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Multi-mode models of flow and of solute dispersion in shallow water. Part 2. Logarithmic velocity profiles

Published online by Cambridge University Press:  26 April 2006

R. Smith
R. Smith
Affiliation:
Mathematical Sciences, Loughborough University of Technology, LE11 3TU, UK
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Abstract

A two-mode model for velocity and solute concentration in shallow-water flows is derived which allows for departures from the logarithmic velocity profile and from vertically well-mixed concentrations. The modelling is tested against exact results for a buoyancy-driven transverse flow and for a modified logarithmic velocity profile.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 286 , 10 March 1995 , pp. 277 - 290
Copyright
© 1995 Cambridge University Press

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References

Chatwin, P. C. 1970 The approach to normality of the concentration distribution of a solute in solvent flowing along a pipe. J. Fluid Mech. 43, 321–352.Google Scholar
Davies, A. M. 1987 Spectral models in continental shelf sea oceanography. Three-dimensional Coastal Ocean Models (ed. N. S. Heaps), pp. 71–106. AGU.
Elder, J. W. 1959 The dispersion of marked fluid in turbulent shear flow. J. Fluid. Mech. 5, 544–560.Google Scholar
Falconer, R. A. 1976 Mathematical modelling of jet-forced circulation in reservoirs and harbours. PhD thesis, Imperial College, London, 237pp.
Fischer, H. B. 1973 Longitudinal dispersion and turbulent mixing in open-channel flow. Ann. Rev. Fluid Mech. 5, 59–78.Google Scholar
Heaps, N. S. 1972 On the numerical solution of the three-dimensional hydrodynamical equations for tides and storm surges. Mem. Soc. Sci. Liege. Ser. 6, 2, 143–180.Google Scholar
Hutton, A. G., Smith, R. M. & Hickmott, S. 1987 The computation of turbulent flows of industrial complexity by the finite element method - progess and prospects. Finite Element in Fluids 7, 289–309.Google Scholar
Lamb, H. 1945 Hydrodynamics. Cambridge University Press, 738pp.
Phillips, N. A. 1957 A coordinate system having some special advantages for numerical forecasting. J. Met. 14, 184–186.Google Scholar
Prych, E. A. 1970 Effect of density differences on lateral mixing in open-channel flow. Keck. Lab. Hydraul. Water Res. Calif. Inst. Tech. Rep. KH-R-21.
Smith, R. 1979 Buoyancy effects upon lateral dispersion in open-channel flow. J. Fluid. Mech. 90, 761–779.Google Scholar
Smith, R. 1982 Non-uniform discharges of contaminants in shear flows. J. Fluid mech. 120, 71–89.Google Scholar
Smith, R. 1995 Multi-mode models of flow and of solute dispersion in shallow water. Part 1. General derivation. J. Fluid Mech. (in the press).Google Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar