Chaotic advection in a Stokes flow

Abstract

Chaotic advection can be produced whenever the kinematic equations of motion for passively advected particles give rise to a nonintegrable dynamical system. Although this interpretation of the phenomenon immediately shows that it is possible for flows at any value of Reynolds number, the notion of stochastic particle motion within laminar flows runs counter to common intuition to such a degree that the range of applicability of early model results has been questioned. To dispel lingering doubts of this type a study of advection in a two-dimensional Stokes flow slowly modulated in time is presented. Even for this very low Reynolds number, manifestly ‘‘laminar’’ flow chaotic particle motion is readily realizable. Standard diagnostics of chaos are computed for various methods of time modulation. Relations to the general ideas of parametric resonance and adiabatic invariance are pointed out.