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

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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.