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The magic number behind hurricanes

From The curious similarity between the shape of hurricanes like Isabel and galaxies far away in space is explained by something called the Golden Ratio.
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As Hurricane Isabel churned toward his office in Baltimore yesterday, astrophysicist Mario Livio pondered the curious similarity between the storm’s shape and that of our Milky Way Galaxy. In fact, Livio knows, the shape is shared by things as diverse as a seashell, water going down a drain and the path of a falcon on the hunt.

IN TERMS OF ORIGIN, development and general physics, there is typically little or nothing that binds these various spirals. Behind them all, however, is a magical number.

In his book, “The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number” (Broadway Books, 2002) Livio describes among other things the remarkable connection between avian flight patterns, stormy weather and cosmic pinwheels.

In a telephone interview, Livio discussed his amazing view of nature.

Phi (not pi) is the number 1.618 followed by an infinite string. Take a rectangle whose sides conform to this Golden Ratio, carve from it a square, and the remaining rectangle still follows the ratio.

The Golden Ratio also describes the ever-expanding nature of what is termed a logarithmic spiral, not to be confused with the boring spiral created by a roll of toilet paper. You’ve probably seen the logarithmic spiral in a familiar seashell belonging to a creature called the chambered nautilus.

Livio said the logarithmic spiral is a key shape for anything that grows, because with growth the ratio does not change. But logarithmic spirals appear in totally unrelated phenomena.

“They also appear, interestingly enough, when a falcon dives toward its prey,” Livio said. The flight pattern allows the bird to maintain a constant angle. Head cocked, its eyes never waver. “It allows the falcon to keep its prey continuously in sight.”

SPINNING A STORM Other than conforming to the Golden Ratio, hurricanes and galaxies share few physical traits. Gravity and angular momentum, or spin, play a role in both cases. But the similarities stop there.

The rotation of a hurricane owes to Earth’s spin. Importantly, a hurricane must rotate in a certain direction. Here’s how it works:

When an area of low atmospheric pressure forms, wind begins to flow toward the center of it, near the surface. All the while, Earth is rotating under the atmosphere. In the Northern Hemisphere, Earth’s spin causes an apparent deflection of the wind to the right, as seen from above.

This Coriolis effect, as it is called, forces a counterclockwise rotation for all storms in the Northern Hemisphere. Storms south of the equator rotate clockwise.

You can visualize the effect by imagining an old-fashioned record album spinning on a turntable. Suppose you draw a chalk line from the edge of the record to the center while it is spinning — the line will be curved even though your motion is straight.

SELF CONTROL Galaxies, by contrast, rotate either direction depending on your point of view — there is no known up or down in the universe. (A study in the late 1990s suggested the universe was directional, but the work was soon refuted.)

Why do galaxies rotate in the first place? The answer goes back to the formation of the universe, when matter raced outward in all directions. Clumps eventually formed, and these clumps began to interact gravitationally. Once stuff moved off a straight course and began to curve toward something else, angular momentum, or spin, set in. The laws of physics say angular momentum must be conserved.

“Masses of material from which galaxies were formed had an initial amount of angular momentum,” explains Rick Perley of the National Radio Astronomy Observatory. As a developing galaxy’s gas, dust and stars contract into a smaller region of space, it all spins faster — just as a skater twirls more rapidly by pulling her arms in.

Astronomers don’t know exactly how a galaxy like the Milky Way gets its spiral arms. But the basics are understood. Gravitational disturbances called density waves, rippling slowly through a galaxy, are thought to cause it to wind up and generate the spiral appearance.

The spiral arms of a galaxy are places where gas piles up at the wave crests. The material does not move with the spirals, but rather is caught up in them.

UNDER CONSTRUCTION Livio, who is head of the science division of the Space Telescope Science Institute, imagines a spiral arm of a galaxy as a highway under construction. Think of cars representing the material in a galaxy, and the highway crew as a gravitational wave crest. Over time, the highway crew moves down the road at an almost imperceptible pace, but wherever it is, you’ll find a higher density of cars.

“That higher density moves along at the speed of the repair crew, not the speed of the cars,” Livio said.

Where the cars pile up, tempers flare. In space, the equivalent is an increased rate of star formation, which makes the spiral arms conspicuous, what with all those hot young stars belching UV radiation faster than the pants can come off a Coppertone kid.

“What exactly causes these density waves is not known,” according to Eric Christian of the Universities Space Research Association at NASA’s Goddard Space Flight Center. One idea is that the waves are generated during a relatively close pass with another galaxy somewhere in history.

Despite their different origins and physics, hurricanes and galaxies do look similar. But they are far from twins.

“There are some superficial similarities, but since the physics and scales involved is so different I don’t think we can draw any conclusions from it,” says Karen Masters, a Ph.D. student in the astronomy department at Cornell University. Masters has pondered the question for the university’s Web-based Ask the Astronomer feature. “Hurricanes are structures in the gravitational field of the Earth, while galaxies are self-gravitating objects in space.”

Which makes the Golden Ratio’s presence all the more remarkable.

DOWN THE DRAIN Back home, all of this has almost nothing to do with your bathtub drain, which creates another spiral shape.

There is a popular myth, though, owing to the rotational direction of a hurricane, that says the water in bathtubs rotates a certain direction in the Northern Hemisphere.

It’s not true.

The Coriolis effect does not determine which way the water swirls in your house. The effect is too tiny to impact such a minor, localized process, all experts agree.

That means water is free to swirl in either direction in tubs in both hemispheres. Which way it goes is determined by the geometry of a particular basin or, if things are perfectly aligned and balanced, then by chance.

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