This grant supports a collaborative team of researchers from Arizona State University, Uni- versity of Wisconsin-Madison and Yale University. The research team is composed of two applied mathematicians and one physicist, representing complementary expertise on theoretical analyses, numerical modeling and experimental studies of mixing in uid dynamics. The project is aimed at quantifying and modeling scalar diusion in the limit where homogenization theory is invalid. This regime of interest is typical when the scalar in the ow is presented with sources or sinks due to physical or biological forces (release-mitigation of contaminants, birth-death, predator-prey interactions in biological species, etc.). As a result, the classical assumptions of isotropy and ho- mogeneity of turbulence do not apply, and the mathematical challenge is to properly represent enhanced diusion (from molecular motion) by the associated uid motion at scales smaller or comparable to the scales of the ow. The interwoven expertise of the research team enables the development of mathematically based models veriable with numerical and physical experiments. The PIs will investigate scalar mixing from a variety of angles. On the one hand, topological mea- sures on the background stirring, based from dynamical systems methods, will be used and tested for modeling turbulent diusion with coherent structures. On the other hand, mixing measures and models associated with sources/sinks will be developed and tested with experiments. Over- all, the PIs will study how mathematical theory can be used/adapted to explain inhomogeneous, anisotropic diusive processes observable from physical experiments. A graduate student will be supported by the grant and co-advised by the PIs.
|Effective start/end date||9/1/12 → 8/31/16|
- National Science Foundation (NSF): $184,276.00