November 13: Themis Sapsis, MIT
Dynamics of Inertial Particles in Fluid Flows
We consider the problem of small inertial (finite-size) particles motion in three-dimensional unsteady flows. The asymptotic particles motion turns out to be governed by a slow manifold (inertial manifold), that can be constructed explicitly up to any order of precision. Through a reduction of the dynamics to this slow manifold we derive a reduced-order equation that we use to compute Lagrangian coherent structures for the characterization of mixing properties of inertial particles. Additionally, an analytical study of the normal stability of the slow manifold reveals regions of high dispersion caused by dynamical instabilities on the reduced-order dynamics. We apply our theoretical findings on the study of inertial particles motion in idealized fluid flows such as the three-dimensional steady Arnold-Beltrami-Childress flow and the two-dimensional model of vortex shedding behind a cylinder in crossflow. More realistic cases will also be discussed, including dust and droplets motion in the realistic flow field of hurricane Isabel (US East coast, 2003).