Tsunami amplitude change question

[primarygun]

When a tsunami comes from a deeper region into a shallower region, its amplitude changes?Would you figure out a equation related to the content of energy of a wave in terms of frequency and amplitude?
How can I get a brighter pattern of diffraction of a water wave besides adjusting the hole between two slits, besides decreasing the frequency to a appropiate size?

 

[LeBrad]

I can't answer your question exactly, but I'll tell you what I have heard about modeling of tsunamis.

Tsunamis can be modeled as solitons, which are solutions to the wave equation

$$u_{t}=6uu_x-u_{xxxx}$$

A soliton is a wave which keeps its shape as it propagates, much like a solution to a linear wave equation. However, this equation is nonlinear and contains a growth or sharpening of the wave term, $$uu_x$$, and a dispersion term, $$u_{xxxx}$$. When these two terms balance out exactly, the wave holds it shape and you have a soliton.

Perhaps a tsunami travels across the ocean as a soliton, and then when it gets near land and hits something on the bottom the dispersion term becomes small compared to the growth term and the wave begins to grow very fast. I don't know for sure though.

Anyway, I don't know if conservation has anything to do with it, but you can search for stuff on solitons and tsunamis and find out whether or not I was lying.

 

[primarygun]

How about a common transverse water wave?

 

[kusal]

I'm sure that this isthe answer
Velocity of a wave decreases as the water gets shallow. As described in-

v*v=gh
(v=velocity
g=gravity
h=depth)

as v=fλ

(λ=wave length
f=frequency)

Either f or λ has to decrease.
But as f is a constant where the same emitter is concerned the wavelength decreases.
Velocity is lower in the front of the wave than the back of it because sea gets shallow near the shore. So the wavelength decreases as it gets to the shore. But the amount of water is the same. So the amplitude has to rise. Water is pushed upwards.