From the wiki article, by the time a large tsunami reaches the shore, it has a wavelength of ~20km, taking ~1-2 minutes to reach the peak of the wave.
And yeah, in the long term, most of the water will go back out to sea (or evaporate off). Of course, areas that were below sea-level before hand, will now be big ponds until they're drained, but by and large, the water will withdraw (which does extra damage!).
And yeah, in the long term, most of the water will go back out to sea (or evaporate off). Of course, areas that were below sea-level before hand, will now be big ponds until they're drained, but by and large, the water will withdraw (which does extra damage!).