  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.
