Mixing Center of a Channel

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.