EAPSI: Identification of Transport Barriers in Two-Dimensional Turbulence

了解流体中传输障碍的位置和演化为预测颗粒如何扩散提供了重要工具，最好的例子是石油如何在海洋表面扩散。像海洋表面一样，湍流的二维流体可以在流体混合和不混合的地方有不同的区域，这决定了颗粒如何在流体表面上传输。这些非混合区域被称为传输屏障，因为外面的粒子不能进入或越过传输屏障。该项目将使用实验室生产的二维湍流来实验测试和改进最近开发的识别运输障碍的新数学方法。这项研究将与澳大利亚堪培拉澳大利亚国立大学的实验二维流体湍流专家夏华博士合作进行。从历史上看，通过有限时间Lyapunov指数来识别流体中的相干结构(传输障碍)是一项密集的任务，需要对流体速度场进行详细的解析。最近，基于辫子理论的识别相干结构的数学方法已经发展起来，并应用于几个测试案例。这些方法的优点是可以从少量的表面粒子轨迹中识别出相干结构，降低了计算成本，增加了方法的适用性。这项研究将通过使用由法拉第波动驱动的湍流实验中获得的表面粒子轨迹来测试算法，从而实现和改进辫子理论识别方案。该项目旨在开发一种计算框架，然后可以在现场应用于实验室实验内外的表面粒子轨迹。该NSF EAPSI奖是与澳大利亚科学院合作资助的。

Knowing the location and evolution of transport barriers within a fluid provides an important tool in predicting how particles disperse, a prime example being how an oil spill spreads on the ocean surface. A turbulent, two-dimensional fluid, like the surface of the ocean, can have distinct regions where the fluid does and does not mix, which determines how particles are transported across the surface of the fluid. Those non-mixing regions are known as transport barriers, as particles outside cannot move into or across the transport barrier. This project will use laboratory-produced two-dimensional turbulence to experimentally test and refine recently developed, novel mathematical methods for identifying transport barriers. This research will be conducted in collaboration with Dr. Hua Xia, an expert in experimental two-dimensional fluid turbulence, at Australian National University in Canberra, Australia.Historically, identifying coherent structures (transport barriers) in a fluid by way of finite time Lyapunov exponents is an intensive task that requires detailed resolution of the fluid velocity field. Recently, mathematical methods for identifying coherent structures based on braid theory have been developed and applied to several test cases. These methods are advantageous as they can identify coherent structures from a small number of surface particle trajectories, decreasing the computational cost and increasing the method applicability. This research will implement and improve the braid-theoretic identification scheme by testing the algorithms with surface particle trajectories taken from experiments in which turbulence is driven by Faraday waves. This project aims to develop a computational framework that can then be applied in situ to surface particle trajectories both inside and outside of laboratory experiments. This NSF EAPSI award is funded in collaboration with the Australian Academy of Science.