NYU scientists show the benefits of being flexible

December 06, 2002

As evidenced by trees bending in the wind or fish swimming in water, flexible structures can reduce the drag caused by fluids by altering their shape in response to the fluid's force. In a study published in the December 6 issue of Nature, a team of scientists from New York University's Courant Institute of Mathematical Sciences and Department of Physics, has analyzed how and to what extent flexible structures can morph themselves to reduce drag.

The team designed an elegantly simple experiment that could be closely matched by a theoretical model. Placing a thin flexible fiber, held at the middle, in the nearly two-dimensional flow of a soap film, the scientists were able to visualize how the fluid flow deformed the fiber as well as measure the force exerted on it, or the drag. As expected, the fiber shape became more and more streamlined as the fluid velocity increased. The interesting part was in how the drag changed and why.

The simplicity of the design allowed the scientists to describe the experiment with a theory containing a single control parameter which captured the combined effects of the velocity of the flow, and the fiber's length, width and flexibility. What they found was that unlike rigid structures for which an increase in velocity causes a squared increase on the drag on the object (u2), the increase in drag for a flexible object was significantly lower - to the power of 4/3 (u4/3) - once the velocity crossed a critical value. The drag is created not by the fiber's overall width presented to the flow, but by the smaller, sharply bent "nose" of the fiber that goes against the fluid.

"What was surprising was that the shapes produced at different velocities can be re-scaled into a basic underlying shape, said Michael Shelley, professor of mathematics and neural science at NYUs Courant Institute. "That self-similarity of shape underlies why you get this new drag law."

The research paper was published in Nature under the title "Drag Reduction Through Self-Similar Bending of a Flexible Body". In addition to Dr. Shelley, the paper's authors are Jun Zhang, assistant professor of mathematics and physics at NYU, and Silas Alben, a graduate student at NYU's Courant Institute. The project was partially funded by the Department of Energy and the National Science Foundation.
The Courant Institute, a division of New York University, is one of the world's leading centers of research and instruction in mathematical analysis, applied mathematics, and scientific computation. It was founded in 1952 by Richard Courant.

New York University, which was established in 1831, is one of the largest and most prestigious private research universities in the U.S. Through its 13 schools and colleges, NYU conducts research and provides education in the arts and sciences, law, medicine, dentistry, education, nursing, business, social work, the cinematic and performing arts, public administration and policy, and continuing studies, among other areas.

New York University

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