Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T22:59:31.207Z Has data issue: false hasContentIssue false

Effect of islands upon dispersion in rivers

Published online by Cambridge University Press:  26 April 2006

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

Abstract

A general formulation is given for the dispersion of conservative tracers in steady flow in multi-connected channels. A multi-index is used to distinguish the different routes for tracer between the source and the observation position. For each route exact formulae are obtained for the time integral, time centroid, and cross-channel average of the temporal variance. The total concentration is the superposition of the contributions from the different routes.

Type
Research Article
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adler, P. M. 1985 Transport processes in fractals – III. Taylor dispersion in two examples of fractal capillary networks. Intl J. Multiphase Flow 11, 241254.Google Scholar
Aris, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 6777.Google Scholar
Chatwin, P. C. 1980 Presentation of longitudinal dispersion data. J. Hydraul. Div. ASCE 106, 7183.Google Scholar
Daish, N. C. 1985 Shear dispersion problems in open-channel flows. PhD thesis, Cambridge University.
Erdelyi, A., Magnus, W., Oberhettingher, F. & Tricomi, F. G. 1954 Higher Transcendental Functions, vol. II. McGraw Hill.
Fischer, H. B. 1969 The effect of bends on dispersion in streams. Water Resources Res. 5, 496506.Google Scholar
Fukuoka, S. & Sayre, W. W. 1973 Longitudinal dispersion in sinuous channels. J. Hydraul. Div. ASCE 99, 195217.Google Scholar
Saffman, P. G. 1969 A mathematical treatment of dispersion in flow through a branching tree. In Circulatory and Respiratory Mass Transport (ed. G. E. W. Wolstenholme & J. Knight), pp. 298301. J & A Churchill Ltd.
Smith, R. 1981 The importance of discharge siting upon contaminant dispersion in narrow rivers and estuaries. J. Fluid Mech. 108, 4353.Google Scholar
Smith, R. 1984 Temporal moments at large distances downstream of contaminant releases in rivers. J. Fluid Mech. 140, 153174.Google Scholar
Smith, R. 1987 Shear dispersion looked at from a new angle. J. Fluid Mech. 182, 447466.Google Scholar
Smith, R. & Daish, N. C. 1991 Dispersion far downstream of a river junction. Phys. Fluids A 3, 11021109.Google 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
Tsai, Y. H. & Holley, E. R. 1978 Temporal moments for longitudinal dispersion. J. Hydraul. Div. ASCE 104, 16171634.Google Scholar
Tsai, Y. H. & Holley, E. R. 1980 Temporal moments for longitudinal dispersion. J. Hydraul. Div. ASCE 106, 20632066.Google Scholar
Ultman, J. S. & Blatman, H. S. 1977 A compartmental model for the analysis of mixing in tube networks. AIChE J. 23, 169176.Google Scholar
Yotsukura, N. & Cobb, E. D. 1972 Transverse diffusion of solutions in natural streams. US Geol. Survey Paper, 582-C.
Yotsukura, N. & Sayre, W. W. 1976 Transverse mixing in natural channels. Water Resources Res. 12, 695704.Google Scholar