Anatomy of Waves

Graphic by Don Foley

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In their most basic incarnation, ocean waves appear perfectly linear and monotonous. They move in a straight line, and their behavior can be predicted by well-defined periodic functions (sines and cosines). These involve three fundamental parameters: Amplitude (A) is the height of a wave from trough to crest. Velocity (v) is the speed and direction at which the wave travels, and wavelength (l) is the distance between two consecutive wave crests.


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WAVE INTERACTION

When two waves overlap, they combine in mathematically predictable ways: Where their peaks line up—a phenomenon known as constructive interference—they combine to form larger waves. Where they don’t line up—destructive interference—they cancel each other out. Top right: In this graph, two waves with slightly different frequencies (X and Y) are combined to form a jagged wave (Z) with tall crests and deep troughs, as well as some relatively flat areas. Bottom right: Waves that overlap from two or three directions at once can turn a calmly rolling sea (A) into an increasingly choppy one (B and C). Variations in wave frequencies and amplitudes can give rise to an infinite number of shapes, the French mathematician J. B. Fourier noted in 1807. This is the basis of Fourier analysis, the mathematical technique at the heart of rogue-wave research, in which complicated wave patterns are broken down into their constituent parts.

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WIND ON WATER

A wave is a disturbance that transports energy and momentum through a medium. The disturbance travels, but not the medium itself. As a wave passes through the ocean, the water spins in circular currents (white arrows) below the surface. Winds over the ocean (blue arrow) also create currents on the surface, pushing the water up one side of the wave and down the other.

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Rogue waves don’t seem to respect the conventional rules of wave interaction. In the turbulent waters where they arise, winds and currents collide from many directions at once, and waves combine in nonlinear ways to form freak amplitudes of astonishing height and power. Left: Rogue waves often cross the water at an angle to the rest of the waves, taking supertankers and offshore rigs by surprise.

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THE BIG KAHUNA

The largest rogue wave ever measured—in the North Sea in 1995—towered 85 feet from trough to crest (as high as a 10-story building). The disturbance measured 1,415 feet across and sped over the water at roughly 45 miles per hour. Such a wave could easily topple an offshore drilling rig, physicist Alfred Osborne says. He believes that rogue waves are far more common than was previously thought.