A Centre Manifold Description of Contaminant Dispersion in Channels with Varying Flow Properties

High-order asymptotic approximations to the equation governing the longitudinal dispersion of a passive contaminant in Poiseuille channel flow are derived, and their validity discussed. The derivation uses centre manifold theory, which provides a systematic and near rigorous approach to calculating each successive approximation. It also enables the derivation of the correct initial conditions for the Taylor model of shear dispersion. Approximations that are valid when the channel is of a varying cross section are systematically derived via this approach, and the effects of time-dependent flow and variable diffusivity are also investigated. The resultant modifications to the effective advection velocity and the effective dispersion coefficient are calculated and some general trends indicated.