Fundamental Mathematical and Experimental Fluid Dynamics

This research project focuses on fundamental fluid phenomena explored through a combination of mathematical hydrodynamic theory and experiment. The majority of this theoretical and experimental research will take place in and around the new UNC Interdisciplinary fluids laboratory, which opened in June 2007. This project will involve 2 mathematics faculty, 1 graduate student, and 1 undergraduate student to perform experimental and theoretical research designed to better understand mixing, entrainment, and flow properties of stratified and/or viscous systems. Research will include assessing the regularization of Stokes flow divergences through density stratifications, finite time enhanced diffusion with rigid boundary conditions, the hydrodynamics of spheres in the presence of time varying shear layers, and the analysis of singular non-self adjoint differential eigenvalue problems. Applications of these techniques to the natural sciences will be explored.

The environment in which we live and breathe is a complex coupled fluid system whose dynamics possess phenomena occurring on a vast range 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 project seeks to provide both improved scientific understanding, and, along the way, new opportunities for research and educational experiences for undergraduate and graduate students of the natural sciences and will have an outreach to middle and high school students through tours and summer research internships. In particular, this project is focused upon research in fundamental fluid dynamics with emphasis on improved understanding of the interaction between immersed bodies moving in stratified fluids in different environments such as in atmospheres and oceans and in biological systems. Specific examples of such behavior include the settling of 'marine snow' in the ocean which is responsible for sequestering carbon dioxide from the atmosphere, as well as the formation of underwater trapped oil plumes such as those occurring in the Deepwater Horizon Gulf of Mexico oil spill.