A simple, dimensionally sound, formula is proposed for expressing the apparent shear stress on the vertical interface between main channel and flood plain in a compound channel. An apparent friction factor is introduced and its dependence on the cross-section shape is examined based on experimental results reported in previous studies. For symmetrical smooth channels, it is found that this friction factor is essentially independent of the flow depth and is well linearly correlated with the width ratio of the compound section, at least within the ranges of practical interest where data are available. Discharge estimates obtained by incorporating the predicted shear stress in the ϕ-index method compare well with experimental results. The suggested approach is sufficiently accurate for practical applications and may be extended to other channel shapes and roughnesses depending on the acquisition of adequate data.
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- A m ,A f :
cross-sectional area of main channel and floodplain
- b :
width of main channel
- B :
total width (of main channel and floodplain)
- C fa :
apparent friction factor at the vertical interface bertween main channel and floodplain.
- g :
accelaration due to gravity
- h :
depth of main channel below the floodplain
- H :
- k :
- Q :
total compound section discharge
- Q m ,Q f :
discharge in main channel and floodplain sub-sections
- Q m′ ,Q f :
respective discharges assuming no interaction
- P :
- R :
- S 0 :
- τ :
- τ a :
average apparent shear stress at the interface between main channel and floodplain
- V :
- ΔV :
difference of mean velocity of the main channel and floodplain subsections
- w :
specific weight of water
- y :
flow depth on the floodplain
- γ :
lateral velocity gradient
- ρ :
density of water
- ϕ m ,ϕ f :
indices accounting for the interaction between main channel and floodplain
- f :
- m :
Baird, J. I. and Ervine, D. A., 1984, Resistance to flow in channels with overbank floodplain flow.Proc. 1st Intern. Conf. Hydraulic Des. in Water Resources Engineering, Southampton, England, Springer Verlag, New York, pp. 4.137–4.150.
Chow, V.T., 1959,Open Channel Hydraulics, McGraw Hill, New York.
Ghosh, S. N. and Jena, S. B., 1971, Boundary shear distribution in open channel compound,Proc. Inst. Civil Engineers, (London, England)49, 417–430.
Hadjipanos, P., 1980, Flow in compound channels with varying roughness, Thesis, University of London.
Knight, D. A. and Demetriou, J. D., 1983, Floodplain and main channel flow interaction,J. Hydr. Eng., ASCE 109(8), 1073–1092.
Knight, D. A. and Hamed, M. E., 1984, Boundary shear in symmetrical compound channels,J. Hydr. Eng., ASCE,110(10), 1412–1430.
Krishnappan, B. G. and Lau, Y. L., 1986, Turbulence modeling of flood plain flows,J. Hydr. Eng., ASCE 112(4), 251–266.
Myers, W. R. C. and Elsawy, E. M., 1975, Boundary shear in channel with floodplain,J. Hydr. Div. ASCE 101[HY7], 933–946.
Myers, W. R. C., 1978, Momentum transfer in a compound channel,J. Hydr. Res. 16(2), 139–150.
Myers, W. R. C., 1987, Velocity and discharge in compound channels,J. Hydr. Eng.,ASCE 113(6), 753–766.
Myers, W. R. C. and Brennan, E. K., 1990, Flow resistance in compound channels,J. Hydr. Res. 28(2), 141–155.
Noutsopoulos, G. K. and Hadjipanos, P., 1983, Discharge computations in compound channels,Proc. 20th IAHR Congress, Moscow, U.S.S.R., V, pp. 173–180.
Noutsopoulos, G. K. and Christodoulou, G. C., 1985, Discussion of ‘Floodplain and main channel flow interaction’, by D. A. Knight and J. D. Demetriou,J. Hydr. Div., ASCE 111(5), 884–886.
Prinos, P. and Townsend, R. D., 1984, Comprison of methods for predicting discharge in compound open channels,Adv. Water Resour. 7, 180–187.
Radojkovic, M. and Djordjevic, S., 1985, Computation of discharge distribution in compound channels,Proc. 21st IAHR Congress, Melbourne, Australia, 3, pp. 367–371.
Rajaratnam, N. and Ahmadi, R. M., 1979, Interaction between main channel and floodplain flows,J. Hydr. Div., ASCE 105(5), 573–588.
Sellin, R. J. H., 1964, A laboratory investigation into the interaction between flow in the channel of a river and that of its floodplain,La Houille Blanche 7, 793–801.
Stephenson, D. and Kolovopoulos, P., 1990, Effects of momentum transfer in compound channels,J. Hydr. Eng., ASCE 116(12), 1512–1522.
Wormleaton, P. R., Allen, J., and Hadjipanos, P., 1982, Discharge assessment in compound channel flow,J. Hydr. Div., ASCE 108(9), 975–993.
Wormleaton, P. R. and Hadjipanos, P., 1985, Flow distribution in compound channels,J. Hydr. Div., ASCE 111(2), 357–361.
Wormleaton, P. R. and Merrett, D. J., 1990, An improved method of calculation for steady uniform flow in prismatic main channel/floodplain sections,J. Hydr. Res. 28(2), 157–174.
Wright, P. R. and Carstens, H. R., 1970, Linear momentum flux to overbank sections,J. Hydr. Div., ASCE 96(9), 1781–1793.
Zheleznyakov, G. V., 1971, Interaction of channel and flood plain streams,Proc. 14th IAHR Congress, Paris, France, pp. 144–148.
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Christodoulou, G.C. Apparent shear stress in smooth compound channels. Water Resour Manage 6, 235–247 (1992). https://doi.org/10.1007/BF00872358
- Compound channels
- flood plains
- shear stress
- momentum transfer
- open channel flow