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Horizontal fractionation of rising and sinking particles in wind-affected currents

Published online by Cambridge University Press:  26 April 2006

Ronald Smith
Affiliation:
Mathematical Sciences, Loughborough University, LE11 3TU, UK

Abstract

The different rise or sinking velocity for different sizes or types of particles gives different vertical sampling of a wind-affected shallow-water flow. This paper derives a mathematical model for the consequent horizontal fractionation of a dilute suspension of particles when the flow is a wind-influenced perturbation from the classical logarithmic open-channel flow. Simple approximations are given for the effective horizontal velocity and for the shear dispersion tensor which preserve the perfect duality between the sensitivity of sinking particles to bed stress and the sensitivity of rising particles to surface stress.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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References

Barton, N. G. 1984 An asymptotic theory for dispersion of reactive contaminants in parallel flow. J. Austral. Math. Soc. B 25, 287310.Google Scholar
Coleman, N. L. 1970 Flume studies of the sediment transfer coefficient. Water Resour. Res. 6, 801809.Google Scholar
Dyer, K. R. & Soulsby, R. L. 1988 Sand transport on the continental shelf. Ann. Rev. Fluid Mech. 20, 295324.Google Scholar
Elder, J. W. 1959 The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5, 544560.Google Scholar
Fischer, H. B. 1973 Longitudinal dispersion and turbulent mixing in open-channel flow. Ann. Rev. Fluid Mech. 5, 5978.Google Scholar
Giddings, J. C. 1968 Nonequilibrium theory of field-flow fractionation. J. Chem. Phys. 49, 8185.Google Scholar
Lungu, E. M. & Moffatt, H. K. 1982 The effect of wall conductance on heat diffusion in duct flow. J. Engng Maths 16, 121136.Google Scholar
Rijn, L. C. VAN 1984 Sediment pick-up functions. J. Hydraul. Engng ASCE 110, 14941502.Google Scholar
Rouse, H. 1937 Modern conceptions of the mechanics of turbulence. Trans. ASCE 102, 463543.Google Scholar
Sankarasubramanian, R. & Gill, W. N. 1973 Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. Lond A 333, 115132.Google Scholar
Smith, R. 1986 Vertical drift and reaction effects upon contaminant dispersion in parallel shear flows. J. Fluid Mech. 165, 425444.Google Scholar
Smith, R. 1991 Wind-augmented transport and dilution in shallow-water flows. J. Fluid Mech. 228, 549560.Google Scholar
Sumer, B. M. 1974 Mean velocity and longitudinal dispersion of heavy particles in turbulent open-channel flow. J. Fluid Mech. 65, 1128Google Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186203.Google Scholar