Optimal discharging in a branched estuary

Abstract. For wastewater discharged into one branch of a narrow estuary, the resulting maximum concentration or temperature can vary markedly depending upon the proximity of the discharge site to the branching and upon how the rate of discharge is adjusted. Explicit formulae are derived for the optimal discharge rate to minimize the maximum concentration or temperature experienced in the estuary, while disposing of a given total wasteload over a tidal period. Graphs are used to show the approximately factors of two reductions in that minimized maximum concentration or temperature when the second branch is large, the discharge close to the branching, the decay rate large or the mean river flow large. By optimizing with respect to one pollutant, there is a reasonably wide range of other pollutants for which the environmental impact is nearly minimized.