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Turbulent dispersion from a steady two-dimensional horizontal source

Published online by Cambridge University Press:  20 April 2006

R. I. Nokes ,
A. J. Mcnulty  and
I. R. Wood
R. I. Nokes
Affiliation:
Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand
A. J. Mcnulty
Affiliation:
Hydrology Centre, Ministry of Works and Development, Christchurch, New Zealand
I. R. Wood
Affiliation:
Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand
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Abstract

The two-dimensional steady-state turbulent-diffusion equation is solved by a separation-of-variables process that leads to a Sturm–Liouville eigenvalue problem. The general solution, for arbitrary velocity and diffusivity distributions, is shown to be in the form of an eigenfunction expansion. For a steady uniform flow in a wide, open channel the velocity distribution in the vertical is well approximated by a logarithmic law and the diffusivity distribution is approximately parabolic. For these distributions the power-series solution technique for ordinary differential equations is used to determine the eigenfunctions and eigenvalues. The solution is compared with the standard solution that Holley, Siemans & Abraham (1972) obtained for a uniform velocity and diffusivity distribution. Experimental results are presented, and these show that

(1) the use of the correct velocity and diffusivity distribution results in a significant improvement in the agreement between experiment and theory; and (2) close to the source the fluctuations of concentration are of the order of the mean values.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 149 , December 1984 , pp. 147 - 159
Copyright
© 1984 Cambridge University Press

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