Fundamental First Principle Modeling of Singularity Formation, Self-Assembly, and Aggregation in Stratified Fluids

The environment in which we live and breathe is a complex coupled fluid system whose dynamics possess phenomena occurring on a vastrange of space and time scales. From the smallest cilia in the lung which provide a hydrodynamic defense mechanism against inhaled contaminants to the atmosphere, oceans, and our climate, we interact directly with our fluid environment. The complete description of such a system remains beyond the computational scope of even the largest supercomputers, and a fundamental scientific endeavor is to characterize, and understand phenomena on different scales, and ultimately to integrate these phenomena to offer a grand picture of how this large scale system functions, as a whole. With this in mind, this proposal invokes a program focusing upon fundamental phenomena explored through a combination of rigorous mathematical hydrodynamic theory and experiment which will improve our understanding of some aspects of our complex environment, and provide the foundation and validation for some of the direct numerical approaches pursued through computational modeling. The majority of this theoretical and experimental research will take place in and around the new UNC Joint Fluids Laboratory. This laboratory will provide an optimal avenue towards broad impact of the proposed research, both through its impact on problems relevant to marine dynamics, as well as through a successful training component of our graduate and undergraduate students. Further, the lab provides broad outreach to middle and high school students through tours and summer research projects. The proposal seeks to provide both improved scientific understanding, and along the way, great motivation and opportunities for research and educational experiences for undergraduate and graduate students of the natural sciences.