Complex fluid flows are ubiquitous, from the air flowing around an airplane or a car, to the turbulent build up of storms, to the intricate flows of charged particles in the Sun, or in plasmas used in attempts to generate electricity by nuclear fusion. Despite its importance, our understanding of fluid flow is far from complete. Theory suggests that understanding the Topological Vortex Dynamics or the "knottedness" of a flow can provide profound new understanding of complex flow. Building on the principal investigator's recent success in generating knotted vortex loops -- akin to smoke rings tied into knots -- and utilizing advances in 3D printing, ultrahigh speed imaging, and high performance computing, this Career Development Award will, for the first time, examine vortices and knottedness in fluids experimentally. If this project is successful, its results will provide a basis upon which to build ways of better understanding or controlling fluid flow. The educational component will leverage concepts from the study of topological structures in knotted physical fields to incorporate modern theoretical and experimental approaches within "classical physics" courses; communicate the joy and importance of science to the public; and, train high school, undergraduate, and graduate students in research especially persons who are underrepresented in science.

Technical Abstract

This Faculty Early Career Award funds a project that will probe the physics of knotted vortex loops in a fluid, for the first time in experiment. Building on our recent demonstration that it is possible to generate knotted vortex loops -- akin to smoke rings tied into knots -- we aim to establish the physics of topological flows in experiment, from the dynamics and rules of topology changing events to probing helicity as a conserved quantity in complex vertical flows. The point of view of a "topological vorticity designer" taken in this research constitutes a new approach to the experimental study of fluid mechanics and provides a rare opportunity to probe the dynamics of topological fields in a real physical system whose structure can be directly imaged. The general interplay between knots and fields has already had a profound impact on our understanding of modern topology and promises to provide additional insights - including new conservation laws - on physical processes in a broad range of systems including quantum fields, classical and superfluid turbulence, and excitations in condensed matter. The educational component will combine contemporary concepts from the study of topological structures in knotted physical fields with the visually striking realization of these concepts in experiment to modernize the experimental and instructional curriculum at the University of Chicago and beyond.

National Science Foundation (NSF)
Division of Materials Research (DMR)
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Tomasz Durakiewicz
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University of Chicago
United States
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