[Editors] MIT reveals the tangle under turbulence

[Elizabeth Thomson]

MIT News Office
Massachusetts Institute of Technology
Room 11-400
77 Massachusetts Avenue
Cambridge, MA  02139-4307
Phone: 617-253-2700
http://web.mit.edu/newsoffice/www

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MIT reveals the tangle under turbulence
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For Immediate Release
WEDNESDAY, MAR. 28, 2007
Contact: Elizabeth A. Thomson, MIT News Office
Phone: 617-258-5402
Email: thomson at mit.edu

IMAGE AVAILABLE


CAMBRIDGE, Mass.--Picture the flow of water over a rock. At very low 
speeds, the water looks like a smooth sheet skimming the rock's 
surface. As the water rushes faster, the flow turns into turbulent, 
roiling whitewater that can overturn your raft.

Turbulence is important in virtually all phenomena involving fluid 
flow, such as air and gas mixing in an engine, ocean waves breaking 
on a cliff and air whipping across the surface of a vehicle. However, 
a comprehensive description of turbulent fluid motion remains one of 
physics' major unsolved problems.

Now, in a paper to be published in an upcoming issue of Physical 
Review Letters, MIT researchers report that they have visualized for 
the first time a convoluted tangle underlying turbulence. This work 
may ultimately help engineers design better planes, cars, submarines 
and engines.

Researchers have long suspected that there's a hidden but coherent 
structure underlying turbulence's messy complexity, but there has 
been no objective way of identifying it, said MIT research group 
leader George Haller, professor of mechanical engineering, who also 
heads Morgan Stanley's Mathematical Modeling Center in Hungary.

"The fluid mechanics community has not reached a consensus even on an 
objective definition of a vortex, or whirlpool effect, let alone the 
definition of structures forming turbulence. The mathematical 
techniques we have developed give a systematic way to identify the 
material building blocks of a turbulent flow," Haller said.

To picture the skeleton of turbulence, the MIT researchers analyzed 
experimental data obtained from co-authors Jori Ruppert-Felsot and 
Harry Swinney of the University of Texas at Austin. The Texas group 
used water jets to force water from below into a rotating tank of 
fluid. They seeded the resulting complicated flow with luminescent 
buoyant particles. When illuminated with a laser, the miniscule 
polystyrene spheres were visible as they raced around the vortices 
and jets.

While the particles looked cool, "most important to our analysis were 
the particles' velocities, which our collaborators obtained by 
recording the particles' motion with a high-resolution camera, then 
using a software tool to figure out which particle moved where in a 
split second," Haller said. "This gave us a high-quality map of the 
whole velocity field of the turbulent flow at each time instance."

The technical analysis of the velocity field was carried out by MIT 
mechanical engineering graduate student Manikandan Mathur, whose work 
is jointly supervised by Haller and co-author Thomas Peacock, 
assistant professor of mechanical engineering at MIT.

Using involved mathematical tools, Mathur uncovered a convoluted 
tangle embedded in the flow. "With this approach, we isolated the 
very source of turbulent mixing, not just its effect on dye or smoke 
as earlier studies did," said Mathur.

The complexity they found surprised the MIT team. They knew that in 
turbulent flow, unsteady vortices appear on many scales and interact 
with each other. What they didn't know was that the complicated, 
constantly evolving flow patterns are driven by two competing armies 
of particles constantly being pulled together and pushed apart.

The researchers identified a complex network of two types of curves 
formed by two distinct groups of particles. The first type of curve, 
which the researchers colored red, attracts other fluid particles. At 
the same time, the second type, colored blue, repels other fluid 
particles. Both sets of curves evolve with the flow.

Imagine that the particles visible in the turbulent water are like an 
army of ants being chased through a bowl of mixed-up red and blue 
spaghetti. "The ants love red spaghetti and want to stay close to it, 
but they hate blue spaghetti and won't touch it. And they have to 
keep running in the bowl under these constraints, stuck in an endless 
maze forever," said Haller.

The resulting images, which look like dense, tangled masses of blue 
and red fibers, are snapshots of this stunning, constantly deforming 
structure. "The chaotic tangle forms the skeleton of turbulence as 
fluid is simultaneously attracted to, and repelled by, its different 
components," Haller said.

The MIT researchers call their discovery the "Lagrangian skeleton" of 
turbulence because their particle-based approach is motivated by the 
work of 19th-century mathematician Joseph-Louis Lagrange. "Lagrange 
developed mathematical tools still used today for calculating 
mechanical and fluid motion," said Peacock.


Among many applications, the new results promise to aid the early 
detection of clear air turbulence that causes those unexpected jolts 
in airplanes; they may also help control the spread of oceanic 
pollution. "Most certainly, they will lead to a better appreciation 
of ants running in a bowl of spaghetti," said Haller.

This work was supported by the National Science Foundation, the Air 
Force Office for Scientific Research and the Office of Naval Research.

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