Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T06:25:29.452Z Has data issue: false hasContentIssue false
  • English
  • Français

Where to put a steady discharge in a river

Published online by Cambridge University Press:  20 April 2006

Ronald Smith
Ronald Smith
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

To avoid high pollution levels along the banks of a river it is desirable to site steady discharges somewhere near the centre of the stream. Here it is shown that the precise location of the optimal discharge site is at the single zero crossing of the first advection–diffusion eigenmode. Simple examples reveal that this position tends to be weighted towards the deeper parts of the channel, and towards the inside bank at the beginning of bends.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 1 - 11
Copyright
© 1982 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Dover.
Fischer, H. B. 1969 The effect of bends on dispersion in streams. Water Resources Res. 5, 496–506.Google Scholar
Ince, E. L. 1956 Ordinary Differential Equations. Dover.
Kay, A. 1982 The effect of a sharp cross-stream depth change upon contaminant dispersion in a vertically well-mixed current. J. Hydraul. Div. A.S.C.E. (submitted).Google Scholar
Rozovskii, I. L. 1961 Flow of Water in Bends of Open Channels (transl. from 1957 Russian edn). OTS60-5113, Department of Commerce, Washington, D.C.
Smith, R. 1979 Calculation of shear-dispersion coefficients. In Mathematical Modelling of Turbulent Diffusion in the Environment (ed. C. J. Harris), pp. 343–362. Academic.
Smith, R. 1981a The importance of discharge siting upon contaminant dispersion in narrow rivers and estuaries. J. Fluid Mech. 108, 43–53.Google Scholar
Smith, R. 1981b Effect of non-uniform currents and depth variations upon steady discharges in shallow water. J. Fluid Mech. 110, 373–380.Google Scholar
Ward, P. R. B. 1974 Transverse dispersion in oscillatory channel flow. J. Hydraul. Div. A.S.C.E. 100, 755–772.Google Scholar
Yotsukura, N. & Cobb, E. D. 1972 Transferse diffusion of solutions in natural streams. U.S. Geo. Survey Paper, no. 582-C.Google Scholar
Yotsukura, N. & Sayre, W. W. 1976 Transverse mixing in natural channels. Water Resources Res. 12, 695–704.Google Scholar