Modeling Depth-Averaged Velocity and Boundary Shear Stress in Rectangular Compound Channels with Secondary Flows
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 1
Abstract
The depth-averaged equation of flow in a rectangular compound channel with secondary flows is established by analyzing the forces acting on the elemental water body and using Newton’s second law. The analytical solution to the transverse variation of depth-averaged velocity is presented that includes the effects of lateral momentum transfer and secondary flow in addition to bed friction. Different forms of boundary conditions at the internal wall between the rectangular main channel and the adjoining floodplain are presented. A comparison with the published experimental data demonstrates that the present model is capable of predicting the distributions of depth-averaged velocity and boundary shear stress. The results also indicate that the secondary flow and boundary conditions have influences on them. Finally, the key parameters in the model, such as the Darcy–Weisbach coefficient, the momentum transfer coefficient, and the secondary flow coefficient are also discussed and analyzed.
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Acknowledgments
The authors gratefully acknowledge the assistance of Professor Donald W. Knight at the University of Birmingham, U.K., who provided the experimental data at <www.flowdata.bham.ac.uk>. The authors gratefully acknowledge the support of the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 201051) and the National Natural Scientific Foundation of China (No. 11072161 and No. 50709021). The authors are also grateful to the anonymous reviewers for their very helpful comments on this paper.
References
Abril, J. B., and Knight, D. W. (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, U.K.
Ackers, P. (1993). “Flow formulae for straight two-stage channels.” J. Hydraul. Res., 31(4), 509–531.
Atabay, S. (2001). “Stage-discharge, resistance and sediment transport relationships for flow in straight compound channels.” Ph.D. thesis, Univ. of Birmingham, Birmingham, U.K.
Bousmar, D., and Zech, Y. (1999). “Momentum transfer for practical flow computation in compound channels.” J. Hydraul. Eng., 125(7), 696–706.
Cao, Z., Meng, J., Pender, G., and Wallis, S. (2006). “Flow resistance and momentum flux in compound open channels.” J. Hydraul. Eng., 132(12), 1272–1282.
Carling, P. A., Cao, Z., Holland, M. J., Ervine, D. A., and Babaeyan-Koopaei, K. (2002). “Turbulent flow across a natural compound channel.” Water Resour. Res., 38(12), 1270.
Ervine, D. A., Babaeyan-Koopaei, K., and Sellin, R. H. J. (2000). “Two-dimensional solution for straight and meandering overbank flows.” J. Hydraul. Eng., 126(9), 653–669.
Knight, D. W., Omran, M., and Abril, J. B. (2004). “Boundary conditions between panels in depth-averaged flow models revisited.” River Flow 2004, Proc., 2nd Int. Conf. on Fluvial Hydraulics, Greco, M., Carravetta, A., and Morte, R. D., eds., Vol. 1, Balkema, 371–380.
Knight, D. W., Omran, M., and Tang, X. N. (2007). “Modeling depth-averaged velocity and boundary shear in trapezoidal channels with secondary flows.” J. Hydraul. Eng., 133(1), 39–47.
Lambert, M. F., and Sellin, R. H. J. (1996). “Discharge prediction in straight compound channels using the mixing length concept.” J. Hydraul. Res., 34(3), 381–394.
Liao, H., and Knight, D. W. (2007). “Analytic stage-discharge formulas for flow in straight prismatic channels.” J. Hydraul. Eng., 133(10), 1111–1122.
Naot, D., Nezu, I., and Nakagawa, H. (1993). “Hydrodynamic behavior of compound rectangular open channels.” J. Hydral. Eng., 119(3), 390–408.
Omran, M., Atabay, S., Knight, D. W., and Seckin, G. (2008). “Boundary conditions for a depth-averaged flow model in overbank flow.” RiverFlow 2008, Altinakar, M. S., Kokpinar, M. A., Aydin, I., Cokgar, S., and Kirkgoz, S., eds., Vol. 1, Cesme, Turkey, 485–492.
Pezzinga, G. (1994). “Velocity distribution in compound channel flows by numerical modeling.” J. Hydraul. Eng., 120(10), 1176–1198.
Rameshwaran, P., and Shiono, K. (2007). “Quasi two-dimensional model for straight overbank flows through emergent vegetation on floodplains.” J. Hydraul. Eng., 45(3), 302–315.
Rezaei, B., and Knight, D. W. (2009). “Application of the Shiono and Knight method in compound channels with non-prismatic floodplains.” J. Hydraul. Eng., 47(6), 716–726.
Schlichting, H. (1960). Boundary layer theory, 4th Ed., McGraw-Hill, New York.
Shiono, K., and Knight, D. W. (1988). “Two dimensional analytical solution for a compound channel.” Proc., Third Int. Symp. on Refined Flow Modelling and Turbulence Measurements, Iwasa, Y., Tamai, N., and Wada, A., eds., Tokyo, Japan, 503–510.
Shiono, K., and Knight, D. W. (1991). “Turbulent open-channel flows with variable depth across the channel.” J. Fluid Mech., 222, 617–646.
Tang, X., and Knight, D. W. (2008a). “A general model of lateral depth-averaged velocity distributions for open channel flows.” Adv. Water Resour., 31(5), 846–857.
Tang, X., and Knight, D. W. (2008b). “Lateral depth-averaged velocity distributions and bed shear in rectangular compound channels.” J. Hydraul. Eng., 134(9), 1337–1342.
van Prooijen, B. C., Battjes, J. A., and Uijttewaal, W. S. J. (2005). “Momentum exchange in straight uniform compound channel flow.” J. Hydraul. Eng., 131(3), 175–183.
Wormleaton, P. R., Allen, J., and Hadjipanos, P. (1982). “Discharge assessment in compound channel flow.” J. Hydr. Div., 108(9), 975–994.
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© 2013 American Society of Civil Engineers.
History
Received: Jun 13, 2011
Accepted: May 30, 2012
Published online: Jul 23, 2012
Published in print: Jan 1, 2013
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