Toward the Design and Control of Dynamical Transport Barriers in Nonlinear Flow

自然和工程系统中的流体流动，如海洋、大气或工业机械中的流体流动，通常在空间和时间上都是复杂和可变的。这样的水流混合起来平均效率很高，而且它们会迅速分散携带的物质。然而，它们并不是均匀混合的。相反，它们会自发地形成复杂的模式，导致持续的不均匀性。例如，在石油泄漏中，石油并不是均匀地从源头转移；相反，石油以卷须和螺旋的形式游离出来，这些卷须和螺旋被锁定在海洋表面流动的底层结构上。近年来，人们已经开发出强大的方法来揭示非定常流动中控制混合的隐藏结构，并分离分离流动不同区域的输运屏障。然而，关于如何控制这些动态障碍的位置或存在，甚至是否有可能这样做，几乎一无所知。该奖项将支持研究，以证明控制这些屏障确实是可能的，并了解屏障如何响应外力或容器的形状容纳流体。这项研究的结果将在一系列应用中产生重大影响。例如，了解海洋中的屏障如何与海岸线形状相关，将为可能排放废物的沿海设施的选址或在环境灾害中有限资源的部署提供信息。在其他情况下，例如在工业搅拌器中，快速混合是可取的，因此了解如何抑制运输障碍的形成将是有价值的。现有的定位运输障碍的方法通常需要了解流动的未来演变，因此作为预测工具的效用有限。这项研究将超越这一限制，不去探究障碍将如何自然演变，而是探究如何操纵和控制它们。在电磁驱动的实验室流程中，将研究两种控制传输障碍的方法：通过时空调制施加的身体力进行控制，以及通过横向和底部边界形状进行控制。通过展示运输障碍如何对这些数量的操纵作出反应，而不是对在实践中难以实现的强加控制速度场作出反应，研究结果将为开发适用于现实情况的可实施控制策略铺平道路。

Fluid flows in natural and engineered systems, such as those in the ocean, atmosphere, or industrial machinery, are typically complex and variable in both space and time. Such flows mix efficiently on average, and they rapidly disperse material that they carry with them. They do not, however, mix uniformly. Rather, they spontaneously form complex patterns that lead to persistent inhomogeneities. In an oil spill, for example, oil does not move away uniformly from its source; instead, the oil wanders out in tendrils and whorls that are locked to the underlying structure of the ocean surface flow. In recent years, powerful methods have been developed to uncover the hidden structures that govern mixing in unsteady flows, and to isolate the transport barriers that separate different regions of the flow. Almost nothing is known, however, about how to control the location or presence of these dynamical barriers, or even whether it is possible to do so. This award will support research to demonstrate that control of these barriers is indeed possible, and to understand how barriers respond to external forces or to the shape of the container holding the fluid. The results of this research will have significant implications in a range of applications. For example, knowing how barriers in the ocean are related to coastline shape will inform the siting of coastal facilities that may discharge waste products or the deployment of limited resources in an environmental disaster. In other situations, such as in industrial mixers, rapid mixing is desirable, and so understanding how to inhibit the formation of transport barriers would be valuable.Existing methods for locating transport barriers often require knowledge of the future evolution of the flow, and so have limited utility as predictive tools. This research will surmount this limitation by asking not how barriers will evolve naturally but rather how they can be manipulated and controlled. Two ways to control transport barriers will be investigated in an electromagnetically driven laboratory flow: control via spatio-temporally modulated applied body forces and control via lateral and bottom boundary shape. By demonstrating how transport barriers respond to manipulation of these quantities rather than to an imposed control velocity field, which is difficult to achieve in practice, the results of the research will pave the way for the development of implementable control strategies for real-world situations.