Researchers move closer to understanding chaotic motion of a solid body in a fluid

February 24, 2010

In a paper appearing in the Feb. 24 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.

Although it goes back to the work of Henri Poincaré at the end of the 19th century, chaos emerged in earnest as a new concept in science in the 1960s. Scientists then realized that even very simple systems, governed by perfectly deterministic laws, could have very complicated and seemingly random behavior. Anyone who has played with dice literally has had hands-on experience with the high sensitivity to initial conditions exhibited by a chaotic system. This makes long-term prediction of the system's evolution virtually impossible, Aref and Roenby explained.

It has long been known that the motion of a solid object through a fluid may be chaotic. Mechanisms that lead to chaotic motion in such systems are important, sometimes because one wants to avoid them, at other times because one wants to exploit them. For instance, when designing aircraft, one strives to prevent chaotic motion, whereas it might be a good strategy for a prey trying to escape a predator to enter a regime of erratic, unpredictable motion.

Fluid-body interactions are not very well understood. It is, however, reasonably well established that the delicate interplay between the body and the vortices shed from it, and present in the fluid, plays a key role. For example, it may be shown that if the motion is strictly two-dimensional and there are no vortices, chaos cannot occur. Chaos can occur for three-dimensional motion of a solid body through a fluid even in the absence of vortices.

To understand how vortices may create chaos in the body motion, Aref and Roenby studied a simplified body-vortex interaction model. The simplicity of the model allowed the scientists to take well-known, non-chaotic solutions as the starting point and then slowly increase the influence of parameters that would cause chaos to occur. It was by triggering the chaos in this controlled manner that the authors discovered two sources of chaos in the model.

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.
-end-
YouTube videos on the work can be found at http://www.youtube.com/user/JohanRoenbyPedersen

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.

Virginia Tech's College of Engineering is internationally recognized for its excellence in 14 engineering disciplines and computer science. As the nation's third largest producer of engineers with baccalaureate degrees, undergraduates benefit from an innovative curriculum that provides a hands-on, minds-on approach to engineering education. It complements classroom instruction with two unique design-and-build facilities and a strong Cooperative Education Program. With more than 50 research centers and numerous laboratories, the college offers its 2,000 graduate students opportunities in advanced fields of study, including biomedical engineering, state-of-the-art microelectronics, and nanotechnology. http://www.eng.vt.edu/main/index.php

Virginia Tech

Related Lead Articles from Brightsurf:

Lead-free magnetic perovskites
Scientists at Linköping University, Sweden, working with the perovskite family of materials have taken a step forwards and developed an optoelectronic magnetic double perovskite.

Researchers devise new method to get the lead out
Researchers in the lab of Daniel Giammar, in McKelvey School of Engineering have devised a simple, quick and inexpensive way to quantify how much lead is trapped by a water filter.

Preventing lead poisoning at the source
Using a variety of public records, researchers from Case Western Reserve University examined every rental property in Cleveland from 2016-18 on factors related to the likelihood that the property could have lead-safety problems.

Silicones may lead to cell death
Silicone molecules from breast implants can initiate processes in human cells that lead to cell death.

Poor diet can lead to blindness
An extreme case of 'fussy' or 'picky' eating caused a young patient's blindness, according to a new case report published today [2 Sep 2019] in Annals of Internal Medicine.

What's more powerful, word-of-mouth or following someone else's lead?
Researchers from the University of Pittsburgh, UCLA and the University of Texas published new research in the INFORMS journal Marketing Science, that reveals the power of word-of-mouth in social learning, even when compared to the power of following the example of someone we trust or admire.

UTI discovery may lead to new treatments
Sufferers of recurring urinary tract infections (UTIs) could expect more effective treatments thanks to University of Queensland-led research.

Increasing frailty may lead to death
A new study published in Age and Ageing indicates that frail patients in any age group are more likely to die than those who are not frail.

Discovery could lead to munitions that go further, much faster
Researchers from the U.S. Army and top universities discovered a new way to get more energy out of energetic materials containing aluminum, common in battlefield systems, by igniting aluminum micron powders coated with graphene oxide.

Shorter sleep can lead to dehydration
Adults who sleep just six hours per night -- as opposed to eight -- may have a higher chance of being dehydrated, according to a study by Penn State.

Read More: Lead News and Lead Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.