CAREER: Spatiotemporal Chaos in Fluid Convection: New Physical Insights from Numerics

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CBET-0747727PaulDespite their importance in many areas of engineering, nonequilibrium systems remain difficult to analyze, to control, to design, or to predict because of the nonlinear way that spatiotemporal patterns affect the transport of energy and matter, which in turn modifies the spatiotemporal patterns. Examples include the weather and climate, the efficiency of combustion and chemical reactions, the convection of biological organisms in the oceans, heart dynamics, crystal growth from a melt, and fluid turbulence. A particular challenge is to understand spatiotemporal chaos, a commonly observed behavior of nonequilibrium systems where properties of the system evolve aperiodically in time and space. New fundamental insights into the spatiotemporal chaos of spatially-extended nonequilibrium systems will be obtained through a detailed numerical investigation of Rayleigh-Benard convection (a thin horizontal layer of fluid heated uniformly from below). The PI has developed parallel numerical methods providing accurate simulations for the precise conditions of experiment. This research builds upon these successes to explore spatiotemporal chaos in large-aspect-ratio convective domains to make predictions that can be verified by experiment. These predictions are only possible by the recent convergence of increased computing power and improved numerical algorithms, including the continuing research progress of the PI. The research will probe the origins and basic building blocks of spatiotemporal chaos to quantify the number, size, and dynamics of the individual chaotic degrees of freedom. Numerical simulations will also shed new insight upon transport in a chaotic flow field. As examples, an exploration of the enhancement of combustion efficiency in premixed gases by complex fluid velocity fields will directly affect energy production and consumption; and an understanding of the fluid convection driven by the activity of biological organisms suspended in oceans will improve models of the climate. The education program is tightly coupled with this research to provide extensive opportunities for students at all levels to participate in state-of-the-art engineering research. The PI's pre-college outreach program is focused upon exposing a large group of students, with special emphasis on under-represented groups, to challenges facing engineering today with the goal of attracting, retaining, and eventually graduating a more diverse group of world-class engineers. The PI is working closely with the Virginia Tech Center for the Enhancement of Engineering Diversity to develop and implement programs that will reach over 400 pre-college students each year. The PI will develop, organize, and lead problem solving sessions that are guided by hands-on interactive numerical experiments. The numerical experiments will be directly related to this research and will spark the interests of young students with such subjects as the difficulty of weather prediction and the scientific meaning of the popular phrase "the Butterfly Effect." The interactive programs will be written in Java and publicly available on a computational science and engineering web site established for this purpose. The PI will mentor undergraduate students each academic year and each summer on projects related to this research. Students will be selected from the Multicultural Academic Opportunities Program (MAOP) and a NSF funded Summer Undergraduate Research Program (SURP). A new multidisciplinary graduate course will be developed entitled "Spatiotemporal Chaos." A major theme of the course will be the quantitative link between theory and experiment provided by the computations of this research. The education program will be carefully assessed and improved through a close collaboration with the Virginia Tech Engineering Education Department.