We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions.
Simple [hopefully] Pre-questions:
1) If the water is only a meter or so deep, then how can there be enough water to produce waves hundreds of meters in amplitude?
2) Are we to assume the source of the waves are tidal forces from the black hole nearby? If so, wouldn't this significantly alter the local gravity experienced by the crew?
3) Would the waves be more appropriately defined as gravity waves or shallow water waves?
In the case of shallow water waves, the phase speed is, assuming a wavelength ($\lambda$) much larger than the water depth ($h$), given by:
$$
\frac{\omega}{k} = \sqrt{g h}
$$
We are told in the movie that $g_{w} = 1.3 \ g_{E}$, or ~12.71-12.78 $m \ s^{-2}$. If we assume a water depth of 1 meter, then the phase speed should have been ~3.6 $m \ s^{-1}$ (roughly 8 mph).
If we ignore surface tension for the moment and assume the waves were gravity waves, then their phase speed is given by:
$$
\frac{\omega}{k} = \sqrt{\frac{g}{k}} \sim \sqrt{\frac{g \ \lambda}{2 \ \pi}}
$$
From my limited memory, I would estimate that the wavelength of these waves was ~100-1000 meters (let's make the numbers easy to deal with) and we already know the gravity, so we have phase speeds of ~14-45 $m \ s^{-1}$ (roughly 32-100 mph).
It's difficult to estimate speeds from a movie, but I am not sure if these results seem reasonable or not. The speeds are certainly more reasonable (i.e., they seem close to the actual movie speeds, I think) than I thought they would be prior to calculation, but the results bother me.
Intuitive Issue [and main question]
The soliton-like pulse of the waves in the movie makes me doubt both the movie and my estimates. The reason is that the phase speed of solitons depends upon their amplitude and FWHM. My intuition says that the amplitude of the waves alone should have resulted in much higher phase speeds than my estimates and the speeds shown in the movie.
Updates
I am not so much worried about the black hole or any direct general relativistic effect it might have on the planet. I am only interested in the waves on the planet.
Questions
- Can anyone suggest a possible explanation that might alleviate my concerns?
- The water is very shallow, as shown by the characters walking through it. So how can there be several hundred meter waves?
- Is it that all the planet's water is coalesced into these wave-like distortions (i.e., Are these just extreme tides?)?
- Are the waves actual a distortion of the planet's surface and the water is still only a meter or so deep?
- [Just to be nit-picky] If the previous question is true, then how would such a world not have significant volcanic activity (e.g., see Jupiter's moon Io)?
- If the waves are entirely water-based (i.e., they are effectively extreme tides) then their amplitude is orders of magnitude larger than the water depth or $\delta \eta/\eta_{o} \gg 1$. Is this a wave or just an extreme tide?
- If a wave, then:
- would the propagation speed of such a wave(?) be dominated by tidal effects?
- would it act like a soliton-like pulse once formed?
- If a tide, then:
- would there not be (extreme?) weather changes near these mounds of water?
- If a wave, then: