Physics of a tsunami

With my parents still in New Zealand and on the coast in Greymouth (in the direct line for any tsunami emanating from the Honshu earthquake) I was reading around the speed of Tsunamis with some personal interest. However, I didn’t have to, since the Pacific Tsunami Warning Center [sic] has all the predicted “hit” times for the arrival of the wave or, more often, waves.

SEA LEVEL READINGS CONFIRM THAT A TSUNAMI HAS BEEN GENERATED WHICH COULD CAUSE WIDESPREAD DAMAGE. AUTHORITIES SHOULD TAKE APPROPRIATE ACTION IN RESPONSE TO THIS THREAT. THIS CENTER WILL CONTINUE TO MONITOR SEA LEVEL DATA TO DETERMINE THE EXTENT AND SEVERITY OF THE THREAT.

ESTIMATED INITIAL TSUNAMI WAVE ARRIVAL TIMES AT FORECAST POINTS WITHIN THE WARNING AND WATCH AREAS ARE GIVEN BELOW. ACTUAL ARRIVAL TIMES MAY DIFFER AND THE INITIAL WAVE MAY NOT BE THE LARGEST. A TSUNAMI IS A SERIES OF WAVES AND THE TIME BETWEEN SUCCESSIVE WAVES CAN BE FIVE MINUTES TO ONE HOUR.

Apologies for the SHOUTING, but this is obviously a rather important message.
UPDATE HERE and again HERE

And there is NZ on the list, with a predicted arrival time of 1930 GMT this evening. That’s 2130 SA time and 0830 tomorrow local time: over 12 hours after the earthquake hit. And that gives you an idea of how massive the scale of this is, because tsunami waves can top 900kph.

The wave speed is the square root of the product of the gravity constant (g) and water depth.

Tsunamis are normally produced by an earthquake or displacement of the seafloor due to plate shifts, etc. This produces a very large wave very rapidly, which then possesses significant energy.

The energy is distributed through the depth of the water initially, as it is displaced, but because of gravity and friction with the seabed, tends to decrease with increasing depth after a short while.
In deep water, the frictional affect on the wave speed is negligible near the surface. The more shallow the water (for instance as it approaches shore), the greater the affect of friction in slowing the mass of water above the seabed; most of the energy of the wave is transferred to the seabed, a small portion is lost to the atmosphere and in heating of the water.

Therefore, the more shallow the water, the slower the wave speed.

And with the Pacific generally being rather deep, the waves are travelling rather fast.

Thankfully, given the distances involved, that still gives my parents significant time to ensure their safety. Sadly, others nearer the epicentre, or without access to this information will probably not be so lucky.

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