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Shedding New Light On Chaotic Motion
July 5, 2010

In a paper appearing in a recent issue of the Proceedings of the Royal Society of London A, Virginia Tech Engineering Science and Mechanics Professor Hassan Aref, and his colleague Johan Roenby at the Technical University of Denmark shed new light on the chaotic motion of a solid body moving through a fluid. They claim to have discovered two basic mechanisms that lead to chaotic motion of the body as it interacts with its vortex wake. The work may lead to better understanding and control of real body-vortex interactions.

So-called "Poincar sections" were used to diagnose chaos in the body-flow interaction study of Johan Roenby of the Technical Univeristy of Denmark and Hassan Aref of Virginia Tech. The regular curves correspond to motions with minimal chaos. The "fuzzy" regions indicate that the chaotic regime has been entered.

The work “shows how a chaotic region grows from a specific type of equilibrium,” the authors claimed. Aref and Roenby knew from classical hydrodynamics that a body in an “unbounded, ideal liquid has a limiting motion between the rocking and tumbling regime. Adding a vortex to this effectively acts as a random torque on the body.” This is one mechanism for chaos. The other chaotic regime arises when the body is made slightly non-circular. For certain parameter regimes this renders the vortex motion, and thereby its force on the body, chaotic. “The kind of parametric scans we have performed may give important clues as to which geometries and parameter regimes to avoid, if one wants to prevent chaotic motion,” the authors said.

As Aref, Roenby and others unravel the forces that come into play when vortices are produced through interaction between a solid body and the fluid surrounding it, they are furthering the understanding of aerodynamic and hydrodynamic forces, the drag and lift that are paramount in virtually all motion of bodies through air or water.

Aref is Virginia Tech’s Reynolds Metals Professor of Engineering Science and Mechanics. He also holds a Niels Bohr Visiting Professorship at the Technical University of Denmark. Roenby is a Ph.D. student in the mathematics department and the Center for Fluid Dynamics at the Danish University. He is currently a visiting scholar at Imperial College, London.

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