If these last few days have been outstanding news, media or social networks you will have noted the enormous hype that was generated by the sad events in Japan . And more often than usual salad terrible confusion and misunderstanding concepts. When these concepts involve my sacred science, physics, my blood boils. That is why I decided to tell here a few basic ideas on the functioning of these amazing phenomena known as tsunamis, tidal waves that have been involved in quite a few films: East of Java ( Krakatoa: East of Java , 1969), The Poseidon Adventure ( The Poseidon Adventure , 1972), Deep Impact ( Deep Impact, 1998), The Perfect Storm (The Perfect Storm , 2000), Tomorrow ( The Day After Tomorrow , 2004), to name a few. should be noted that a simple yet full understanding of the behavior of a phenomenon such as a tsunami is of great importance, even beyond mere scientific curiosity can you eat unhealthy gut. Note that a large proportion of the misfortunes that occurred, for example, in 2004 when it came to pass the infamous tsunami in Indonesia, was caused by simple lack of basic physical mechanisms that could have been learned at school if we teach once and for all the things that truly interested. For example, lack of knowledge about the time intervals between the different phases of the tsunami phenomenon prevented many people take simple preventative measures they had most likely saved their lives. I am referring to basic concepts, elementary theory of waves , namely: wavelength, period, speed. Return to this point along the post. Previously, some introductory roll.
The word tsunami comes from Japan and comes to mean "harbor wave" or "harbor wave" and the Japanese understand this a while. There tsunamis historically recorded from as early as the seventeenth century. Thus, in 1605, in Nankaido (Japan) killed 5,000 people, in 1703 in Tokaido and Kashima (Japan) as many, the same year and also in Awa (Japan) was another killer wave more than 100,000 lives, four years later, again in Tokaido and another 30,000 died Nankaido humans, 40,000 more in 1782 South China Sea, the legendary event of Krakatoa in 1883 ended with 36,000 lives in the first century XX, in 1908 in Messina (Italy) killed another 70,000.
From the standpoint of physics, a tsunami is simply a wave sustained by Earth's gravity (and not by wind, like waves on the beach. Neither is correct the term "tidal wave" because the tides are not the reason for its origin) in shallow water. Here it should be noted that people often confused with it. Indeed, who at least knows who else that tsunamis occur at sea, where the depth of the ocean can reach several kilometers. How is it then that we speak of waves in shallow water? Really easy. Let me explain. You see, when physicists say that something is too big or too small, we always do by comparison. So, in this case, talk about shallow depth means that this is small when compared with the wavelength of the waves, ie the distance between two crests (or two troughs) in succession. There are several types of tsunamis: the weather, interns, and local microtsunamis. These latter are those who try to tooooodo loooooong of the post. Typically, they arise from different causes of nature, whether direct impacts of meteorites, landslides in the ocean, volcanic eruptions and earthquakes.
The behavior of tsunamis is quite well understood, unlike what happens with earthquakes. The former are relatively difficult to predict (as will be revealed later), but instead, once generated, the following procedure does not present major difficulties, because they have well-known equations. On the other hand, the seismic waves produced by earthquakes, although reasonably well understood But not so with the process of breaking or fracturing of the soil or with elastic and gravitational energies at play, whose associated equations are unknown.
There are three characteristic lengths to be considered in an earthquake: the length of the fracture, L , the width of the fracture, W and the net vertical displacement occurs at the surface fracture, d . area A = L x W is a parameter of great importance in defining the magnitude of the earthquake. Approximately, we can consider that the stresses The fracture is stored in a volume proportional to A 3 / 2 , and energy of earthquake is therefore proportional to the same amount. The magnitude earthquake (still often referred to the Richter scale) is based on the logarithm of the previous power. Live It concluded that two earthquakes whose magnitudes differ by one unit (7 and 8, for example, 8 and 9, etc..) Correspond to relative energies of 10 3 / 2 = 31.6. This means that a magnitude 8 earthquake releases 31.6 times more energy another magnitude 7. The accurate estimation of the width A of rupture presents difficulties and therefore often give different estimates on the magnitude of earthquakes. In 2004, in the Indian Ocean, have come to take a break values \u200b\u200branging from 1200 km x 150 km to 1200 km x 900 km. The elevation varies between 5 and 20 meters.
When all this tremendous energy is released and enters the ocean water, nearly 99% of it is lost in various dissipative processes. 1% taken, the subsequent tsunami itself, still barely passed 10% of that value. Such figures, an earthquake that would produce an energy release of about 2 exajoules (2 trillion joules), which corresponds to a magnitude of 9.2 deposited in the water-hundredth of that value and the tsunami would reach only 2 petajoules (2,000 trillion joules), plus or minus one-thousandth of the initial value.
