U.S.-Hungary Mathematics Research on the Effects of Tracer Inertia in Active Chaotic Flows

University Of Maryland, College Park, College Park MD

Investigators

Abstract

INT 0000526 Grebogi This U.S.-Hungary mathematical research project between Celso Grebogi of the University of Maryland, College Park, and Tamas Tel of Eotvos University in Budapest features motion of small, chemically or biologically active particles in non-zero inertia, advected by hydrodynamical flows. The researchers expect the motion of the advected particles to be typically chaotic and will examine the reaction kinetics and population dynamics of the advected chemical components and biological species. Grebogi and Tel intend to define the conditions under which this chaos in phase space can possess a component observable in the physical space of coordinates. Mathematically, when this happens, the dynamics of the material lines present an exponential growth leading to the enhancement of chemical/biological activity in the flow. Particles that are lighter or heavier than the fluid are expected to obey different reaction equations because their interaction with the centers of vorticity in the fluid differs. The model flows to be considered are flow past a cylinder, a convective cellular flow, and a velocity field induced by point vortices. Results should contribute to new numerical algorithms for finding and visualizing invariant chaotic sets and for chaos control. If successful, such results have potential for interdisciplinary applications to a variety of phenomena, including chemical and biological activity in the atmosphere or an aquatic medium, with implications for fields such as oceanography, chemical engineering, and ecology. This project in applied mathematics fulfills the program objectives of advancing science by enabling leading experts in the U.S. and Central Europe to combine complementary talents and pool research resources in areas of strong mutual interest and competence.