constant values for the main channel and floodplains, and (2) the equations of Devi and Khatua (2017), which related the secondary flow coefficient to the relative depth and width ratio. It was found that the secondary flow coefficient was dependent on the relative depth and width ratio. As a result, the equation optimized based on the Devi-Khatua approach outperformed the Rameshwaran-Shiono technique in estimating the lateral distribution of the velocity, with a 10.2% lower error.


Abril, J. & Knight, D. (2004). Stage-discharge prediction for rivers in flood  applying a depth-averaged model. J. Hydraul. Res., 42(6), 616–629.
Ackers, P. (1991). Hydraulic design of straight compound channels. Hydraulics Research Ltd., Wallingford.
Alawadi, W., Al-Rekabi, W.S. & Al-Aboodi, A.H. (2018). Application of the Shiono and Knight Method in asymmetric compound channels with different side slopes of the internal wall. Appl. Water Sci. 8(4), https://doi.org/10.1007/s13201-018-0663-4.
Bousmar, D. & Zech, Y. (2004). Velocity distribution in non-prismatic compound channels. In: Proceedings of the Institution of Civil Engineers-Water Management, 157(2), 99-108.
Das, B.S., Khatua, K.K. & Devi, K. (2018). Application of Lateral Distribution Method and Modified Lateral Distribution Method to the Compound Channel Having Converging Floodplains. In: Proceedings of the International Conference on Microelectronics, Computing and Communication Systems, 293-303.
Devi, K. & Khatua, K. (2017). Depth-averaged velocity and boundary shear stress prediction in asymmetric compound channels. Arab J Sci Eng. 42(9), 3849–3862.
Han, L.J., Zeng, Y.H., Chen, L. & Huai, W.X. (2016). Lateral velocity distribution in open channels with partially flexible submerged vegetation Environ. Fluid Mech., 16(6), 1267-1282.
Harris, E.L., Babovic, V. & Falconer, R.A. (2003). Velocity predictions in compound channels with vegetated floodplains using genetic programming. International Journal of River Basin Management, 1(2), 117-123.
Huai, W., Gao, M., Zeng, Y. & Li, D. (2009). Two-dimensional analytical solution for compound channel flows with vegetated floodplains, Appl. Math. Mech.-English Ed., 30, 1121-1130.     
Knight, D. & Abril, C.J. (1996). Refined calibration of a depth-averaged model for turbulent flow in a compound channel. Proc Inst Civ Eng Water Marit Energy, 118(3), 151–159.
Knight, D.W. & Shiono, K. (1996). River channel and floodplain hydraulics. In: Floodplain Processes, Anderson, M.G., Walling, D.E., Bates, P.D., eds., Chichester: Wiley, 139-181.
Knight, D.W. & Hamed, M.E. (1984). Boundary shear in symmetrical compound channels. J. Hydraul. Eng., 110(10), 1412–1430.
Knight, D.W., Yuen, K.W.H. & Alhamid, A.A.I. (1994). Boundary shear stress distributions in open channel flow. In: Physical mechanisms of mixing and transport in the environment, Beven, K., Chatwin, P. and Millbank, J., eds., Wiley, New York, 51–87.
Lashkar Ara, B. & Dehghani, I. (2016). Calibration of Shiono and Knight Model to Estimate Shear Stress for Trapezoidal Channel. Irrigation Sciences and Engineering, 38(4), 189-201.
Liu, C., Luo, X., Liu, X. & Yang, K. (2013). Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. Advances in Water Resources, 60, 148-159.
Mohseni, M., Samani, J.M. & Ayyubzadeh, S.A. (2013). Depth-averaged Velocity Distribution in Compound Channel with Vegetated Floodplains. Journal of Hydraulics, 8(3), 63-75. (In Persian)
Mohseni, M. (2015). Development a 2D Suspended Load Transport in Non-Submerged, Rigid Vegetated Floodplain of Compound Channel, Ph.D thesis, Tarbiat Modares University, Tehran, Iran.
Nepf, H. (1999). Drag, Turbulence and Diffusion in Flow Through Emergent Vegetation. Water Resources Research, 35, 479–489.
Pasche, E. & Rouve, G. (1985). Overbank flow with vegetatively roughened flood plains., Journal of Hydraulic Engineering, 111,1262.
Posey, C.J. (1967). Computation of discharge including over-bank flow. Civ. Eng., 37(4), 62–63.
Pu, J.H., Hussain, A., Guo, Y.K., Vardakastanis, N., Hanmaiahgari, P.R. & Lam, D. (2019). Submerged flexible vegetation impact on open channel flow velocity distribution: An analytical modelling study on drag and friction. Water Science and Engineering, 12(2), 121-128.
Rajaratnam, N. & Ahmadi, R.M. (1979). Interaction between main channel and floodplain flows. J. Hydr. Div., 105(5), 573–588.
Rameshwaran, P. & Shiono, K. (2007). Quasi two-dimensional model for straight overbank flows through emergent., J Hydraul Res, 45(3), 302-315.
Sellin, R.H.J. (1964). A laboratory investigation into the interaction between the flow in the channel of a river and that is over its floodplain. Houille Blanche, 7, 793–802.
Shiono, K., Takeda, M., Yang, K., Sugihara, Y. & Ishigaki, T. (2012). Modeling of vegetated rivers for inbank and overbank flows, Proceedings of the International Conference on Fluvial Hydraulics, San Jose, Costa Rica, 263 - 269.
Shiono, K. & Knight, D. (1991). Turbulent open-channel flows with variable depth across the channel. J Fluid Mech, 222, 617–646.
Shiono, K. & Knight, D.W. (1990). Mathematical models of flow in two or multi stage straight channels. In: Proceedings of the International Conference on River Flood Hydraulics. New York: John Wiley & Sons, 229-238.
Sun, X.K. & Shiono, K. )2008(. Modelling of velocity and boundary shear stress for one-line vegetation along the edge of floodplain in compound channel, ICHE, Nagoya.
Sun, X. & Shiono, K. (2009). Flow resistance of one-line emergent vegetation along the floodplain edge of a compound open channel., Adv Water Resour, 32(3), 430-438.