Dynamical system models of patchiness in estuaries
We develop three models for the flow in an estuary. The first being a 2 1-dimensional time-periodic model of a flow in the vertical cross section. The second model adds a third un-coupled velocity field U, in the along-estuary direction. The final model is a 3 + 1-dimensional, fully-coupled, time-periodic flow. We study the transport of material in each model using what are called lobe diagrams. Such diagrams allow us to separate the flow into different regions and then calculate the transport of material between adjacent regions. We also study the presence and bifurcations of curves which form partial barriers (ie. cantori and barriers formed from segments of unstable and stable manifolds of hyperbolic periodic points) or complete barriers (ie. KAM curves and other invariant circles) to transport. We use these models to develop an understanding of both the mixing within the flow and the formation and leakage of patches of higher concentration within a cloud of pollution released into the estuary. We also study the time taken for particles to exit the bounds of the estuary. As a result we get an understanding of which regions of the flow flush pollution out of the estuary in the least time and out of which end of the estuary they flush the pollution. We apply this understanding, and that gained from studying the mixing and formation of patches, to the problem of the optimal discharge of effluent into an estuary.