The simplest model that is usually set to describe the behavior of a tsunami is basically assume that it propagates in one direction, ie, what physicists call a one-dimensional model, with no losses and considering water as an incompressible fluid without viscosity. If you write the equations that verify a dimensional wave for the case where the wavelength is much greater than the depth of water (above what I called shallow water waves), it can be shown with only a simple algebraic manipulations the giant wave speed is independent of wavelength, depending solely on the depth of the water. If you also apply the principle of conservation of energy is the wave amplitude (the distance between the crest of the wave and the level of the sea surface) decreases in inverse proportion to the square root of the length wave. What effect have these events? Attentive ...
When there is first the tsunami, usually at sea, the water depth typically of the order of several kilometers, while as the tsunami approaches the coast, the water depth decreases drastically and so ends up happening with that speed. Let's do some numbers. Around 00:58 (UTC) on December 26, 2004, about 160 miles north of Sumatra in Indonesia, there was the famous earthquake and subsequent tsunami that would cause many still keep in memory and Unfortunately, we have returned to remember the events of recent days on the coast of Japan. Located in the Indian Ocean, covering nearly 10,000 km from one end to another, and covers an area of \u200b\u200balmost 70 million square kilometers, its maximum depth reaches 7,725 meters on the southern coast of Java, while the average is around 4,200 meters. Well, taking 4,000 meters as a round figure is obtained for the killer wave speed no less than 720 km / h, comparable to the cruising speed of a Boeing 737 (if the disturbance were to originate in the Trench Marianas, the rate would reach 1,200 km / h, similar to that of a Boeing 747). Even when almost reaches the beach, at a depth of only a mere 10 meters, the speed will reach 36 km / h, almost the average speed of an elite athlete, a specialist in the 100 meter dash. So Therefore, it is understood that it is not possible to escape it, once you realize that comes at you and you have not put out of reach. You see, with a little basic physics, which never taught you in school or at least minimally showed you interested in learning, you could have delivered the fatal plunge. And you would not believe, still need more. I'll hear you like it or not, because the next time your teacher will talk about waves and oscillatory movement might want to pay more attention. Read, read a little more.
wavelengths of tsunamis (I remind you that the wavelength is the distance between two consecutive crests or, equivalently, between two valleys) usually the order of hundreds of kilometers (a very large value when compared with the thousands of meters of ocean depth and therefore the condition of waves in shallow water). Since the amplitude (the height of the wave) varies inversely with the square root of the wavelength, a tsunami that reached the coast with waves about 15 feet high, would have started offshore, in waters about 4,000 meters deep , with a height of a mere 38 centimeters. Now you will understand why the first post I said that was extremely difficult to predict. A wave of 38 centimeters is virtually impossible to perceive as the scary monster they will finish developing. In fact, there are proposals to use gravitational wave detectors to track rapid movements of huge masses. devices such as LIGO VIRGO or track too high frequencies (of the order of tens of Hz) while the signal from a typical round tsunami Hz tenths of a system like LISA was between 3,000 km and 10,000 km away could be used. Unfortunately, its location will fall too far, one of the Lagrange points the Earth-Sun L2, 1.5 million kilometers from Earth. alternatives such as satellite GOCE could also serve in the near future, as their sensitivity and precision to achieve the required detection threshold. So, perhaps constitute the fastest alarm systems.
Venture a little further. Let's take the previous wave, which traveled at 720 km / h. If your period is calculated, ie the time it takes to travel a distance equal to its wavelength and admit to it a typical value of 100 km, we see that it amounts to little more than 8 minutes. This time will remain unchanged when the wave finally reaches the coast, as although the water depth is reduced to 10 meters, the wavelength proportionally decreased to 5 km and the same will happen with speed. And this fact is unknown to most people who come to the beach after watching how the waters recede mysteriously, as indeed the wave period is the time period until it reaches again the mass of water, all his rage and fury contained. Although the theoretical model we have considered is very basic with considerable accuracy describes the behavior of tsunamis, at least in regard to the period and wave speed. Obviously, there are other different and more sophisticated models, which can even be applied when included in them variations in water depth, for example. Thus, depending on the distance from the tsunami to the coast, it can be shown that the wavefront will describe a change in orientation, drawing a curve with a radius can be calculated without much difficulty. In the 2004 tsunami in southern India, the ocean moves from a depth of 2,000 meters about 500 km from the coast to another 100 meters close to it. The radius of the curve described by the ridges to change direction shifted from 640 km to only about 140 miles closer to shore. Improvements
further refined taking into account the two-dimensional nature of the propagation of waves across the surface the ocean. In this sense, we can consider two variations: one in which the Earth is treated as if it were flat and another that takes into account the curvature of the planet, obviously, this latest variant is the one that provides better empirical results (though the results predicted by both coincide almost to distances of less than 4,000 kilometers from the epicenter), but not in regard to the speed or wave period (for this is simply very well our previous sencillito dimensional model), but While its amplitude, ie the same height. This model reproduces quite well the values \u200b\u200bof the amplitudes, both quantitatively and qualitatively. I explained. Consider a tsunami that originated on one of the poles of the planet (just a guess, something purely hypothetical). From that point, the waves are propagating and extending concentrically, spreading from its origin. With this, their amplitudes must be decreasing with distance, but only until they have traveled a distance on the surface of the Earth of 10,000 km, equivalent to a quarter of the length of a meridian. From there, due to the curvature of the earth's surface, the waves have crossed the Ecuador and must re-converge, which means that their amplitudes tend to increase again. If no energy is dissipated in the time it reaches the opposite should also recover the original values. Of course, all this reasoning remains valid regardless of the point of origin of the tsunami.
