Relative celerities of mobile bed flows with finite solids concentrations

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.

[1]  R. Bagnold,et al.  The flow of cohesionless grains in fluids , 1956, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[2]  Granino A. Korn,et al.  Mathematical handbook for scientists and engineers , 1961 .

[3]  D. Quinney.  An introduction to the numerical solution of differential equations , 1988 .

[4]  J. Cunge,et al.  Practical aspects of computational river hydraulics , 1980 .

[5]  R. Redheffer,et al.  Mathematics of Physics and Modern Engineering , 1960 .

[6]  J. P. Beverage,et al.  Hyperconcentrations of Suspended Sediment , 1964 .

[7]  H. Ohmori.  Change in the Mathematical Function Type Describing the Longitudinal Profile of a River through an Evolutionary Process , 1991, The Journal of Geology.

[8]  P. Carling,et al.  Structure, composition and bulk properties of upland stream gravels , 1982 .

[9]  J. W. Kamphuis,et al.  DETERMINATION OF SAND ROUGHNESS FOR FIXED BEDS , 1974 .

[10]  R. Garde,et al.  AGGRADATION IN STREAMS DUE TO OVER LOADING , 1980 .

[11]  Thomas C. Pierson,et al.  A rheologic classification of subaerial sediment-water flows , 1987 .

[12]  M. Hampton,et al.  The Role of Subaqueous Debris Flow in Generating Turbidity Currents , 1972 .

[13]  J. Ribberink,et al.  Aggradation in rivers due to overloading , 1984 .

[14]  Marcelo Horacio Garcia,et al.  Entrainment of Bed Sediment into Suspension , 1991 .

[15]  J. Ribberink,et al.  Aggradation in rivers due to overloading - analytical approaches , 1985 .