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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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    $\begingroup$ "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. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Apr 12, 2012 at 14:59
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    $\begingroup$ 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) $\endgroup$
    – bear foot
    Commented Apr 12, 2012 at 15:44
  • $\begingroup$ Hm, good question. And welcome to Physics Stack Exchange! $\endgroup$
    – David Z
    Commented Apr 12, 2012 at 17:25

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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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There is more to the story about whether matter has net motion / displaced i.e. transported (spontaneously advected), in the linked video there is what is called stokes drift, and also the next link which talks about mass transport in water waves:

Action Lab YouTube video quote based on paper called “Generation and reversal of surface flows by propagating waves” in Nature Magazine

Quote Ref-1: “ the velocity at the bottom of the circle is faster than the velocity of the bottom of the circle, there’s actually a net movement of each individual water particle moving with the waves “

Quote from Ref-2 “ apart from their orbital motion, a steady second-order drift velocity (usually called the mass-transport velocity) “

REFERENCES:

Reference-1=https://youtu.be/vjenjCZcBbE?si=Wg8ST8y9uyHWopX2

Reference-2= https://royalsocietypublishing.org/doi/10.1098/rsta.1953.0006

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  • $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$
    – Miyase
    Commented Sep 10 at 23:53
  • $\begingroup$ (+1) Is there an equivalent experiment like you mentioned but performed underwater vs an underwater target? $\endgroup$
    – James
    Commented Sep 11 at 3:20
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    $\begingroup$ @James are you asking if the boundaries (free surface + floor) are affecting this behavior? $\endgroup$
    – L92MD14
    Commented Sep 12 at 3:46
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    $\begingroup$ @L92MD14 The action lab video places the oscillator material right on the water surface, right? I wonder if he lowers the oscillator to make the waves deep underwater (neither near the bottom nor near the surface), could he get the tractor beam effect to work, in that case? $\endgroup$
    – James
    Commented Sep 12 at 3:53
  • $\begingroup$ As long as the exerted pressure pulse still allows for it $\endgroup$
    – L92MD14
    Commented Nov 24 at 23:46
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As others have mentioned, waterbeaves are not transverse waves, but involve a longitudinal component. The transverse component is important however, as it is what allows longitudinal oscillations in an incompressible fluid.

When a wave comes ashore, the transverse motion is disrupted. The water moves upward and forward to form the crest, but then cannot move downward even after its vertical momentum has been exhausted. Without the resistance from falling into and pushing forward a body of water, the water that formed the crest retains it's forward momentum for an unusually long time.

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