Roving thoughts and provocations

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Tsunamis: A Primer

NOAA
Energy propagation pattern of the March 11, 2011 tsunami

I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped—not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles per hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.

—John Scott Russell, 1834

For those who saw video footage of it, the tsunami that hit Japan’s north coast on Friday and then moved inland with overpowering force was a terrifying sight. Three days later, this wall of water, generated by a magnitude 8.9 earthquake offshore, is blamed for thousands of deaths and untold destruction in Japan. I am neither an oceanographer nor a hydrodynamicist, but I have learned a little about the physics of tsunamis that I would like to share. More learned readers will no doubt have corrections.

The word tsunami is a compound. Tsu in Japanese means harbor and nami means wave. I do not know why this name was chosen. At one time they were called “tidal waves” but they have nothing to do with tides. Even earlier they were known as “orphan waves” since their connection to earthquakes occurring thousands of miles away was unsuspected. In fact, earthquakes are not the only way to produce such waves; they can also be caused by underwater volcanic eruptions and even nuclear explosions—anything that can lift a large mass of water. But as in the case of Japan, quakes have historically caused some of the largest tsunamis. In 1946, a 7.4 magnitude earthquake on a fault that runs along the North American Pacific coast produced a 100-foot tsunami that struck the Aleutian Islands, about 90 miles from the epicenter, with such catastrophic force that it was impossible to transmit warnings to Hawaii, whose shorelines were subsequently hit and severely damaged.

What happens is that the ocean floor is pushed up by the tectonic process that produces the quake. The water above it is incompressible so it gets pushed up bodily. Then it falls back down causing large displacements of water. This process provides the energy that creates the waves, which initially move out in concentric circles from the source. (Not every earthquake produces tsunamis. It depends on how the tectonic plates have been moved.)

A mini-example can be seen if you drop a stone into a still pond. As the tsunami waves expand, their circularity become less evident. By the time the Japanese tsunami waves arrived at our west coast they were for all intents and purposes straight lines. This happens near the shore because the portions of the wave closest to the shore move slower and the parts father away catch up. Imagine soldiers marching in a semicircular formation with the front one moving more slowly. The waves that are produced have very long wave lengths—a hundred miles or more and travel at speeds of up to 500 miles per hour. In the Japanese case, the wave was probably formed about 80 miles offshore and reached land within an hour.

Tsunamis are nothing like the wind generated waves near a beach, which have relatively short wave lengths and arrive on the beach one after the other in rapid succession. One must also be clear that it is not the original water displaced by the quake that travels. The beaches of Hawaii and California are not inundated with the water that was pushed up off the coast of Japan. One ocean disturbance generates another and it is these disturbances that travel.

A tsunami wave on the high seas is largely imperceptible. The wave crests are very far apart and are not very high. The crests can be as much as 300 miles from each other. Regarding how fast they move, the waves also have an interesting property. The speed is proportional to the square root of the ocean depth. The wave length is much longer than the ocean depth so these waves are sometimes referred to as “shallow water waves.” In mid-ocean these waves can move 500 miles per hour or even faster; close to landfall, they are more likely to be traveling a few miles per hour—still terrifying if you are in front of one, but slow enough that people with proper warning and escape routes can ideally be evacuated.

Even more remarkable, tsunami waves are apparently examples of what physicists call a “soliton,” a phenomenon that was first described by John Scott Russell in 1834. They do not dissipate like sound waves. You do not hear conversations from Tokyo on Santa Monica beaches. They lose very little energy as they travel. When they get to the shallow water near shore they slow down, but since the energy remains the same the wave increases in height to compensate for the diminishing speed. These gargantuan waves are what cause the damage. As is well-known they can arrive in a series. The first one to arrive may not be the most dangerous. There have been many larger aftershocks since the first quake and such an aftershock could also generate a tsunami. There is, by the way, a similar fault line off the coast of California.

The reactors at Fukushima Daiichi nuclear power plant were damaged by the quake. The diesel engine electric generators that were being used to provide coolant for the reactors were disabled by the tsunami water. As I write this, the fate of these reactors is still unclear.

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