IGOR MEZIC
Department of Mechanical and Environmental Engineering
University of California Santa Barbara
Santa Barbara, CA 93106-5070, USA
mezic@ana.ucsb.edu
Abstract:
Mathematical techniques for describing the details of this mechanism
are well developed in the case of two-dimensional flows, due to
the Hamiltonian nature of equations for particle
motion. The Hamiltonian structure is lacking in three dimensions.
We present a geometrical theory that allows for description and
prediction of chaotic advection mechanisms in three-dimensional steady
and unsteady flows. We present a comparison
with recent experiments on low Reynolds number flows in a circular cylinder.
The mathematical methods that we describe are kinematic in nature and thus do not directly reveal influence of various physical mechanisms on particle motion. For example, in an incompressible Newtonian fluid it could be possible to discern influences of inertial and viscous forces on existence or absence of chaotic motion. We show that the geometrical theory can be coupled with classical boundary layer concepts to achieve this goal. As an example, we treat the Wavy Vortex Flow in the Taylor-Couette apparatus. Axial flux in this regime of flow between concentric cylinders has been measured in a number of experiments and its behavior with increasing Reynolds number contains some surprises. We explain this behavior using the coupling of boundary layer concepts with geometrical three-dimensional chaotic advection theory.