Why did it take 7 hours for the tsunami to reach Africa?

In summary, the low waters seen on the coasts during a tsunami are caused by a collapse or shaking of the ocean floor, while the high waters are due to the energy of the wave being concentrated in a smaller area as it approaches the coast. Possible explanations for these high waters include wave dispersion, wave breaking near the coasts, and the well-known law for deep-water wave propagation which shows that the phase velocity depends on the wave vector k. The main cause for the high waters is most likely the energy of the wave, which is initially due to the shaking of the ocean floor. The energy of a tsunami wave can be represented by the equation v_{ph} = \sqrt{\frac{g}{k}}, which takes into account the
  • #1
lalbatros
1,256
2
I would like to understand a little more about the low waters and high waters observed during a tsunami.

My first understanding was that the bottom of the ocean collapsed by a few meters in a 500 km² region in front of Sumatra.
I could then understand low waters on the coasts.
However, I could not understand the 10 m high waters that followed.
Possible explanations are:
  • shaking of the bottom of the ocean instead of a simple collapse
  • wave breaking near the coasts
  • wave dispersion
The well-known law for deep-water wave propagation tells us that the phase velocity depends on the wave vector k :

[tex]v_{ph} = \sqrt{gk}[/tex]​
The wave dispersion will distord an initial disturbance.
An initially negative disturbance (low water) can even change its sign and show positive portions (high water).
It is quite easy to check that numerically by a simple Fourier analysis.

But now the question is: what is the main reason for the high waters?
Is it dispersion?
Is it shaking?
Is it a coastal effect?
Is it still something else?

Any idea ? Any reference ?

Thanks
 
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  • #2
It's ENERGY (which is initially due to the "shaking"). A tsunami in mid ocean would be a wave that is not very high but has a lot of energy. As that wave approaches the coast the water becomes shallower (that's the "coastal effect") that energy becomes "focused" in less area so the water builds up.
 
  • #3
HallsofIvy

I have two questions now!

- Do you mean that a dip in surface caused by earthquake would remain a dip until it reaches shallow waters? Or do you think the 'overshoot' is due to another reason? If it remains a dip (negative displacement) you hint that it will increase when the wave reaches the coast?

- What do you think is the expression that represent the energy of a wave ?

Thank,

Michel
 
  • #4
/SQRT gk is dimensionally incorrect--should be /SQRT gd.Can anybody here give a derivation for the phase velocity?
 
  • #5
It isn't a matter of a "dip" that remains a dip. The instantaneous dip becomes a wave: with both troughs and heights.
 
  • #6
gptejms:

Sorry for the typing error, the phase velocity for deep water waves is given by:

[tex]v_{ph} = \sqrt{\frac{g}{k}}[/tex]​

You can find the derivation on this site for example:

http://www.ocean.washington.edu/people/faculty/parsons/OCEAN549B/lwt-lect.pdf [Broken]​

I found an interresting discussion about tsunamis there:

http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_02.htm​

You can read there that tsunami waves have typically a wavelength of 100km.
Therefore, the shallow water phase velocity applies instead of the deep water limit.

HallsofIvy:

I agree with your remark. I come to realize that the shaking of the ocean floor produces troughs and heights.
However, are the amplitudes of these wave troughs and heights essentially the image of the floor motions? (more or less periodic motions then)
Or does the dispersion of the wave play a non negligible role ?
Indeed, since the phase velocity depends on the wavelength, and since the excitation is certainly not harmonic, the wavepacket could change its shape quite a lot. It can even develop heights when the initial condition contains troughs only.

In addition, I have the belief that the floor of the ocean does not move up and down but that it repeatedly moves downward.
If that was true, then I don't know how wave heigths could be explained without dispersion.
Obviously, I would need better information on the boundary condition for typical tsunamis.

Thank a lot
 
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  • #7
i was wondering how fast a Tsunami travels ..it was all over the news that Tsunami's travel at hundreds of miles an hour , i don't agree with that.
 
  • #8
As the wavelength of Tsunamis on open sea is larger then the depth of the water they can be thought of as 'shallow water' waves. The speed of such a wave is:

[tex]v=\sqrt{gd}[/tex]

With g the gravitational acceleration and d the depth of the water. E.g. for a depth of 5km thi syields a speed of about 800km/h.
 
  • #9
then how come it took so long to hit Africa ?
it seems like it took till the next day to hit the east coast of Africa..
 
  • #10
From what I understand, the waves weren't that high. Hawaii has 30 foot waves every now and then. Mavericks, near the bay area near San Fransisco has similar waves on good days. That's a 60+ foot wave face that the surfers are negotiating.

The issue with the 20ft or so Tsunami waves is their length, not their height. The larger amount of energy results in a wave that affects larger masses of water as it passes through. As the waves reach a shoreline, their exteme length causes them to continue flowing inwards for quite a ways.

Bigger waves move at faster speeds. At Mavericks, the really big waves require the surfers be towed into the wave front with a jet ski pulling the surfer.
 
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  • #11
Some big wave pics here:

http://billabongxxl05.com [Broken]
 
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  • #12
willib said:
then how come it took so long to hit Africa ?
it seems like it took till the next day to hit the east coast of Africa..

It took about 7 hours. This may seem like a long time, until you think about how far it travelled. The wave crossed the ocean in roughly the same amount of time it takes to cross by passenger jet. To get from the quake epicenter to the coast of Africa in 7 hours, the wave had to travel about 800 kph (500 mph).
 

1. What is a tsunami?

A tsunami is a large, powerful wave caused by a disturbance in the ocean floor, such as an earthquake, volcanic eruption, or underwater landslide. It can travel at high speeds and cause significant damage and destruction when it reaches the shore.

2. How do tsunamis form?

Tsunamis form when a large amount of water is displaced by a sudden movement of the ocean floor. This displacement creates a series of waves that radiate outwards in all directions, similar to how ripples form when you drop a stone in a pond.

3. What is wave dispersion?

Wave dispersion is the process by which waves of different frequencies and wavelengths travel at different speeds. In the case of tsunamis, this means that longer wavelength waves will travel faster than shorter wavelength waves, causing the wave to spread out and decrease in height as it moves towards the shore.

4. How does wave dispersion affect tsunamis?

Wave dispersion can cause a tsunami to lose energy and change shape as it travels over long distances. The longer wavelength waves will travel faster and arrive at the shore first, while the shorter wavelength waves will lag behind. This can result in a more gradual and less destructive wave at the shore.

5. Can we predict the dispersion of a tsunami?

Yes, scientists use mathematical models and data from past tsunamis to predict how a tsunami will disperse as it travels. However, it is still a complex and challenging process, and predicting the exact behavior of a tsunami is not always possible.

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