Mixing Center of a Channel
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 2
Abstract
For longitudinally uniform stretches of waterways there is a mixing center for the across-channel location of a steady point source in steady flow, such that complete mixing is achieved as soon as possible and there is no concentration overshoot at either of the two shorelines. A mathematical definition of the mixing center is the zero of the first oscillatory cross-channel diffusion mode. With the shorelines plus four interior data points across the channel, the starting estimate for the mixing center suffices to keep peak shoreline concentrations to within 6% of optimal. For comparison, a source at mid flow gives 18% shoreline concentration overshoot in the test case. Should very high precision be required, the Appendix gives an iterative construction that converges to the first oscillatory diffusion mode.
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References
Fox, L. (1957). The numerical solution of two-point boundary value problems, Oxford University Press, London.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K.
Smith, R.(1982). “Where to put a steady discharge in a river.” J. Fluid Mech., 115, 1–11.
Yotsukura, N., and Sayre, W. W.(1976) “Transverse mixing in natural channels.” Water Resour. Res., 12, 695–704.
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Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Mar 19, 2002
Accepted: Jun 17, 2003
Published online: Jan 16, 2004
Published in print: Feb 2004
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