Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-29T14:41:34.804Z Has data issue: false hasContentIssue false
  • English
  • Français

Interaction of buoyant plumes in open-channel flow

Published online by Cambridge University Press:  17 February 2009

P. J. Wicks
P. J. Wicks
Affiliation:
Depart, of Applied Maths and Theoretical Physics, University of Cambridge, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, a model for lateral dispersion in open-channel flow is studied involving a diffusion equation which has a nonlinear term describing the effect of buoyancy. The model is used to investigate the interaction of two buoyant pollutant plumes. An approximate analytic technique involving Hermite polynomials is applied to the resulting PDEs to reduce them to a system of ODEs for the centroids and widths of the two plumes. The ODEs are then solved numerically. A rich variety of behaviour occurs depending on the relative positions, widths and strengths of the initial discharges. It is found that for two plumes of equal strength and width discharged side-by-side, the plumes move apart and the rate of spreading is inhibited by their interaction, whereas when one plume is initially much wider than the other, both plumes tend to drift to the side of the narrower plume. Finally, the PDEs are solved numerically for two sets of initial conditions and a comparison is made with the ODE solutions. Agreement is found to be good.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 4 , April 1992 , pp. 451 - 473
Copyright
Copyright © Australian Mathematical Society 1992

References

[1] Erdogan, M. E. and Chatwin, P. C., “The effect of curvature and buoyancy on the laminard ispersion of solute in a horizontal tube”, J. Fluid Mech. 29 (1967) 465–481.CrossRefGoogle Scholar
[2] Prych, E. A., “Effects of density differences on lateral mixing in open channel flows”, Keck Lab. Hydraul. Water Resources, Calif. Inst. Tech. Rep. KH-R-21 (1970).Google Scholar
[3] Smith, R., “Asymptotic solutions of the Erdogan-Chatwin equation”, J. Fluid Mech. 88 (1978) 323–337.CrossRefGoogle Scholar
[4] Smith, R., “Buoyancy effects upon lateral dispersion in open-channel flow”, J. Fluid Mech. 90 (1979) 761–779.CrossRefGoogle Scholar
[5] Smith, R., “Similarity solutions of a non-linear diffusion equation”, IMA J. Appl. Math. 28 (1982) 149–160.CrossRefGoogle Scholar