In this sense, the Pacific Ocean is a great test lab at the time of study and contrast the various theoretical models that simulate the propagation of a tsunami, for several reasons: it covers almost a third of the earth's surface, the tsunami that occur along the "ring of fire " can cross great distances with relative ease and is dotted with many small islands represent only points of interference with the waves, but instead provide ideal platforms at the time of recording the amplitudes of the waves.
On November 15, 2006 an earthquake of magnitude 8.3 took place on the southeast coast of the Kuril Islands. The amplitudes of the tsunami waves were recorded following his footsteps by as many as 93 different positions, along with their respective distances from the epicenter. The value of the maximum amplitude was recorded in the observing station nearest to it, south of the islands and turned out to be 88 centimeters.
The effects of tsunami waves can be much stronger in one direction than another, depending on the nature and source of local geographical features. The latter may contribute to the formation of so-called " seiches, which are only one type of waves. In 1946, the tsunami reached the shores of Hawaii had a period in waves of about 15 minutes. When he arrived, finally, Hilo Bay, the natural resonance of this, about 30 minutes (the time between two consecutive wave fronts), every second wave caused the tsunami was "in phase" with the Bay (the crest of a wave coincided with the peaks of the others.) Hilo suffered the worst effects of the tsunami, the waves reached 14 meters high and 159 people perished.
Finally, with respect, again, the event of the Kuril Islands in the Pacific Ocean, there were also noteworthy developments which demonstrate once again the critical importance of geographical peculiarities of the places the tsunami passes. Jackson's Bay and Timaru are respectively the northwest and southeast coasts of the North Island of New Zealand. Their distances from the epicenter of the earthquake of 2006 are 10,186 and 10,273 km. However, the tsunami travel times to reach the two destinations were very different: 14 hours and 6 minutes the first for 18 hours and 49 minutes the second. The cause was due to Timaru was in the "shadow" of the island (the opposite side of land that directly hit the waves), so that both processes occurred as diffraction refraction (change of direction in the spread as a result of encountering physical barriers) that significantly slowed wave speed, delaying its arrival. and said all that, here I stop. If you come at this very moment to head the post title, I mean, certainly there are many kinds of grandmothers. I sincerely hope that your are able to understand what I tried to explain above. As for me, you know that "I have no grandmother" ...
Fuentes:
Tsunamis and Earthquakes: What Physics is Interesting? David Stevenson. Physics Today, 10-11, June 2005.
Explaining the physics of tsunamis to undergraduate and non-physics students . G. Margaritondo. European Journal of Physics. Vol. 26, 401-407, 2005.
The Physics of Tsunami: Basic understanding of the Indian Ocean disaster . M.N.A. Halif and S.N. Sabki. American Journal of Applied Sciences. Vol. 2 (8), 1188-1193, 2005.
Understanding the tsunami with a simple model . O. Helene and M.T. Yamashita. European Journal of Physics. Vol. 27, 855-863, 2006.
Modeling the 2004 Indian Ocean Tsunami for Introductory Physics Students . Gregory A. DiLisi and Richard A. Rarick. The Physics Teacher. Vol. 44, 585-588, December 2006.
Modelling tsunamis . A. Constantin and R.S. Johnson. Journal of Physics A: Mathematical and General. Vol. 39, L215-L217, 2006.
May Gravity Reveal Tsunami? D. Fargion. Chinese Journal of Astronomy and Astrophysics. Vol. 6, Suppl. 1, 398-402, 2006.
Alternative tsunami models . A. Tan and I. Lyatskaya. European Journal of Physics. Vol. 30, 157-162, 2009.
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