Validation of the double-averaging velocity profile in decelerating flows over coarse-bed rivers

Document Type : Research Article


1 The School of Civil Engineering, Iran University of Science & Technology, Tehran, Iran

2 Water Engineering Civil Engineering Department Iran University of Science and Technology


A clear understanding of the interaction of bed-form and flow characteristics in natural streams is essential for a variety of ecological and river engineering projects such as river rehabilitation, pollution control, and stable channel design. The present study deals with the logarithmic layer of double-averaged (in time and space) streamwise velocity profiles in non-uniform flows, decelerating flow, in coarse-bed Rivers. The streamwise velocity profiles were obtained from field measurements conducted in the Haraz and Rostam Abad Rivers. Velocity measurements were collected at 200 Hz and 120 seconds by using ADV. Both riverbeds composed of coarse gravel and cobble, with relative submergences ( ) from 4.4 to 10.4. Due to the limit application of the double-averaging method in Iranian Rivers, the validity of this method was investigated by using the logarithmic law and the boundary layer characteristic method. From the observations, the flow may be divided into two different layers: the inner layer (logarithmic layer) and the outer layer. In the inner layer ( ) the double-averaged velocity profiles confirmed the logarithmic law, however, the velocity data deviated from the logarithmic law in the outer region without a particular pattern. The results of this study can help a better estimation of hydraulic parameters in coarse-bed streams, decreasing the cost of hydraulic plans in rivers.


