After a bout of what shook the world over, tsunami is perhaps the most glaring example of what is perhaps understood as the absolute wrath of the Almighty. Ads by Google
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Tsunamis are frequently (and inappropriately) called "tidal waves" and are a serious concern whenever an off-shore earthquake is detected. Although tsunamis are only a meter or so high as they propagate in the deep ocean, they can grow to several meters by the time they reach shore. These are typically generated by earthquakes or underwater landslides; and although rare, these are like dormant volcanoes that can shake your world up at any given time. In earthquakes, the strain energy is released and propagated away primarily in the form of p- (longitudinal) and s- (shear) waves propagating through the solid earth. If the earthquake is in the ocean, a portion of this energy is also carried by the free surface of the ocean. In this sense, the tsunami is simply one of the natural modes of vibration of the earth-ocean system.
Of course tsunamis have nothing to do with the tides driven by the gravitational forces between the earth and the moon. Thus, to call a tsunami a "tidal wave" is not only inappropriate, but is likely to lead to confusion among lay-people. By large tsunamis are just ordinary water waves and comply with the same physics as waves in your coffee cup or bathtub. However, as they are generated by geophysical forces they also have the potential to carry geophysical energy and momentum levels which can be devastating to mere humans!
One of the interesting characteristics of tsunamis is that they can travel at speeds approaching 500 mph while in the deep ocean, making it unfit for the characteristics of a wave, leave alone a tidal wave. In turn, this observation is due to the fact that the tsunamis are frequently shallow water waves, even while propagating in water they are not more than perhaps a mile deep or even more. In water of depth 4 km, you can verify that the tsunami speed is about 200 ms or 400 mph.
Occurrence of a Tsunami wave
When the tsunami approaches 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"? Well, to surprise you even further by mentioning that this is not the case. Conservation of mass certainly holds, but this is only true for fixed masses. The wave is propagating relative to the fluid mass and such simple-minded reasoning fails. The primary principle at work is 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 general idea that waves amplify in spatially varying media (in this case, it is the depth which is varying in the direction of wave propagation), is a well-known fact in the general theory of waves and can be found in most fields of mechanics and applied physics. Perhaps the first place engineers encounter waves, which amplify when the medium varies is in elementary optics. The devastation that the tsunami wave has brought about is beyond description, it's just a matter of minutes before everything stands washed out, rather unlike a typical tsunami wave, but definitely exceptional. Of course, the waves never attain infinite amplitude as predicted by Green's law. These waves typically break forming a white water region known as a moving hydraulic jump or "bore". What we observed is a figment of the Almighty's wrath so far! Read more at Buzzle: http://www.buzzle.com/editorials/1-10-2005-63941.asp
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