Hydraulic dispersion of diurnal reactive constituents in an open channel eutrophic flow

- To formulate the concentration transport process with a diurnal reaction.
- To present an analytical study of the longitudinal dispersion model for coupled scalar substances.
- To analyze the concentration evolution under the combination of hydraulic dispersion and diurnal reaction.
- To illustrate the evolution of contaminant cloud in terms of critical length and duration for five typical pollutions.

SummaryClosely related to the solar photocycle, plankton growth in eutrophic waters displays a diurnal variation because of photosynthesis and respiration. Presented in this paper is an analytical study of the diurnal variation of mean concentration of plankton and nutrient in an open channel eutrophic flow initiated by an instantaneous emission. The evolution of the concentration is shown driven by the combination of hydraulic dispersion and diurnal reaction between plankton and nutrient. The analytical solution for longitudinal distribution of concentration is rigorously derived and illustrated, based on the time dependent hydraulic dispersivity. Numerical results are presented and characterized by the reaction rate, yield factor and period for the diurnal reaction and the Péclet number of the flow. For typical applications such as ecological risk assessment and environmental impact assessment, the upper and lower limits of critical length and duration of five typical pollutant concentrations are concretely illustrated for given concentration criterions. Remarkable diurnal variations are revealed up to around one third in the critical length and duration for plankton, and about ten percent for nutrient.