Author:
BOYLAND PHILIP L.,AREF HASSAN,STREMLER MARK A.
Abstract
A new approach to regular and chaotic fluid advection is presented that utilizes the
Thurston–Nielsen classification theorem. The prototypical two-dimensional problem
of stirring by a finite number of stirrers confined to a disk of fluid is considered. The
theory shows that for particular ‘stirring protocols’ a significant increase in complexity
of the stirred motion – known as topological chaos – occurs when three or more stirrers
are present and are moved about in certain ways. In this sense prior studies of chaotic
advection with at most two stirrers, that were, furthermore, usually fixed in place and
simply rotated about their axes, have been ‘too simple’. We set out the basic theory
without proofs and demonstrate the applicability of several topological concepts to
fluid stirring. A key role is played by the representation of a given stirring protocol
as a braid in a (2+1)-dimensional space–time made up of the flow plane and a time
axis perpendicular to it. A simple experiment in which a viscous liquid is stirred by
three stirrers has been conducted and is used to illustrate the theory.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
131 articles.
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