Waves

On 1 January 1995 the Draupner oil platform in the North Sea, about 150 kilometres off the coast of Norway, recorded a single wave about 25.6 metres high in a sea whose typical waves were around 12 metres (check the figures). Sailors had told stories of such freak waves for centuries and scientists had dismissed many of them. The Draupner measurement was one of the first instrumental records, and it helped to turn "rogue waves" from a legend into a subject of research. This chapter explains what a wave is, how wind makes waves, how they travel across oceans as swell, why they break on a beach, and what makes a tsunami a different kind of wave altogether.

Anatomy of a Wave

A wave is a disturbance that moves through the water, not water that moves along. Float a cork and it bobs up and down, and in a circle, but ends up roughly where it began. Energy travels; the water mostly stays.

How Wind Makes Waves

Wind blowing across water drags on it and makes ripples; the ripples give the wind more to push against, and they grow. Three things set the size of the waves:

• Wind speed. Stronger wind, bigger waves.
• Duration. How long the wind has been blowing.
• Fetch. The distance of open water over which the wind blows.

When all three are large enough the sea is said to be fully developed, and the waves cannot grow further for that wind speed. A gale across the small Firth of Forth can only make short, steep waves because the fetch is short, whereas the same gale in the open Atlantic makes far larger ones. The Beaufort scale, devised in the early 19th century, rates wind strength from 0 to 12 by its observed effect on the sea (check).

What Happens at the Shore

In deep water a water particle moves in a circle, and the circles shrink with depth until they vanish at about half a wavelength down. When a wave reaches water shallower than about half its wavelength, the bottom begins to drag on it.

1. The wave slows down, but its period stays the same.
2. Since speed falls, the wavelength shortens and the wave bunches up and grows taller.
3. The front slows more than the back, so the wave becomes steeper.
4. When the height reaches roughly three-quarters of the water depth, or the wave is too steep to be stable, the crest topples forward and the wave breaks (check the figure).

Waves also bend as they approach a coast, because the part in shallower water slows first. This refraction turns wave crests to line up with the shoreline and focuses energy on headlands, which is why headlands erode faster than bays.

Tsunamis

The word comes from Japanese and means "harbour wave". A tsunami is not made by wind but by a sudden displacement of a large volume of water: most often a large undersea earthquake at a subduction zone (Chapter 2), but also submarine landslides, volcanic eruptions and, rarely, meteorite impacts.

Because a tsunami's wavelength is so much greater than the ocean's depth, it behaves as a shallow-water wave everywhere, and its speed is given by the square root of g times d, where g is 9.8 metres per second squared and d is the depth. In 4,000 metres of water that is about 200 metres per second, or 700 kilometres per hour. As it enters shallower water it slows and grows, building up in height and sometimes arriving as a rapidly rising tide or a bore rather than a breaking wave.

Rogue Waves

A rogue (or freak) wave is usually defined as one more than twice the significant wave height of the sea around it, where significant wave height is the average of the highest third of the waves (check). After the Draupner record, satellite surveys and later measurements showed they happen more often than the old statistics predicted. Several mechanisms are proposed: waves of different speeds briefly stacking up, waves running against a strong current such as the Agulhas Current off South Africa, and nonlinear effects that focus energy (check). The subject is an active research area, so be careful of claims that it is settled.

Exercises