Tsunami wave explained

Savannah Walsh, of Balclutha Primary School, asked:

How are water waves made?

John Campbell, a physicist at the University of Canterbury, responded:

Wind produces most, but as that has already been responded to, I will deal with a rare way: a tsunami.

Earthquakes are caused by large slabs of earth moving against each other. In an undersea earthquake, in the case of when the relative movement is mostly vertical, the sea above the uplift is raised. This sea level is now above that of the sea above the area not raised, so the water flow is from the high level to the lower level. The normal altitude change is a small number of metres, e.g., during the Kaikoura earthquake, parts of the coast were raised 4 metres.

A tsunami is a wall of water coming towards us. As it travels, the front of the wave slowly alters from a step function to a more rounded face. Just ahead of it, the wave dips lower than the unshifted water. That is why the first indication of a tsunami (apart from the earthquake) is that the tide level slowly lowers. This isn’t really observable by a yachtsperson at sea, as the change in altitude is just a couple of metres or so above normal over about half an hour.

However, an English girl saved many lives at the beach during the Indonesian earthquake by recognising that the tide going out more quickly than usual was the precursor to a tsunami, and warned the beachgoers to run for higher ground rather than admire the exposed sea floor.

In deep ocean, the tsunami speed is about the speed of a jet aircraft. We can estimate this speed using a technique called ‘‘dimensional analysis’’. What can the speed depend on? Obviously the acceleration (g) due to gravity [LT2] is trying to pull the wave back to its normal level. So to get a speed [LT1] we need to multiply the acceleration due to gravity by a ‘‘length = L’’ and then take the square root. Velocity is proportional to the square root of gL.

What is this length? In deep ocean, the ‘‘length’’ is the wavelength of the wave, the distance between wave peaks. Yachtspersons becalmed in the windless sea first know of approaching wind when slow languid waves of long wavelength first appear, because they travel faster than the wind. These longwavelength waves are only noticed when the wavelength is about the distance to the horizon of a standing person, i.e., about 5km. So the speed is about the square root of 10x5000, i.e., about 200m/s or 700kmh.

In shallow water, the most obvious ‘‘length’’ is depth. The speed of a surface wave, for example, on a canal of depth 4 metres is thus the square root of 10 times 4, about 6m/s. You can tell that the canal depth has changed because the speed of the surface waves changes.

This speed being proportional to the square root of depth also explains why waves always break parallel to the shore on a sandy beach no matter what direction they initially came from. The depth slowly gets shallower so the wave gets slower and the part of the wave in deeper water and travelling faster catches up.

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