Tsunami Physics

Tsunami at Patong, Phuket in Thailand December 2004

Scott Sturman
fliesinyoureyes.com

In December 2004 an 8.8 Richter scale earthquake generated a massive tsunami which devastated costal areas of Thailand, Indonesia, and Sri Lanka. When I visited Phuket, Thailand in 2010, most of the damage in the hard struck city of Patong was repaired. Interestingly, some nearby areas which were immediately in the path of the wave escaped the onslaught. How did this happen?

A tsunami wave can travel at great speeds and long distances without losing energy. These two traits make them particularly deadly. During a powerful earthquake massive volumes of water are displaced when large areas of the sea floor elevate or subside over a short period of time. The wave is generated at the junction of two tectonic plates, where one plate dives beneath the other. On the seismically active Pacific Rim large population centers typically are located in close proximity to these faults.

Let’s reacquaint ourselves with a few terms regarding simple waves:

Period (T) is the time taken for 1 cycle to occur.
Wavelength (λ) is the distance between corresponding points on the wave, i.e., crest to crest.
Frequency (f) is the number of cycles per unit time.
The period (T) is the reciprocal of the frequency (f) or T=1/f
The height (h) or amplitude of the wave is the distance between the wave crest and the average level of the sea.

Tsunami physics are based on shallow wave theory where (h) divided by λ approaches 0 or h/λ→0. The amplitude of the wave is very small compared to its wavelength. When at the beach, consider a typical ocean wave generated by the wind with T=10 seconds and λ=150 meters. Tsunami waves are altogether different. λ= 100-500 kilometers, and the period can be up to two hours. Yet in the open ocean, the tsunami wave is imperceptible. It is after all a shallow wave, but a shallow wave 500 kilometers long and traveling at 500 miles per hour carries a tremendous amount of energy.

As a wave travels, it loses energy depending on 1/λ. Normal waves with short wavelengths quickly dissipate energy, but tsunami waves with exceeding long wavelengths force the value 1/λ→0. In other words very little energy is lost between where the wave is propagated and where it will eventually strike land.

If the power of these waves was not enough, the speed at which they travel over open water ensures their ability to cause havoc. The speed of the tsunami wave is mostly dependent on the depth of the ocean over which it travels: Speed = √(9.8 meters)/(sec2) x (ocean depth in meters). The average depth of the Pacific Ocean is 4000 meters, so the speed at which the waves travels is about 440 miles/hour. At depths of 5000 meters the speed is nearly 500 miles/hour, which warrants the comparison to the speed of a jet airliner.

As the tsunami approaches land, the water over which it is traveling becomes more shallow. The last equation shows that the speed will diminish in proportion to the square root of the ocean depth. Energy must be conserved, however, so as the wave slows its height increases. When the wave strikes land, the wall of water is sufficiently high to effect structures far inland.

As shown in the accompanying picture, the city of Patong, Phuket, was inundated by gigantic tsunami waves, however, only a few miles to the north the beach was spared. The ocean floor adjacent Patong is a gradual upslope and does little to absorb the energy of the tsunami. However, in the surrounding areas which were also in the path, the depth of the ocean floor abruptly diminishes at a distance from the shore. In this case much of the force of the tsunami was absorbed by the island’s geology, so the wave was considerably weakened by the time it hit landfall.

Large coastline population centers situated near geologically active regions will always be at risk from tsunamis. Many of these countries produce few petrochemicals, so nuclear power maintains a special position in the country’s energy policy. Bad things happen, however, when the position is on an exposed shore next to two competing tectonic plates.