How to get order out of stirring things up.
Now, researchers suggest that a simple mechanism may underlie many of the situations in which coherent structures lumps - persist in the midst of the turbulent flows that surround them.
"Our work implies that coherent structures are in fact generic in any flow generated by stretching and folding," says Troy Shinbrot of the chemical engineering department at Northwestern University in Evanston, Ill. "Moreover, the work tells us exactly how to perturb a given system to create, manipulate, or destroy these structures."
The notion that mixing can be regarded as the stretching and folding of a material originated with British physicist Osborne Reynolds, who first described this process in 1894. The idea was revived in the 1980s by Northwestern's Julio M. Ottino, who used stretching and folding to model how disorder can emerge out of a simple mixing process.
As any mixture is stirred, the material is first stretched out - elongating like a wad of taffy - then folded over into a horseshoe shape. With each successive stretch and fold, any two particles along the horseshoe's legs get farther apart, eventually ending up separated by some random distance.
Shinbrot, working with Ottino, wondered whether the same stretching and folding process can also preserve coherent structures. He noticed that particles very close to a fold move only a short distance apart. Thus, after an initial stretch and fold, the movement of these particles can be minimized by getting the second fold to occur at roughly the same point as the first. By keeping successive folds near a specific point in a mixture or a stirred fluid, the material near the fold remains intact.
To demonstrate the effect, Shinbrot and Ottino turned to an apparatus consisting of two cylinders, one inside the other but placed off center. By pouring a thick liquid into the space between the cylinders, then slowly rotating the inner and then the outer cylinder back and forth, the researchers could induce flows in the liquid that produce patterns characteristic of stretching and folding.
Typically, a sequence of rotations would rapidly distribute a drop of dye injected into the body of the liquid throughout the material. But by adjusting the sequence of rotations to keep the folds within a certain region, a drop of dye injected into that region would essentially stay put (see diagram and photo).
By modifying the rotation sequences, the two researchers can independently control the location of a coherent structure and any movements that occur inside it. Conversely, they can also specify the type of stirring needed to guard against incomplete mixing.
These results, which apply to flows within a closed system, represent only a first step toward understanding structures -- like the Great Red Spot, Jupiter's remarkably stable whirlpool -- that arise in turbulent flows. The researchers are considering ways of extending their work to more complex situations such as wakes produced by fluid moving past an object.
Shinbrot will describe his findings later this month in Albuquerque, N.M. at a meeting of the American Physical Society's fluid dynamics division.
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|Title Annotation:||controlling coherent structures in turbulent flows|
|Date:||Nov 13, 1993|
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