Theoretical Modeling of Inertial Phenomena in Chaotic Advection Dynamics

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This project focusses on discovering and modeling fundamental properties of inertial particle transport in open (large-scale) fluid flows, using a novel approach that combines advanced methods from nonlinear dynamics and chaos theory with Lagrangian fluid dynamics. Large-scale inertial phenomena are of significant interest to a wide range of physical processes involving the advection of small rigid particles, whose trajectories may deviate from the trajectories of the fluid elements due to particle finite-size and density. The research will: 1) characterize the impact of inertial effects on single-particle and ensemble dynamics, including the possible formation of attractors and voids; 2) determine the particle and fluid parameters that can lead to the PI's recently discovered fluid-dynamic trapping and clustering of heavy inertial particles in two-dimensional open fluid flows; 3) explore applications of these results to situations involving segregation, mixing, and reactive processes with inertial particles. The expected results include the systematic characterization of inertial phenomena and would be transformative both to the basic theory and the many applications. The proposed research will help advance the understanding of mechanisms underlying natural processes such as rain formation and planet formation, and of applications ranging from chemical to environmental engineering. The planned research activities will involve a graduate student and undergraduate students, including students from underrepresented groups. The project is also expected to impact the PI's course on nonlinear dynamics and chaos and his outreach activities at a local public high school.