'Whirling Dervish' Skirts Ruled By Same Force That Moves Tornadoes

By Gabrielle Jonas on November 26, 2013 6:15 PM EST

Engineers have come up with a formula that explains the twirling of the Whirling Dervishes skirts, and the creation of tornadoes, all in one fell swoop. (Photo courtesy of Matt Lingard, Flickr)
Engineers have come up with a formula that explains the twirling of the Whirling Dervishes skirts, and the creation of tornadoes, all in one fell swoop. (Photo courtesy of Matt Lingard, Flickr)

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File another one in the "everything is related department": The same type of force that describes how the rotation of the earth can whip up warm air into a tornado is the same one that can defines how the Turkish dancers called Whirling Dervishes twirl their skirts into a vision of mesmerizing beauty, three physicists said in a new study published on Wednesday.

Both rotating earth and dancer are governed by a set of simple equations which determine how fixed structures, such as our earth, or free-flowing structures, such as a skirt, behave when rotating, co-author of the study, Dr. James Hanna, assistant professor in the Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University, along with Dr. Jemal Guven from Universite de Lorrain in France and Dr. Martin Michael Müller of the Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, said. The Coriolis force accounts for how entities are deflected over a rotating surface - whether that surface is the earth's atmosphere or a dancer's dress.

"A force of Coriolis type is felt by a body that is moving with respect to a rotating surface," Hanna told the International Science Times. "This could be air on the rotating earth, or fabric on a rotating skirt, or an ant on a spinning baseball: You name it." According to Hanna, the importance of the study was that it explained something observable in real life. "We thought it was very interesting that such a minimal, simple model could share similar features as this real, complicated physical system," he said

The mathematical formula, which is a new way to illustrate the motion of sheet-like, or two-dimensional, flexible objects, is similar to how others have described the motion of string-like, one-dimensional, flexible objects. The formula has implications for many disciplines, Hanna said. "This type of modeling approach could be used to describe other systems, some of them practical: rotating machine components, flapping flags, energy harvesting for green power devices. It could also stimulate some new theoretical ideas in mechanics."

In the case of a tornado, warm, moist outside air flowing in toward the center of a tropical disturbance curves or spirals toward the middle of the disturbance, rather than flowing in a straight line. This spiral effect comes from the rotation of the Earth - as air moves over large distances, the earth's rotation deflects winds clockwise in the Northern Hemisphere and counter-clockwise in the Southern Hemisphere. When those two opposing wayfarers come up against each other, they spiral madly together, forming cyclones.

In the case of the dress, the Coriolis force accounts for the unexpected patterns that form on the surface of the Whirling Dervishes' skirts. The equations generate the sharp peaks and gentle troughs that appear along the flowing surface of the fabric. "The dancers don't do much but spin around at a fixed speed," Hanna wrote in Wednesday's issue of the Institute of Physics and German Physical Society's New Journal of Physics, "but their skirts show these very striking, long-lived patterns with sharp cusp-like features which seem rather counterintuitive."

An illustration of the coordinates and orthonormal triad used in this paper. These are drawn on a generalized cone, a shape specified by a curve on the unit sphere.
An illustration of the coordinates and orthonormal triad used in this paper. These are drawn on a generalized cone, a shape specified by a curve on the unit sphere.


In the same spirit, the formula-heavy journal article also has a counter intuitive name: "Whirling skirts and rotating cones." Said Hanna, "The flow of a sheet of material is much more restrictive than the flow of the atmosphere, but nonetheless it results in Coriolis forces. What we found was that this flow, and the associated Coriolis forces, plays a crucial role in forming the dervish-like patterns."

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