Connecting Dynamical Structure and Statistical Analysis in Quasi-2D Fluid Flow

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****NON-TECHNICAL ABSTRACT****This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Complex systems that are far from equilibrium are ubiquitous in nature; common examples include fluid flows, weather systems, and many biological systems. Developing accurate and efficient models for these types of systems is very important, but has proved to be tremendously challenging. One of the central problems in modeling complex systems is how to identify the salient features that produce the majority of the observed phenomena. Statistical tools, which have proven very valuable in treating equilibrium systems, have often been applied to complex systems as a way to capture the average properties, with varying degrees of success. Models have also been proposed that rest on the tendency of nonequilibrium systems to self-organize spontaneously into dramatic structures, such as long-lived vortices in fluid flows. This project seeks to bring these two approaches together by conducting laboratory experiments in a two-dimensional fluid flow, a flexible model system that both forms coherent structures and has well characterized statistics. This project will provide concrete tools for determining accurate simplifications of complex systems, and will lay the groundwork for the next generation of models that combine structure and statistics. The project will support the training of a Ph.D. student in both nonlinear physics and in modern, high-precision fluid measurement techniques. Undergraduates will also be involved in the research, both giving them research experience in an interdisciplinary field and helping the Ph.D. student acquire mentoring skills.****TECHNICAL ABSTRACT****This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). This project seeks to find a link between two common descriptions of complex, nonlinear systems: one based on specification of the statistical properties, and one based on self-organized dynamical structures. Both approaches have been studied previously, but little progress has been made on joining the two. This project will address the connection between statistics and structures using a model experimental system: a quasi-two-dimensional fluid flow (generated by electromagnetic forcing of stably stratified thin layers) that can be operated in the laminar, spatiotemporally chaotic, or turbulent regimes. Several types of self-organized structures will be studied, including dynamic topological singularities, spatially extended structure such as vortices, and clusters of fluid elements that move and deform with the flow. The system will be characterized by powerful particle-tracking techniques, which will be released to other researchers as a part of this project. Additionally, a database of the raw particle trajectories will be made available. The award will support a Ph.D. student, who will carry out the experiments and thereby be trained in the high- precision, flexible particle-tracking techniques employed in the research. Undergraduates will also be involved in the project, giving them strong research experience in an interdisciplinary field.