A Centre Manifold Description of Contaminant Dispersion in Channels with Varying Flow Properties
- 1 December 1990
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 50 (6) , 1547-1565
- https://doi.org/10.1137/0150091
Abstract
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.Keywords
This publication has 24 references indexed in Scilit:
- Kuramoto–Sivashinsky Dynamics on the Center–Unstable ManifoldSIAM Journal on Applied Mathematics, 1989
- Ck centre unstable manifoldsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988
- Mathematical Models of Dispersion in Rivers and EstuariesAnnual Review of Fluid Mechanics, 1985
- The application of centre manifolds to amplitude expansions. II. Infinite dimensional problemsJournal of Differential Equations, 1983
- Amplitude Equations for Systems with Competing InstabilitiesSIAM Journal on Applied Mathematics, 1983
- Applications of Centre Manifold TheoryPublished by Springer Nature ,1981
- The theory of dispersion of chemically active solutes in a rectilinear flow fieldFlow, Turbulence and Combustion, 1978
- The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipeJournal of Fluid Mechanics, 1970
- On the susceptibility of a ferromagnetic above the Curie pointProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957
- On the dispersion of a solute in a fluid flowing through a tubeProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1956