Date: 02/26/09

Speaker: T. Sapsis

Title: Where Do Inertial Particles Go in Fluid Flows?

Abstract:
In this talk, we will discuss recent results on the asymptotics of inertial
(finite-size) particle motion in three-dimensional unsteady flows. The
asymptotic particle 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, by combining the reduced-order equation with
results from ergodic theory we derive analytic criteria to predict
sub-manifolds in the flow where inertial particles will cluster. We apply
our theoretical findings on the study of inertial particle motion in
idealized fluid flows such as the three-dimensional steady
Arnold-Beltrami-Childress and the Hill's spherical vortex. More realistic
cases will also be discussed, including particles in a two-dimensional model
of vortex shedding behind a cylinder in crossflow, dust and droplets motion
in the realistic flow field of hurricane Isabel (US East coast, 2003) as
well as predator-prey interactions in jellyfish feeding.