An Introduction to Chaotic Advection

Abstract

Understanding particle advection in incompressible laminar fluid flow, apart from being of theoretical interest, holds much relevance for technological applications. Properties of emulsions, dispersion of contaminants in the atmosphere and ocean, sedimentation, and mixing, are just a few examples. Chaotic advection is the complex behaviour a passive scalar— a fluid particle, or a passively advected quantity such as temperature or concentration of a second tracer fluid — can attain, driven by the Lagrangian dynamics of the flow. The surprise is that even laminar flow at low Reynolds number is capable of producing such behaviour. The importance of chaotic advection lies not least in the enhancement of transport it produces. In this review we provide an introduction to theoretical results, numerical simulations, and laboratory experiments on chaotic advection in two-dimensional unsteady, three-dimensional steady, and three-dimensional unsteady flow.