There are craters that are permanently dark at the Moon's poles, since the Moon's axis tilt is so small that the sun never rises above the crater rim. On the Moon these get incredibly cold, since there is no atmosphere to transfer heat.
What would the atmospheric/weather effects be if this situation existed on a planet with an Earthlike atmosphere?
Specifically, assuming something like Whipple crater on the Moon - 3 kilometer deep crater in permanent shadow, with a high plateau in near-permanent sunlight right next to it, almost directly at the pole? Assume that the atmosphere, solar flux, etc. is the same as Earth's and the axial tilt is zero.
Presumably the atmosphere would work to transfer heat by convection from the sunlit to the shadowed regions. But how violent would this be? Would it be like a constant super-hurricane, a constant supercell thunderstorm, or relatively gentle but continuous winds?
I'm specifically thinking about the local weather, not the planet's general climate. In case it matters, though, the planet's climate is much more stable due to not having seasons, but the average temperature and range of topography and biomes is similar to Earth - as is the ocean/land ratio.