Mixing and diffusion in coherent vortices

混合是流体流动中的一个重要过程。流体的流动，无论是海洋还是大气，都可以将浮游生物或污染物等示踪剂的混合增强许多个数量级。这对工业过程和自然环境具有重要影响。例如，混合会加速化学反应和燃烧。在海洋和湖泊中，混合会影响营养物质的分布，从而影响动植物的分布。在大气尺度上，混合对于确定污染物的扩散和南极涡旋中臭氧的破坏很重要。许多流体流动是由相干涡旋主导的：涡旋流体流动的长期区域。它们具有特别有趣和微妙的混合特性，因为混合会影响流体流动的结构(通过被称为“涡度”的量的混合，这可以被认为是流体的局部角动量)。这导致了复杂的混合，一些区域混合得很好，而另一些区域则很差。这在大规模的数值模拟中可以看到，例如对大气的模拟，但在数学上还没有得到很好的理解。这项研究的目的是研究涡度和其他示踪剂在相干涡旋中的混合特性，并使用数值和分析技术相结合的方法确定不同的区域。

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.