This is the wall of water I have been asking about. Of course this illustration shows a wall of water much higher than 13 meters, but it could be imagined as being that height.
Did Japan experience one of these things that was 13 meters?
There's a couple of problems with the above picture. It depicts a breaking wave, and as you'll probably recall from childhood science classes a wave breaks when it enters water ~half the depth of the wave height (I think, I don't recall the general ratio). Obviously that means a really tall wave isn't going to break right on shore like that picture - it would break miles out to sea and what you'd get on shore is the run up - think the surge of waves up a beach, only enlarge in scale appropriately.
Of course the reality is Tsunamis don't generally break like this at all, except for the very largest. That's because they have such long wavelengths - hundreds of km when out to sea. While the wave will "stack up" as it comes into shore (a phenomena called "wave shoaling") it takes a long time to reach it's maximum height. Meanwhile it's also losing speed dramatically, which also interferes with any chance of the wave forming a breaker.
This is mostly because of the slope of the seafloor and how rapidly it shallows. As any surfer will be able to tell you, steeper beaches form cleaner breakers, technically known as plunging waves. This is because wave amplitude increases rapidly, much faster than the wave can decelerate, thus the top of the wave is trying to move forward faster than the bottom of the wave (which is experiencing friction from the sea floor). Thus the wave curls over. This is the "classic" surfing wave, which is also much more dangerous to surf as a plunging wave is much more destructive (it it plunges onto a board it can quite happily snap it in half).
On a gentler slope, you don't get plunging waves, but instead spilling waves. Instead of curling over, these grow to height more gradually and slow at a more similar pace, just the top part of the wave, instead of curling over, "spills" down the front of the wave as whitewater. This is a much safer wave to surf as you're riding "atop" the wave rather than under the face of it.
For a wave as large as a Tsunami, of course, covering such vast distances and with such a long wavelength, virtually
any beach has a gentle slope, relatively speaking, and a Tsunami won't cause a plunging wave. Even if it hit a steep enough continental drop-off that it
did form a curling breaker, this would happen miles and miles out to sea, and would still only hit the coast as a giant surge of foam and surf, not as a curling wave.
More normally, the sea floor slopes very gradually (relative to the wavelength of the Tsunami) thus instead of plunging waves, it forms a spilling wave. These will start to "break" miles out to sea (as we see in the video with the coastguard ship) but as a spilling wave breaks over a long period of time, we see them still breaking as white foam when they hit the shore.