Abstract
A simple formula is proposed to predict the vertical distribution of a suspended load concentration in a 2D steady turbulent flow. The proposed formula significantly improves the well-known Rouse formula where sediment concentration has an infinitely large value at the channel bottom and a zero value at the water surface. Based on this formula and the logarithmic velocity profile, a theoretical elementary function for the transport rate of a suspended load is developed. This equation improves the Einstein equation in which the unit-width suspended sediment discharge must be solved by numerical integration and a contradiction between the lower limit of the integral and that of velocity distribution exists.
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References
Asaeda, T., Nakai, M., Manandhar, S.K., Tamai, N., 1989. Sediment entrainment in channel with rippled bed. Journal of Hydraulic Engineering ASCE, 115(3):327–339.
Bechteler, W., 1987. Stochastic model of suspended solid dispersion. Journal of Hydraulic Engineering ASCE, 113(1):16–28.
Bogardi, J., 1974. Sediment Transport in Alluvial Streams. Akademial Kiodo, Budapest.
Charafi, M.M., Sadok, A., 2000. Quasi-three-dimensional mathematical modeling of morphological processes based on equilibrium sediment transport. International Journal of Modern Physics C, 11(7):1425–1436. [doi:10.1142/S0129183100001267]
Einstein, H.A., Chien, N., 1954. Second Approximation to the Solution of the Suspended Load Theory. Chien’s Collection of Research Papers (1990). Qinghua University Press, Beijing, p.30.
Engelund, F., 1965. A criterion for the occurrence of suspended load. La Houille Blanche, 6:607.
Graf, W.H., Cellino, M., 2002. Suspension flows in open channels: experimental study. Journal of Hydraulic Research, 40(4):435–447.
Grass, A.J., 1971. Structural factors of turbulent flow over smooth and rough boundaries. Journal of Fluid Mechanics, 50(2):233–255. [doi:10.1017/S0022112071002556]
Jiang, J., Law, A.W.K., Cheng, N.S., 2004. Two-phase modeling of suspended sediment distribution in open channel flows. Journal of Hydraulic Research, 42(3):273–281.
Krzyk, M., Cetina, M., 2003. A two-dimensional mathematical model of suspended-sediment transport. Strojniski Vestnik-Journal of Mechanical Engineering, 49(3):173–184.
Larsen, E.M., 1980. A Sediment Concentration Distribution Based on a Revised Prandtl Mixing Theory. International Symposium on River Sedimentation. Wiley-Interscience, New York, p.237–244.
Mctigue, D.F., 1981. Mixture theory for suspended sediment transport. Journal of Hydraulic Division ASCE, 107(6): 659–673.
Orton, P.M., Kineke, G.C., 2001. Comparing calculated and observed vertical suspended-sediment distributions from a Hudson River Estuary turbidity maximum. Estuarine Coastal and Shelf Science, 52(3):401–410. [doi:10.1006/ecss.2000.0747]
Smaoui, H., Boughanim, F., 2007. 1D vertical model for suspended sediment transport in turbulent tidal flow: Application to the English Channel. Computers and Geosciences, 33(9):1111–1129. [doi:10.1016/j.cageo.2006.11.016]
Sun, Z., 2003. Equilibrium bed-concentration of non-uniform sediment. Journal of Zhejiang University SCIENCE, 4(2):194–196.
Umeyama, M., 1992. Vertical distribution of suspended sediment in uniform open-channel flow. Journal of Hydraulic Engineering ASCE, 118(6):936–941. [doi:10.1061/(ASCE)0733-9429(1992)118:6(936)]
Umeyama, M., 1999. Velocity and concentration fields in uniform flow with coarse sands. Journal of Hydraulic Engineering ASCE, 125(6):653–656. [doi:10.1061/(ASCE)0733-9429(1999)125:6(653)]
Vanoni, V.A., 1946. Transportation of suspended sediment by water. Transaction ASCE, 111:67–133.
van Rijn, L.C., 1982. Equivalent roughness of alluvial bed. Journal of the Hydraulics Division, 108(10):1215–1218.
White, L., Deleersnijder, E., 2007. Diagnoses of vertical transport in a three-dimensional finite element model of the tidal circulation around an island. Estuarine Coastal and Shelf Science, 74(4):655–669. [doi:10.1016/j.ecss.2006.07.014]
Williams, J.J., Bell, P.S., Thorne, P.D., Trouw, K., Hardcastle, P.J., Humphery, J.D., 2000. Observed and predicted vertical suspended sediment concentration profiles and bed-forms in oscillatory-only flow. Journal of Coastal Research, 16(3):698–708.
Wilson, K.C., 2005. Rapid increase in suspended load at high bed shear. Journal of Hydraulic Engineering ASCE, 131(1):46–51. [doi:10.1061/(ASCE)0733-9429(2005)131:1(46)]
Wren, D.G., Bennett, S.J., 2005. Distributions of velocity, turbulence and suspended sediment over low-relief antidunes. Journal of Hydraulic Research, 43(1):3–11.
Wright, S., Parker, G., 2004. Flow resistance and suspended load in sand-bed rivers: Simplified stratification model. Journal of Hydraulic Engineering ASCE, 130(8):796–805.
Zhang, R., Xie, J., 1993. Sedimentation Research in China. China Water and Power Press, Beijing, p.48–57.
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Project (Nos. 50079025 and 40231017) supported by the National Natural Science Foundation of China
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Huang, Sh., Sun, Zl., Xu, D. et al. Vertical distribution of sediment concentration. J. Zhejiang Univ. Sci. A 9, 1560–1566 (2008). https://doi.org/10.1631/jzus.A0720106
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DOI: https://doi.org/10.1631/jzus.A0720106