I'm interested in knowing which type of wave a tsunami is, in a strictly mathematical sense.
I'm gonna cite from Wikipedia for this:
As the tsunami approaches the coast and the waters become shallow, wave shoaling compresses the wave and its speed decreases below 80 kilometres per hour (50 mph). Its wavelength diminishes to less than 20 kilometres (12 mi) and its amplitude grows enormously – in accord with Green's law.
Except for the very largest tsunamis, the approaching wave does not break, but rather appears like a fast-moving tidal bore.
While the first property strongly hints at a tsunami being a shallow water wave, the latter fact, namely that they usually don't break would rather suggest for the tsunami being a soliton-solution of a Korteveeg-de-Vries-type equation.
I thought the latter property would not be inherent to shallow water waves although Wikipedia, again seems to argue differently, however only with a picture.
So maybe someone can clarify:
- Which equations govern the surface profile of a tsunami? Has this model been tested against satellite measurments?