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Mixing Center of a Channel
Authors:Ronald Smith
Affiliation:Professor, Mathematical Sciences, Loughborough Univ., Loughborough?LE11 3TU, U.K.
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.
Keywords:Channels, waterways  Steady flow  Mixing  
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