If you have ever seen a whirling dervish in action, you may have been mesmerised by the complex three-dimensional patterns these dancers produce with their flowing skirts. It turns out that the patterns are buffeted by the same Coriolis force that produces destructive hurricanes.
Dervishes are Sufi Muslims who take a vow of poverty. Their whirling, ritual dance, which dates back to 13th century Persia, has become a tourist attraction in places such as Istanbul in Turkey. Fascinated, physicists James Hanna at Virginia Tech in Blacksburg, Jemal Guven at the National Autonomous University of Mexico in Mexico City and Martin Müller at the University of Lorraine in Metz, France, decided to work out the physics behind the skirt's motion.
In particular, the team set out to try and explain mathematically why the skirt sometimes takes on the shape of a triangular based pyramid – or tetrahedron – with its apex near the dancer's midriff. The material forms three gently concave faces, separated by three remarkably sharp ridges that extend down from the dervish's belt. "We wanted a simple model that could produce the qualitative features of the skirt," says Hanna.
That meant ignoring complexities such as the influence of gravity, the stiffness of the skirt material and its interaction with the surrounding air. Instead, they considered only the inertia of the skirt and the tension within the material.
The three physicists found they could still recreate the pyramidal shapes – but only if their simple model took into account the Coriolis force.
This force influences objects moving on the surface of a rotating body. Most notably, the Coriolis force acts on Earth's atmosphere, sometimes generating hurricanes in the winds that move across the surface of our spinning planet.
The whirling dervish dance obviously involves spinning: the dancer and skirt complete a full rotation once each second. And it turns out that the pyramid shape generated by the skirt spins too – but at a slower rate. This means that the skirt material flows over the slowly rotating pyramid, just as our planet's atmosphere flows over the more slowly rotating Earth. Consequently the skirt material, like the atmosphere, experiences a Coriolis force, even though the pyramid is merely a shape rather than a solid object.
What puzzles the researchers is that they also found this Coriolis parameter was essential if their model was to generate the rotating pyramid shape in the first place – when the parameter is removed from their simple model, the pyramidal patterns don't emerge. "But why that is the case, we don't know," says Hanna.
It should be possible to use the model as the basis for a more sophisticated version that includes factors such as gravity. These models may be useful in industry for calculating the stresses experienced by rotating components in machinery. However, these potential practical applications are of secondary importance to Hanna. "This was really a curiosity driven exercise," he says.
Journal reference: New Journal of Physics, doi.org/p8n
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