Transport and bifurcation in a non-area-preserving two-dimensional map with applications to the discharge of pollution in an estuarine flow

We present an extension of the theory of transport in a fluid via lobe dynamics to the case of non-area-preserving two-dimensional maps. This extension is then applied to a two-dimensional invariant manifold occurring on a surface of a three-dimensional map of a (3+1)-dimensional flow. This flow is a time-periodic, volume preserving, cartoon of turbulent flow in an estuary. These extensions are of great use because such two-dimensional manifolds occur naturally on the bounding surfaces of three-dimensional fluid dynamical models. The study of bifurcation and transport in such models provides insight into the difficult problem of transport and pattern formation in fully coupled three-dimensional time dependent flows. We also present an application to pollution dynamics in an estuary. In particular we concentrate on the transport of material and the patchiness of clouds of pollution in such a flow.