TI-289Earth19th century

In deep water a tsunami is a low swell moving at jet speed

A tsunami in the open ocean is often under a metre high and hundreds of kilometres long, travelling at about 700 to 800 kilometres an hour. It stands up only when the sea becomes shallow.

Established2 min read

A tsunami is a shallow-water wave even in deep ocean, because its wavelength is so long that the whole water column feels the bottom. Its speed is the square root of g times the depth. At four thousand metres that is about two hundred metres a second — roughly 700 kilometres an hour. The height, spread over that length, can be tens of centimetres. A ship in deep water rises and falls by less than the swell it already ignores. Nothing breaks. The energy is in the length and the speed, not in a face of water.

When the depth falls, the speed falls with it, the wave behind catches the wave in front, and the height grows. That is the shoaling, and it is why the same pulse that was invisible at sea can run up a beach as a bore of several metres, or of tens of metres if the bay focuses it. The warning problem is the jet-speed part. From an earthquake at the trench to a shore a thousand kilometres away is not a day. It is an hour or two. The sea looked ordinary for the whole trip.

Caveats

  • ‘Under a metre’ is the open-ocean height of many damaging tsunamis, not a maximum. A very large source can be taller than that offshore and still be a long swell rather than a breaking crest.
  • The speed falls as soon as the bottom rises. Seven hundred kilometres an hour is the deep-ocean figure, not the speed at the beach.

Sources

  1. 1Levin B. W., Nosov M. A.. Physics of Tsunamis. Springer, 2009.

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