What happens when tsunamis surpass the speed of sound?

[Loren Booda]

A news broadcast tonight claimed that a tsunami following the 1883 Krakatoa explosion may have moved at speeds approaching 800 miles per hour. What would be the mechano-acoustic effect of such a supersonic phenomenon? For instance, how would this water waveform change due to turbulent feedback from the contiguous air?

 

[Andrew Mason]

A news broadcast tonight claimed that a tsunami following the 1883 Krakatoa explosion may have moved at speeds approaching 800 miles per hour. What would be the mechano-acoustic effect of such a supersonic phenomenon? For instance, how would this water waveform change due to turbulent feedback from the contiguous air?

There would be a shock wave created by the water wave that would propagate up and out from the water wave front. Someone in an airplane might hear a sonic boom. But no one on the ocean will hear a thing until it hits (assuming it did not slow to subsonic speed before hand).

AM

 

[russ_watters]

This is like asking "since sound travels at the speed of sound, does it make a shock wave" Well, in a way, it is a shock wave, but it doesn't create any.

In deep water (where the tsunami moves that fast), a tsunami is barely visible and affects individual molecules of water very little. A molecule of water on the surface will slowly rise up, then slowly fall back down to where it was before (or, perhaps cycle up and down a few times) - only moving a total of a few centimeters. Its wavelength will be kilometers long.

 

[Hurkyl]

Wave motion through water causes molecules to move in a more circular fashion, doesn't it? Obviously a normal wave doesn't cause all that much lateral displacement, is the same true of the tsunami? I would have guessed a lot of lateral displacement, based on their behavior upon reaching land.

 

[Andrew Mason]

This is like asking "since sound travels at the speed of sound, does it make a shock wave" Well, in a way, it is a shock wave, but it doesn't create any.

In deep water (where the tsunami moves that fast), a tsunami is barely visible and affects individual molecules of water very little. A molecule of water on the surface will slowly rise up, then slowly fall back down to where it was before (or, perhaps cycle up and down a few times) - only moving a total of a few centimeters. Its wavelength will be kilometers long.

I was thinking of the wave in question as being a height of water racing across the sea, pushing the air horizontally at supersonic speeds.

Obviously water moved horizontally in the Indonesian tsunami. This may seem like a naive question, but how did so much water move horizontally from sea to land if it was just a small up and down undulation as you have described?

AM

 

[russ_watters]

Wave motion through water causes molecules to move in a more circular fashion, doesn't it?

I was thinking about that after I typed it - I'm not sure now, and it may be different for waves on the surface and under it. I'm trying to picture a bobber on a fishing line - I think it just moves vertically, but the water in the wave would have to move horizontally as well, otherwise it couldn't pile-up.

Obviously a normal wave doesn't cause all that much lateral displacement, is the same true of the tsunami? I would have guessed a lot of lateral displacement, based on their behavior upon reaching land.

In the open ocean, tsunamis have an amplitude of at most a couple of meters, but wavelengths of kilometers. Maybe they move in stretched-out elipses?

I was thinking of the wave in question as being a height of water racing across the sea, pushing the air horizontally at supersonic speeds.

Obviously water moved horizontally in the Indonesian tsunami. This may seem like a naive question, but how did so much water move horizontally from sea to land if it was just a small up and down undulation as you have described?

When the tsunami slows down on reaching the continental shelf, the slowing compresses the wave. If you take a wave that's say, 2m high and 10km wide and compress it to half a km, that would make it 50m high (or something like that).

 

[Astronuc]

Just reminder - the speed of sound in air is about 790 mph ( 350 m/s), but the speed of sound in water is higher - about 1480 m/s, or 0.92 mi/s or 3300 mph (slightly more than a factor of 4).

So a tsunami at 800 mph well below supersonic speed in the medium in which it propagates.

One also has to look at the acoustic coupling between gas and liquid, which is usually quite low do to the significant difference in density.

 

[Bystander]

I was thinking about that after I typed it - I'm not sure now, and it may be different for waves on the surface and under it. I'm trying to picture a bobber on a fishing line - I think it just moves vertically, but the water in the wave would have to move horizontally as well, otherwise it couldn't pile-up. In the open ocean, tsunamis have an amplitude of at most a couple of meters, but wavelengths of kilometers. Maybe they move in stretched-out elipses? When the tsunami slows down on reaching the continental shelf, the slowing compresses the wave. If you take a wave that's say, 2m high and 10km wide and compress it to half a km, that would make it 50m high (or something like that).

Wave tank observations on "near sinusoidal waves" are that: 1) at the surface, a point moves in a nearly circular path (wave motion from left to right results in a counterclockwise rotation, the end of the path being slightly to the right its beginning); 2) moving from the surface toward the bottom, the paths flatten, the vertical motion extremes decreasing in magnitude more rapidly than the horizontal; 3) near the bottom, the path becomes a nearly linear oscillation from left to right, and is of a magnitude approaching zero; 4) there is a return flow in the opposite direction of the surface movement along the bottom of the tank. There are assorted constraints and conditions on this as far as wave height:wavelength, wavelength:depth, and wave shape.

For the other question, the tidal bulge at the equator is moving faster than sound in air --- it is considered a wave.

 

[hehe]

Why does sound in water go faster than the normal small waves you can see?
I thought higher forces would result in higher speeds and tsunami's seem to confirm this?

 

[Andrew Mason]

Why does sound in water go faster than the normal small waves you can see?
I thought higher forces would result in higher speeds and tsunami's seem to confirm this?

This is a good question. I am not sure of the complete answer, particularly regarding Tsunamis, but I will give it a shot and maybe others will add to it.

The speed of any wave in matter depends upon the magnitude of the restoring accelerations of a displaced molecule. Since sound is a compression wave in which the molecules undergo lateral motion about an equilibrium position, the restoring forces are the molecular forces (ie. electrical forces between molecules). In a small purely transverse wave in which the molecules essentially move up and down only, the restoring force is largely gravity, (as well as surface tension). So you can see why they would move at different speeds because of the different restoring forces. In 0 gravity, you will still have sound in water but you would not have surface waves.

A Tsunami is different (as any large water wave) because it is a combination of compressive lateral and vertical motion: the only way to have a large vertical change in height of water is to move water laterally (ie out of the way to make a trough and compressed to make a peak). So as the wave moves, the water moves laterally forward (in the wave peaks) and laterally backward (in the troughs). For a Tsunami, this means there is a huge lateral movement of water. For the physics of Tsunamis, the Canadian government has a very good site with charts and animations at:
http://www-sci.pac.dfo-mpo.gc.ca/osap/projects/tsunami/tsunamiphysics_e.htm

AM

 

[hehe]

Thanks.
I thought surface movement was a result of pressure waves or the other way around, i didnt know they were two different types.
I will need to take some time on this... :)