Mixing and diffusion in coherent vortices

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Mixing is an important process in fluid flows. The flow of a fluid, be it the sea or atmosphere, can enhance the mixing of tracers such as plankton or pollutants by many orders of magnitude. This has important implications for industrial processes and the natural environment. For example mixing speeds up chemical reactions and combustion. In oceans and lakes mixing affects the distribution of nutrients and so the distribution of plant and animal life. On the scale of the atmosphere, mixing is important in determining the dispersal of pollutants and the destruction of ozone in the South Polar vortex. Many fluid flows are dominated by coherent vortices: long-lived regions of swirling fluid flow. These have particularly interesting and subtle mixing properties, because mixing affects the structure of the fluid flow (through the mixing of a quantity called the `vorticity', which may be thought of as the local angular momentum of fluid). This leads to complex mixing, with some regions being well-mixed, and others very poorly. This is seen in large-scale numerical simulations, for example of the atmosphere, but is not well-understood mathematically. The aim of the proposed research is to investigate the mixing properties of vorticity and other tracers in coherent vortices, and to determine the different regimes, using combination of numerical and analytical techniques.