Relative Celerities of Mobile Bed Flows with Finite Solids Concentrations
Publication: Journal of Hydraulic Engineering
Volume 122, Issue 6
Abstract
The relative magnitudes of the celerities at which disturbances on the water surface and the bed are propagated play a key role in the mathematical modeling of mobile bed flow. Earlier analyses assumed that the solids concentration of the flow was negligible. This assumption is inappropriate both for some natural streams and for many aqueous mine-waste disposal applications. Here, the relative celerities of mobile bed flow are determined for flows with finite solids concentrations. The solids concentration is assumed to be a function of the velocity and depth of flow. The analysis confirms and extends the results of earlier analyses. It is shown that the movement of the sediment and the water can be considered to be mathematically independent of each other only within very limited ranges of solids concentration and Froude number. This severely constrains the application of numerous existing mathematical models to mobile bed flows with relatively high solids concentrations.
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References
1.
Bagnold, R. A.(1956). “The flow of cohesionless grains in fluids.”Philosophical Trans., Royal Soc. of London, London, England, Ser. A, 249, 235–297.
2.
Beverage, J. P., and Cuthbertson, J. K.(1964). “Hyperconcentrations of suspended sediment.”J. Hydr. Engrg., ASCE, 90(6), 117–126.
3.
Bogardi, J. (1974). “Sediment transport in alluvial streams.”Akademiai Kiado, Budapest, Hungary.
4.
Carling, P. A., and Reader, N. A. (1982). “Structure, composition and bulk properties of upland stream gravels.”Earth Surface Processes and Landforms, Vol. 7, 349–365.
5.
Chrystal, G. (1964). Algebra, Part 1 . Chelsea Publishing Co., Inc., New York, N.Y.
6.
Cunge, J. A., Holly, F. M. Jr., and Verwey, A. (1980). Practical aspects of computational river hydraulics . Pitman Publishing Ltd., London, England.
7.
De Vries, M. (1965). “Considerations about non-steady bed load transport in open channels.”Proc., 11th Int. Congr., Int. Assoc. for Hydr. Res., Delft, The Netherlands, 3.8.1–3.8.11.
8.
De Vries, M. (1971). “Solving river problems by hydraulic and mathematical models.”Publ. No. 76II, Delft Hydr. Lab., Delft, The Netherlands.
9.
De Vries, M. (1973). “River bed variations—aggradation and degradation.”Proc., Int. Seminar on Hydr. of Alluvial Streams, Int. Assoc. for Hydr. Res., Delft, The Netherlands, 1–10.
10.
Garcia, M., and Parker, G.(1991). “Entrainment of bed sediment into suspension.”J. Hydr. Engrg., ASCE, 117(4), 414–435.
11.
Hampton, M. A. (1972). “The role of subaqueous debris flows in generating turbidity currents.”J. Sedimentary Pet., Vol. 42, 775–793.
12.
Kamphuis, J. W.(1974). “Determination of sand roughness for fixed beds.”J. Hydr. Res., 12(2), 193–203.
13.
Korn, G. A., and Korn, T. M. (1961). Mathematical handbook for scientists and engineers . McGraw-Hill, Book Publishing Co., Inc., New York, N.Y.
14.
Morris, P. H. (1993). “Two-dimensional model for subaerial deposition of mine tailings.”Trans., Inst. of Min. and Metallurgy, London, England, Vol. 102, A181–A187.
15.
Ohmori, O. (1991). “Change in the mathematical function type describing the longitudinal profile of a river through an evolutionary process.”J. Geol., Vol. 99, 97–110.
16.
Pierson, T. C., and Costa, J. E. (1987). “A rheologic classification of subaerial sediment flows.”Rev. in Engrg. Geol., Geological Soc. of Am., Vol. 7, 1–12.
17.
Quinney, D. (1987). An introduction to the numerical solution of differential equations . John Wiley & Sons, Inc., New York, N.Y.
18.
Ribberink, J. S., and van der Sande, J. T. M. (1984). “Aggradation in rivers due to overloading.”Communications on Hydr., Rep. No. 84-1, Dept. of Civ. Engrg., Delft Univ. of Technol., Delft, The Netherlands.
19.
Ribberink, J. S., and van der Sande, J. T. M.(1985). “Aggradation in rivers due to overloading—analytical approaches.”J. Hydr. Res., 23(3), 273–283.
20.
Rodine, J. D. (1974). “Analysis of mobilization of debris flows,” PhD thesis, Stanford Univ., Stanford, Calif.
21.
Sokolnikoff, I. S., and Redheffer, R. M. (1966). Mathematics of physics and modern engineering . McGraw-Hill, Book Publishing Co., Inc., New York, N.Y.
22.
Soni, J. P., Garde, R. J., and Ranga Raju, K. G.(1980). “Aggradation in streams due to overloading.”J. Hydr. Engrg., ASCE, 106(1), 117–132.
23.
Williams, D. J., and Morris, P. H. (1989). “Comparison of two models for subaerial deposition of mine tailings slurry.”Trans., Inst. of Min. and Metallurgy, London, England, Vol. 98, A73–A77.
24.
Wu, C. M. (1973). “Unsteady flow in open channel with movable bed.”Proc., Int. Symp. on River Mech., Int. Assoc. for Hydr. Res., Delft, The Netherlands, 477–488.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 122 • Issue 6 • June 1996
Pages: 311 - 315
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jun 1, 1996
Published in print: Jun 1996
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