Afzalimehr, H. (2010). Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed. Hydrological Processes, 24(3), 331–341.
Afzalimehr, H., & Anctil, F. (1998). Estimation of gravel-bed river flow resistance. Journal of Hydraulic Engineering, 124(10): 1054–1058.
Afzalimehr, H., & Anctil, F. (2000). Accelerating shear velocity in gravel-bed channels. Hydrological Sciences Journal, 45(1): 113–124.
Afzalimehr, H., Barahimi, M., & Sui, J. (2017a). Non-uniform flow over cobble bed with submerged vegetation strip. In Proceedings of the Institution of Civil Engineers-Water Management (pp. 1–16).
Afzalimehr H, Maddahi M. R., Sui. J. (2017b). Bedform Characteristics in a Gravel-Bed River. Journal of Hydrology and Hydromechanics, 65 (4): 366–377.
Afzalimehr, H., & Dey, S. (2009). Influence of bank vegetation and gravel bed on velocity and Reynolds stress distributions. International Journal of Sediment Research, 24(2): 236–246.
Afzalimehr, H., Moradian, M., & Singh, V. P. (2017). Flow Field around Semielliptical Abutments. Journal of Hydrologic Engineering, 23(2): 4017057.
Afzalimehr, H., & Rennie, C. D. (2009). Determination of bed shear stress in gravel-bed Rivers using boundary-layer parameters. Hydrological Sciences Journal, 54(1): 147–159.
Buffington J. M. and Montgomery D.R. (1997). A systematic analysis of eight decades of incipient motion studies, with special reference to gravel bedded rivers. Water Resources Research, 33(8): 1993-2029.
Barenblatt, G. I. (1982). Similarity, self-similarity, and intermediate asymptotics Theory and applications to geophysical hydrodynamics. Leningrad Gidrometeoizdat.
Bendat, J. S., & Piersol, A. G. (1986). Random data: measurement and analysis procedures. Wiley New York
Bolhassani, R., Afzalimehr, H., & Dey, S. (2015). Effects of relative submergence and bed slope on sediment incipient motion under decelerating flows. Journal of Hydrology and Hydromechanics, 63(4): 295–302.
Chanson, H. (1999). The Hydraulics of Open Channel Flow: an Introduction. Sediment Transport Mechanisms 1. Bed-load Transport.
Dey, S., (2014). Fluvial Hydrodynamics: Hydrodynamic and Sediment Transport Phenomena. Springer-Verlag, Berlin.
Emadzadeh, A., Chiew, Y. M., & Afzalimehr, H. (2010). Effect of accelerating and decelerating flows on incipient motion in sand bed streams. Advances in Water Resources, 33(9): 1094–1104.
Chanson H. (1999). The Hydraulics of Open Channel Flow: An Introduction. John Wiley & Sons. p .544
Fazlollahi, A. Afzalimehr, H. Evaluation of the validity of double-averaging for wall law application on pool (2013). Journal of Hydraulics. 8(1): 19-28 (In Persian)
Franca, M. J., Ferreira, R. M. L., Cardoso, A. H., & Lemmin, U. (2010). Double-average methodology applied to turbulent gravel-bed river flows. In Proceedings of the River Flow 2010 Conference, 56–65.
Franca, M. J., Ferreira, R. M. L., & Lemmin, U. (2008). Parameterization of the logarithmic layer of double-averaged streamwise velocity profiles in gravel-bed river flows. Advances in Water Resources, 31(6): 915–925.
Gloyi, M. Motamedi, A. Najafabadi E. (2016). Application of shear velocity derived from double-averaging on dunes. Iranian Hydraulic Conference, Iran, Qazvin (In Persian).
Gaudio, R., Miglio, A., & Dey, S. (2010). Non-universality of von Kármán’s κ in fluvial streams. Journal of Hydraulic Research, 48(5): 658–663.
Goring, D. G., & Nikora, V. I. (2002). Despiking Acoustic Doppler Velocimeter Data. Journal of Hydraulic Engineering, 128(1): 117–126.
Graf, W. H., & MS Altinakar. (1998). Fluvial hydraulics: Flow and transport processes in channels of simple geometry.
Kabiri, F., Afzalimehr, H., & Sui, J. (2017). Flow structure over a wavy bed with vegetation cover. International Journal of Sediment Research, 32(2): 186-194.
Kironoto, B. A., & Graf, W. H. (1995). Turbulence characteristics in rough non-uniform open-channel flow. Proceedings of the Institution of Civil Engineers-Water Maritime and Energy, 112(4): 336-348.
Najafabadi, E. F., Afzalimehr, H., & Rowiński, P. M. (2018). Flow structure through a fluvial pool-riffle sequence–Case study. Journal of Hydro-Environment Research, 19(October 2016): 1-15.
Nezu, I., & Nakagawa, H. (1993). Turbulence in open channels. IAHR/AIRH Monograph. Balkema, Rotterdam, the Netherlands.
Nikora, V., Goring, D., McEwan, I., & Griffiths, G. (2001). Spatially averaged open-channel flow over rough bed. Journal of Hydraulic Engineering, 127(2): 123-133.
Nikora V., McEwan I., McLean S., Coleman S., Pokrajac D., and Walters R. (2007). Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: Theoretical Background. Journal of Hydraulic Engineering, 133(8): 873-883.
Nortek, A. S. (2009). Vectrino velocimeter user guide. Nortek AS, Vangkroken, Norway.
Omid, M. & Nasrabadi, M. (2006). Sediment engineering, Manual and practice. University of Tehran Press. Tehran
Plott J.R., Diplas P. Kozarek J.L. Dancey C.L. Hill C. Sotiropoulos F. (2013). A generalized log law formulation for a wide range of boundary roughness typically encountered in natural streams. Journal of Geophysical Research Atmospheres 118(3): 1419-1431.
Reynolds, A. J. (1974). Turbulent flows in engineering. J. Wiley & Sons, New York.
Schlichting H. (1979). Boundary- layer theory. McGraw‐Hill Book Company Co. Toronto.
Shahmohammadi, R., Afzalimehr, H., & Sui, J. (2018). Impacts of turbulent flow over a channel bed with a vegetation patch on the incipient motion of sediment. Canadian Journal of Civil Engineering, 45(9): 803-816.
Simons, D. B., & Şentürk, F. (1992). Sediment transport technology: water and sediment dynamics. Water Resources Publication.
Smith, J. D., & McLean, S. R. (1977). Spatially averaged flow over a wavy surface. Journal of Geophysical Research, 82(12): 1735-1746.
Song, T. Graf. W.H. (1994). Non-uniform open-channel flow over a rough bed. Journal of Hydro science and Hydraulic Engineering, JSCE, 12: 1-25.
Song T., Chiew Y. M. (2001). Turbulence measurement in non-uniform open channel flow using Acoustic Doppler Velocimeter (ADV). Journal of Engineering Mechanics-ASCE 127(3): 219-232.
Song, T., Graf, W. H., & Lemmin, U. (1994). Uniform flow in open channels with movable gravel bed. Journal of Hydraulic Research, 32(6): 861-876.
Tennekes, H., & Lumley, J. L. (1972). A first course in turbulence. MIT press.
White, F. M. (1974). Viscous fluid flow. New York: McGraw-Hill.
Wolman, M. G. (1954). A method of sampling coarse river‐bed material. EOS, Transactions American Geophysical Union, 35(6): 951-956.
Wu B., Molinas A., and Julein P.Y. (2004) Bed-material load computations for nonuniform sediments. Journal of Hydraulic Engineering, ASCE, 130(10): 1002-1012
Yalin, S.‌ M. (1972). Mechanics of sediment transport. Pergamon Press, Oxford, New York.
Yanda, R., Harada, M., & Tamagawa, I. (2018). Study on double-averaged velocity profile for rough bed and low-flow conditions, Journal of Japan Society of Civil Engineers, JSCE, 74(4): 619-624.