EAPSI: Identification of Transport Barriers in Two-Dimensional Turbulence

了解流体中运输屏障的位置和演变为预测颗粒如何分散提供了重要工具，一个典型的例子是石油泄漏如何在海洋表面扩散。湍流的二维流体，如海洋表面，可以有不同的区域，在这些区域中流体可以混合和不混合，这决定了粒子如何在流体表面上传输。那些不混合的区域被称为传输屏障，因为外面的粒子不能进入或穿过传输屏障。该项目将使用实验室产生的二维湍流来实验测试和改进最近开发的用于识别传输障碍的新颖数学方法。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，通过有限时间李雅普诺夫指数来识别流体中的相干结构（输运屏障）是一项艰巨的任务，需要流体速度场的详细分辨率。近年来，基于编织理论的相干结构识别的数学方法得到了发展，并应用于多个测试案例。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，提高了方法的适用性。本研究将通过对法拉第波驱动湍流实验中获得的表面粒子轨迹进行测试，来实现和改进辫状理论识别方案。该项目旨在开发一个计算框架，然后可以在实验室实验内外就地应用于表面粒子轨迹。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.