Chaotic advection, transport and patchiness in clouds of pollution in an estuarine flow

We present an application of the transport theory developed for area preserving dynamical systems, to the problem of pollution and in particular patchiness in clouds of pollution in partially stratified estuaries. We model the flow in such estuaries using a $3+1$ dimensional uncoupled cartoon of the dominant underlying global circulation mechanisms present within the estuarine flow. We separate the cross section up into different regions, bounded by partial and complete barriers. Using these barriers we then provide predictions for the lower bound on the vertical local flux. We also present work on the relationship between the time taken for a particle to leave the estuary, (ie. the exit time), and the mixing within the estuary. This link is important as we show that to optimally discharge pollution into an estuary both concepts have to be considered. We finish by suggesting coordinates in space time for an optimal discharge site and a discharge policy to ensure the continually optimal discharge from such a site (or even a non optimal site).