Low-dimensional boundary-layer model of turbulent dispersion in a channel

Abstract

We analyse dispersion of contaminants in turbulent boundary layer using centre manifold technique. The method describes long-term asymptotics of the contaminant concentration as it becomes spread across the entire layer and is weakly distorted by the velocity shear. The dispersion is investigated in two cases: (a) logarithmic and (b) power velocity profile across the layer according to a traditional and a more recent theory respectively. We deduce an advection-diffusion equation for the depth-average concentration in each case. The equation represents a leading approximation of the dynamics and can be extended to include higher-order derivatives for better precision.