Researchers find why willows bend, daffodils dance

Objects flow in boundary between smooth and turbulent winds

January 19, 2003|By Kenneth Chang | Kenneth Chang,NEW YORK TIMES NEWS SERVICE

NEW YORK - Bend, don't break.

With an experiment of soap film and a short glass fiber, mathematicians at New York University have worked out some underlying principles of how something like a willow tree withstands powerful gusts.

The same researchers showed two years ago in a similar experiment why flags flap in the wind.

Years ago, biologists started observing how plants had adapted to the flow of wind and waves around them. Some, such as Steven Vogel, a professor of biology at Duke University, put sections of trees in wind tunnels and videotaped how leaves rolled up into tight streamlined cones when buffeted by high winds.

Other biologists, including Mimi A.R. Koehl, a professor of integrative biology at the University of California at Berkeley, have studied how the undulating motion of underwater kelp forests rolls with the motion of waves.

"Natural structures tend to be more flexible than the stuff we build," Vogel said. "We build to a criterion of stiffness. Nature tends to build to a criterion of strength. It usually takes less material."

Those observations allowed scientists to describe in general terms what was occurring, but not the equations that underlie nature's engineering.

An experiment

The NYU researchers - Jun Zhang, a professor of mathematics and physics; Michael Shelley, a professor of mathematics; and Silas Alben, a graduate student - built an experiment to study a much simplified version of the dynamics.

"Then you have an example where you can say precisely what is going on," Shelley said.

The experiment, a rarity for mathematicians, consisted of a tank that squirted a steady downward stream of soapy water along two vertical threads. Drawing the threads apart produced a soapy film that slid down between the threads at adjustable speeds, from 1.5 feet a second to 10 feet a second.

In experiments several years ago, the researchers placed a silk thread in the flow to simulate the motion of a flag. Up to that point, most scientists had thought that flapping was inevitable, caused by quick changes in the speed of air flowing on either side of the flag.

The NYU team showed that at low speeds the silk thread remained stretched out straight. At quicker speeds, the thread flapped back and forth in a steady pattern.

In the latest experiments, the researchers placed a short flexible piece of glass fiber broadside in the soapy flow and observed the bending of the fiber and the turbulent whirls behind. "You might think of this like a piece of the tree branch," Shelley said.

For a rigid object, if the flow rate doubles, the resulting drag force on the object quadruples. A flexible object like the fiber, however, bends more as the flow quickens. The fiber, the scientists found, always settled at the boundary between the smooth flow and the turbulent whirls, and regardless of the length or diameter of the fiber or the speed of the flow, the bending always followed a universal shape.

"It's cutting down its cross-sectional area that it presents to the flow," Shelley said. "You get a greater reduction of the drag than you think you would."

The findings appeared in a recent issue of the journal Nature. Future experiments will look at flows past fibers with varying diameters and three-dimensional flexible objects. Longer, thinner fibers should also begin to flap. The researchers are also setting up an experiment to look at the fluid dynamics of a zebra fish as it swims.

"We've got a lot to learn from nature," Vogel said. "This is the way it ought to happen. An experimental biologist who takes some measurements and some physical scientists who say, `Hey, maybe there's a general principle involved.'"

Always daffodils

Vogel has found that some plants, such as daffodils, not only bend, but also twist.

Because daffodil flowers always flop to one side (unlike tulip flowers, which stand straight) when strong winds blow, daffodils twist, so that the back of their petals face into the wind.

Vogel snipped off a few daffodils from the thousands on the Duke campus. "We just swiped what we needed," he said. "One razor blade is your collecting equipment."

Wind tunnel experiments showed that with their backs to the wind, daffodils experienced one-third less drag. "By being deliberately weak and twisting," he said, "they avoid being stressed so much in bending."

The twisting, coupled with the inconstant winds, is what inspired poets to write of dancing daffodils, not dancing roses or dancing tulips. Wordsworth, for one, waxed:

The waves beside them danced, but they

Out-did the sparkling waves in glee;

A poet could not but be gay,

In such a jocund company.

"It's always daffodils," Vogel said.

"The reason is because daffodils have this asymmetrical structure. It's kind of cute."

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