Wave with mass transport?

I don't think this question has been asked on this forum before (at least I didn't find it).

In the case of a tsunami, an earthquake generates a wave which will travel with the sea/ocean as the medium. However, what I remember from high school is that mechanical waves transfer energy but energy only. On a sectional view we represented molecules of water going up and down as the wave travels but the molecules never moved horizontally.

Then why does a tsunami can flood half of a country? in that case the water does move horizontally. what am I missing?

I have read that for regular waves, the problem is different and their momentum comes from wind streams, but I don't think this is the case for tsunami.

I would appreciate some pieces of answer.

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"On a sectional view we represented molecules of water going up and down as the wave travels but the molecules never moved horizontally." Hmmm...that's not entirely accurate. Near the surface they move backward and forward by a modest distance (less than one wavelength), but once the wave has passed they settle back near their original positions. See this nice answer for a animated picture, but take note that water is rather less compressible than the animation. – dmckee Apr 12 '12 at 14:59
Silly me! They do indeed oscillate horizontally. But is that enough to explain the distance covered by a tsunami in the land? (some edge effect) – bear foot Apr 12 '12 at 15:44
Hm, good question. And welcome to Physics Stack Exchange! – David Z Apr 12 '12 at 17:25

Far away from shore the water is moving in a roughly circular motion. If you put a ping pong ball or some other warker on the water you'll find it flows towards the approaching wave and away from the retreating wave. There are loads of animations of this out there; a quick Google found http://www.youtube.com/watch?v=7yPTa8qi5X8 and this is a pretty good description. As you move down in the water the size of the circles decreases until at about one wavelength down the water is no longer moving. Again courtesy of Google, a more technical discussion is http://www.ihad.tmd.go.th/lect18.html.

The problem comes when the depth gets shallower than one wavelength because the sideways oscillation becomes larger and larger as the water gets shallower. When any wave (a tsunami is just an extreme example) hits the shore the oscillation means the water first moves away from the shore then back onto the shore as evey peak hits the shore. In the case of the tsunami the wave is so big that you get first the characteristic sea withdrawal, then the flooding over the shore and onto the land.

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For water waves in general, there will be no net displacement of water. Consider the wind blowing over a closed lake. You will definitely see waves traveling, but there is no flooding at the other end. Water waves can be seen as eddies or recirculating flows, that causes the local water level moving up and down, making it look like a wave.

As long as these circulating are not hindered from the bottom, they will keep circulating, until they are dissipated by viscosity (and they are not gaining energy by wind). Near the shores, these eddies are hindered by the bottom, which demonstrates itself in overturning waves at the beach.

The fundamental difference with a tsunami is the size of the phenomena. For tsunamis, the wavelength can reach the order of 100km, which is $10^5$ larger than ordinary wind waves. This also comes with larger timescales, which is in the order of multiple minutes, as compared to regular water waves with periods of less than a second.

The destructive nature of a tsunami has the same reason as overturning waves. Near the shore, the sea gets shallower, pushing the tsunami wave up to several meters, where the propagating energy is effectively used to demolish everything on its path.

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Thank you very much for this clear answer. – bear foot Apr 16 '12 at 12:23