How do the contours of the seafloor affect the height of a tsunami?

Question

how does the seafloor topography affect the height of tsunamis? Can the tsunami wave get higher depending on the seafloor texture?

Answer 1

Good Question.

A wave has vertical oscillating particles from its crest down into the water column where it dissipates.  When these oscillating particles are uninterrupted by the seafloor, and also assuming that wind is negligable, the wave height remains constant. When the wave trasverses into shallower water and the oscillating particles start to interact with the seafloor, the wave bottom is now undergoing friction, which slows the wave bottom. The wave in return grows vertically and eventually crashes. This is why you see waves crash at the beach. They look peaceful from a distance, but break as they come ashore. So, in effect, a tsunami that approaches a shore that shallows quickly is the most dangerous, because it still has a lot of kinetic energy whereas a gradual coast will remove most of the kinetic energy before the wave approaches the coast.

Answer 2

Unlike a wind-generated wave, a tsunami wave's energy moves through the entire water column from the surface to the sea floor.  As the sea floor becomes more shallow, the top of the wave overrides the base of the wave causing it to attain a great height.  The total energy is preserved.