What is the wavelength of tsunami waves?

[omerusta]

Why tsunami waves have a very long wavelengths?

 

[sophiecentaur]

Because the speed is very high and the time for the pulse is very long (the movement of the ground under the sea takes many seconds to complete. Actually, it is more of a Pulse Length than a "wavelength", because the disturbance is not a continuous wave. The shape of this pulse / step change will change as it travels because of dispersion.

The speed of waves on the surface of deep water is roughly proportional to the square root of the wavelength, so the original pulse will become more and more distorted as time progresses.

 

[omerusta]

Because the speed is very high and the time for the pulse is very long (the movement of the ground under the sea takes many seconds to complete. Actually, it is more of a Pulse Length than a "wavelength", because the disturbance is not a continuous wave. The shape of this pulse / step change will change as it travels because of dispersion.

The speed of waves on the surface of deep water is roughly proportional to the square root of the wavelength, so the original pulse will become more and more distorted as time progresses.

Pulse is a wave also. This is a good explanation but it is not the answer to my question.
Why the speed is very high?

 

[AtomicJoe]

Because they only happen ever 10 years or so or more?

 

[sophiecentaur]

This link http://en.wikipedia.org/wiki/Wind_wave" has a formula for the speed of a continuous wave. The wavelength of a continuous wave will be related to the width of an impulse or the rise time or slope of a step transition (the specifics don't really matter at this point). The speed is proportional to the root of the wavelength. The wavelength is very long because the disturbance takes a long time - that's a reasonable statement if you think of the displacement of the ground being in the same direction for a long time - hence the speed is high. If you think this is a bit of a re-entrant argument just look at the formula and possibly follow the other references in the article.
I assume you know the basic wave equation:
c = fλ

 

[janger]

I read a while ago that tsunamis are actually classed as shallow water waves (until they hit land). The velocity of shallow water waves is proportional to the square root of the water depth, IIRC. This is why a tsunami travels fast out in the ocean, but slows down when they reach land.

 

[omerusta]

The wavelength is very long because the disturbance takes a long time

How long time it takes to have a wavelength of hundreds of miles long?

 

[sophiecentaur]

I think you are confusing wavelength with the profile of a pulse. Wavelength in the formula is the distance between peaks of a repeating, continuous disturbance.
It is, of course, possible to base a study of waves on something other than sinewaves (Fourier approach) but all the basic stuff assumes infinitely long trains of repeated wave shapes. - Not what a Tsunami is like. - so you need to approach the familiar formulae with care.

 

[olivermsun]

Why tsunami waves have a very long wavelengths?

Simplistic answer: because the disturbance in the bottom that excites the water wave has a very long wavelength.

 

[omerusta]

Tsunami is a series of waves of extremely long wave length and long period generated in a body of water by an impulsive disturbance that displaces the water. As it crosses the deep ocean, its length from crest to crest may be a hundred miles or more, and its height from crest to trough will only be a few feet or less.
The rate at which a wave loses its energy is inversely related to its wavelength. Since a tsunami has a very large wave length, it will lose little energy as it propagates. The question is not only how tsunamis have a very long wavelengths, but also why?

The main factor which determines the initial size of a tsunami is the amount of vertical sea floor deformation. This is controlled by the earthquake's magnitude, depth, fault characteristics and some other factors. There are other features which influence the size of a tsunami along the coast. Such as shoreline configuration, the velocity of the sea floor deformation, the water depth near the earthquake source, and the efficiency which energy is transferred from the Earth's crust to the water column. But what about the wavelength? What factor is responsible for the extreme length of tsunamis? I have an idea about it and would like to share it with you.

Vertical ground movement in a big earthquake disturbs a very large area of ocean water and forces it to move. Potential energy of this large pool of water suddenly turns into a moving kinetic energy. This energy gradient must be depleted as soon as possible. Whenever an energy distribution is out of equilibrium a gradient of a potential (or thermodynamic force) exists that the world acts to dissipate or minimize. Tsunamis may be considered as one of the abiotic dissipative structures of which energy gradient must be depleted as fast as possible. This energy can only be depleted and carried away by a very long wavelength waves with a very short height. Because only these waves are able to disperse a very large body of water disturbance. Kinetic energy of water must be dissipate as soon as possible. This can only be accomplished by a wave with a very large wave length which is able to carry this energy to very long distances.

This is not the whole story though. I would like to know what do you think up to this point.

 

[sophiecentaur]

I would like to know how many significant sized cycles that a (typical) tsunami consists of. All the diagrams seem to show continuous waves which I find a bit inadequate. I guess it would be a bit like a stone thrown into a pool or a bow wave from a boat.