The construction of zonal models of dispersion in channels via matched centre manifolds

Abstract Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. However, often we need multi-mode models to resolve finer details in space and time. Here we construct zonal models of dispersion via the new principle of matching their long-term evolution with that of the original problem. Using centre manifold techniques this is done straightforwardly and systematically. Furthermore, this approach provides correct initial and boundary conditions for the zonal models. We expect the proposed principle of matched centre manifold evolution to be useful in a wide range of modelling problems.