Here’s an interesting discussion on the mechanics of wind generated waves vs tsunamis. The picture that most people have of a "classic" tsunami is typified by Hawaiian surf -- a single big, curling wave like the wave depicted in Hokusai's famous 19th century print. Why should a tsunami "break" differently than the type of wave exploited by surfers? Wave breaking is always a non-linear process and therefore extremely difficult to describe analytically, but in essence most non-linear wave phenomena are due to a dependence of the wave speed on the wave amplitude. To illustrate how this can lead to a steepening and overturning of the wave, consider the formula for the wave speed in shallow water: (gh)^1/2 where h is the undisturbed water depth and g = the acceleration of gravity. The speed of the top portion of the wave will be the largest, while the speed of the bottom of the wave will be the lowest. Because the top of the wave travels the fastest, the wave will steepen toward the front and eventually topple over. In effect the height increases until the wave can no longer support its own weight and it collapses catastrophically. This gives an idea of the classical picture of wave breaking. So far, so good. Now, unlike wind generated surf, tsunamis are frequently shallow water waves (long periods and wavelengths) even while propagating in water a mile deep or more. "Typical" wind generated waves rhythmically rolling in, one wave after another, might have a period of about 10 seconds and a wave length of 150 m. A tsunami, on the other hand, might have a wavelength measured in 100's km and a period on the order of one hour. From the formula above you can verify that in an ocean, say, 4000 meters deep the tsunami speed is about 200 m/s or around 400 mph. ((9.8 x 4000)^1/2= 200 ms-1= 700 km/h). Because the rate at which a wave loses its energy is inversely related to its wave length, tsunamis not only propagate at high speeds, they can also travel trans-oceanic distances with little energy loss. In contrast to wind-generated waves, in which water is momentarily displaced vertically, tsunami waves transport water forwards and backwards. Although the wave is shortened from its deep-water wavelength as it approaches shore, unlike any wind-generated wave it still extends several kilometers crest to crest, and, on approaching the shore it amplifies due to the decrease in depth. The layperson tends to associate this amplification with a conservation of mass principle. After all, the depth is getting smaller -- shouldn't the wave height get larger to "conserve mass"? The answer is no! Conservation of mass certainly holds, but only for fixed masses. The wave is propagating relative to the fluid mass and such reasoning fails. This is just conservation of energy. Ultimately, this energy conservation law implies that the amplitude increases as h^ -1/4, where h is again the local water depth. This -1/4 law is referred to as Green's law and has been known for over a century. The waves never attain infinite amplitude as predicted by Green's law and typically break forming a stepwise white water region known as a moving hydraulic jump or "bore" -- a turbulent vertical wall of water. Longer waves that feel the bottom before shorter waves become unstable and break further offshore in deeper water. In conclusion, a much more accurate depiction of a super-tsunami would be a wall of turbulent white water, not a Hawaii-style big curling wave.

Sentinel by Gary Tonge