Spinning Coin Could Solve Swirling Debate

The toy version of Euler's disk.

A two-bit, tabletop experiment may help settle a decades-old controversy in fluid dynamics. Spin a coin and it will wobble faster and faster as it tips over, until it abruptly stops. Now, a mathematician says he knows why the motion ends with a rattling flourish, and his explanation, reported 20 April in Nature, may provide an example of a type of fluid flow whose very existence is debated.

The 18th century French mathematician Leonhard Euler was the first to study disks rolling on surfaces, and mathematicians have long known that as a rolling disk tips over, the point of contact whizzes around faster and faster. But no one had explained precisely how the disk loses its energy and why it suddenly poops out, instead of lingering in motion like a pendulum gradually coming to rest. Then 2 years ago, Keith Moffatt, a fluid dynamicist at Cambridge University in the United Kingdom, spotted a toy called "Euler's disk," a heftier version of the spinning coin, in a mail-order catalogue while shopping for his grandchildren's Christmas presents. He ordered one and decided to figure out how it works.

Moffatt realized that as the disk spins nearly horizontally, it squeezes air between itself and the table. The disk stirs this air, much as a kid stirs the filling of a sandwich-style cookie by twisting its two faces. The flowing air soaks up the disk's energy, Moffatt hypothesized, and causes it to list even more. Indeed, he calculated that at a definite time, the disk should become horizontal and the point of contact should go around infinitely fast. In reality, nature doesn't allow that. Rather, Moffatt says, the coin's edge loses its grip on the table surface a split second earlier, and the coin suddenly slides down flat.

But the fact that the equations say the disk should move infinitely fast at a definite time may help explain other phenomena, says Hassan Aref, a physicist at the University of Illinois, Urbana-Champaign. Experts have argued for decades whether such infinities--called finite time singularities--arise from the complicated equations of fluid dynamics. If singularities do exist, they may be the seeds for violent phenomena such as turbulence in the atmosphere or eruptions on the sun's surface, even if, as with the disk, nature always finds a way to dodge the infinite at the last instant. "The emergence of the singularity may not just appear in an executive's toy," Aref says. "It may be something that appears in more complicated systems, too."

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