Density Functions for Entrainment and Deposition Rates of Uniform Sediment
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 8
Abstract
A model has been developed for the prediction of the density functions of bed-elevation and entrainment and deposition rates of sediment in sand bed streams within the lower regime flow condition. The model incorporates both statistical and deterministic parameters in its form. A total of 46 experimental runs have been carried out in a recirculating tilting flume under the equilibrium flow condition using three grain sizes of uniform gradation to validate the model and estimate its parameters. The model parameters are related to the hydraulic conditions of flow and fluid and sediment properties through dimensional and regression analyses. The study has shown that the density functions of bed elevation and entrainment and deposition rates can be approximated quite satisfactorily with the normal distribution curve. Transformation of the density functions into the standardized normal distribution curve provides a unique pattern for all the experimental runs regardless of the sediment grain size, flow condition, and shapes and dimensions of the bed forms. The developed density functions have been utilized to provide a closure for the probabilistic Exner equation for uniform sediment.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bagnold, R. A. (1941). The physics of blown sand and desert dunes, Methuen, London.
Blom, A., and Parker, G. (2004). “Vertical sorting and the morphodynamics of bed form-dominated rivers: A modeling framework.” J. Geophys. Res., 109, F02007.
Chaudhry, M. H. (1993). Open channel flow, Prentice-Hall, N.J.
Einstein, H. A. (1950). “The bed load function for sediment transportation in open channel flows.” Tech. Bull. No. 1026, U.S. Dept. of Agriculture, Soil Conservation Service, Washington, D.C.
Elhakeem, M. (2004). “A probabilistic approach to the modeling of entrainment, deposition and transport of bed load sediment.” Ph.D. thesis, Univ. of South Carolina.
Elhakeem, M., and Imran, J. (2005). “A bed-load model for uniform sediment derived from the movement of bedforms.” Proc., 4th IAHR Symp. on River, Coastal and Estuarine Morphodynamic, Urbana-Champaign, Ill., 853–860.
Engelund, F. (1966a). “On the possibility of formulating a universal spectrum function for dunes.” Basic Res. Progress, Rep. No. 18, Tech. Univ. of Denmark, Hydr. Lab.
Engelund, F. (1966b). “Hydraulic resistance of alluvial streams.” J. Hydr. Div., 92(2), 315–327.
Engelund, F., and Fredsoe, J. (1976). “A sediment transport model for straight alluvial channels.” Nord. Hydrol., 7, 293–306.
Ertel, H. (1966). “Kinematik und dynamik formbestandig wanderder transversaldunen.” Monatsberichte der Deutschen Akademie der Wissenschaften, Zu Berlin, Band 8, Heft 10 (in German). [Quoted from Raudkivi, A. J. (1990). Loose boundary hydraulics, 3rd Ed., Pergamon, Oxford, U.K.]
Exner, F. M. (1925). “Uber die wechselwirkung zwischen wasser und geschiebe in flusen.” Sitz-Ber. Akad. Wiss. Wien, Abt. II-a, Band 134 (in German). [Quoted from Raudkivi, A. J. (1990). Loose boundary hydraulics, 3rd Ed., Pergamon, Oxford, U.K.]
Graf, W. (1970). Hydraulics of sediment transport, McGraw-Hill, New York.
Hino, M. (1968). “Equilibrium range spectra of sand waves formed by flowing water.” J. Fluid Mech., 34(3), 565–573.
Jain, S. C., and Kennedy, J. F. (1971). “The growth of sand waves.” Proc., Int. Symp. on Stochastic Hydraulics, Pittsburgh.
Kennedy, J. F. (1969). “The formation of sediment ripples, dunes and antidunes.” Annu. Rev. Fluid Mech., 1, 147–168.
Nordin, C. F., and Algert, J. H. (1966). “Spectral analysis of sand waves.” J. Hydr. Div., 92(5), 95–114.
Parker, G. (1990). “Surface based bed load transport for gravel bed rivers.” J. Hydraul. Res., 28(4), 417–436.
Parker, G., Paola, C., and Leclair, S. (2000). “Probabilistic Exner sediment continuity equation for mixtures with no active layer.” J. Hydraul. Eng., 126(11), 818–826.
Richards, K. (1980). “The formation of ripples and dunes on an erodible bed.” J. Fluid Mech., 99, 597–618.
Vanoni, V. A., and Brooks, N. H. (1957). “Laboratory studies of the roughness and suspended-load of alluvial streams.” Rep. No. E-68. Sedimentation Lab., California Inst. of Tech., Pasadena, Calif.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 133 • Issue 8 • August 2007
Pages: 917 - 926
Copyright
© 2007 ASCE.
History
Received: Aug 31, 2004
Accepted: Jan 4, 2007
Published online: Aug 1, 2007
Published in print: Aug 2007
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.