What would a mile/kilometer high wave actually look like? This is regarding waves with heights in the single digit miles or kilometers, which is about the limit on Earth's oceans.
Would there would be any physical processes that would cause such a large wave to not resemble an enlarged version of what we are used to. Meaning this.

My understanding of the factors involved is as follows:

*

*Such large waves cannot move slower than a few hundred mph. Due to the resulting high airflow, formation of large wind waves riding on the wave, and foaming due to these waves is more likely.


*The high Re number will encourage turbulence and thus foaming


*The wave will also pick up disproportionate amounts of soil, possibly causing it's color to not be blue or foaming white.
So, how would these waves differ from the example pictured in terms of color and texture?
 A: One usually distinguishes between deep water waves and shallow water waves, where the latter happens when the wavelength is longer than the depth of the water. When that happens breaking will start to occur.
If the amplitude of the wave is comparable to the depth, it will also experience the water as shallow. Since the average ocean depth is 3.8 km, the wave cannot be more than say 1 km without this happening - and on continental shelves the depths are an order of magnitude lesser, so the super-wave will be breaking there.
In the deep case the wave will look and behave like any other wave; you just rescale the units of length and time properly and use a Stokes wave model.
When you reach shallow water and breaking begins you may use the Iribarren number to describe what happens. The continental slope is about 0.1°, so unless $\sqrt{H_0/L_0}<2\tan(\alpha)\sim 0.0035$ the effect is a spilling wave instead of a grand breaker.
So it will look more like the black tsunami "pancake" seen in the Tohoku earthquake (but on a vast scale) than the blue surfing wave in the question. The texture would obviously be extremely turbulent, and presumably have some similarities with a landslide.
The only physical processes capable of causing waves like these are very big meteor impacts, and while the initial hydrodynamics is complex, uncertain and controversial at some distance the impact would produce huge waves. However, given that much of the ocean isn't shallow compared to the wave it would quickly dissipate a lot of energy as turbulence until it was a lot of standard-sized (!) megatsunami waves.
