An averaged model of dispersion of pollutant in a channel: logarithmic flow

Abstract

We construct a model of dispersion of pollutants in turbulent channel flows expressed in terms of depth-averaged concentration. While there are different approaches to averaging, we use the most consistent approach based on centre manifolds. The method describes long-term asymptotics of the concentration as it becomes quickly spread across the entire depth by turbulence and is then weakly distorted by the velocity shear. For the velocity we adopt a classical logarithmic profile across the flow. A partial differential equation is derived describing evolution of the average concentration against time and downstream coordinate. The equation involves high-order spatial derivatives.