Particle dynamics and mixing in the frequency driven "Kelvin cat eyes" flow.

Abstract

The "Kelvin cat eyes" stream function is used as a simple fluid flow model to study particle dynamics, mixing and transport in a two-dimensional time-dependent flow field. Lagrangian formulation is used to describe the motion of small spherical particles present in the flow. Individual particle trajectories, under the influence of various flow parameters are studied. The equation describing the motion of these particles constitutes a set of first-order nonlinear differential equations describing a dynamical system. The time-dependent Eulerian flow field is studied as a nonintegrable Hamiltonian system in order to get insight into the underlying nonlinear properties of the system, which directly influence its complicated transport and mixing behavior. Chaotic advection (Lagrangian turbulence) was observed for heavy particles (high Stokes numbers) while no stochastic behavior was observed for light particles. The introduction of perturbation had only a limited effect on individual particle trajectories. However, the introduction of perturbation caused a shrinking of the phase space where bounded stochastic or quasi-periodic motion occurs. This phenomenon can lead to a better understanding of the link between the behavior of the underlying flow in the Hamiltonian formulation and the dynamics of the passive scalars in the Lagrangian description. The Eulerian flow field itself was found to behave chaotically under the influence of a periodic perturbation, because the stable and unstable manifolds associated with neighboring hyperbolic points intersected. This coincides with the better mixing of the fluid. Stochasticity was also discovered close to the periodic points of the system using Poincare maps. Mixing and transport properties are analyzed as a function of the perturbation frequency. (c) 2001 American Institute of Physics.