Two-zone model of shear dispersion in a channel using centre manifolds

Abstract

[Summary]: To achieve better precision in describing contaminant dispersion in channels some authors resort to dividing a channel into two zones, fast and slow, leading to a pair of coupled evolution equations for cross-sectionally-averaged concentrations in the zones. We construct a two-zone model whose accuracy is guaranteed by centre manifold theory. The model leads to evolution equations that differ from existing models. We also formulate modified initial conditions for the model to obtain closer correlation between the manifold solution and real solution. Effectiveness of the modified initial conditions is demonstrated numerically by a comparison between the manifold solution and direct numerical simulations of the original advection–diffusion equations.