What does absolute humidity do in a large space with a temperature gradient?
Situation: Enclosed space, approximately 8 meters in height. The space is nearly leak-proof, essentially no air being transferred between the inside and the outside. There is a significant temperature difference between the floor and the ceiling. The temperature of the air is around 35 degrees C at the floor, and around 85 degrees C at the ceiling. There is no liquid water in the space, and no condensation occurs. There is some air movement in the space, but it is minimal and only caused through natural methods, no forced air movements with fans.
I am aware that if there was no temperature gradient the absolute humidity (gr/m^3) would stay the same and relative humidity would change depending on the temperature (for this instance also assuming that the outer envelope is not entirely leak-proof, so the pressure stays the same with the increase of temperature). But what happens when there is a temperature gradient in the space? My initial thought would be that absolute humidity would be the same at every height, making it easy to calculate the relative humidity at each height. But my knowledge on this subject is limited, and I have not been able to find any information to confirm or contradict my thought.
The following question seems to come closest to my own question, albeit with two connected rooms and not a single space with a temperature gradient: Which is the same between two connected rooms, relative or absolute humidity?
The answer provided by dmckee states “ Thus the absolute fraction of water will be the same at both ends and the relative humidity will vary.” But the response from the user asking the questions ends with “…temperatures mean different mass densities as well. If this approach isn't wrong, then both absolute and relative humidity’s in the two bottles will be different.”
So I am uncertain what this actually means for my situation. Even if the absolute humidity is not the same at different heights, can somebody provide with some information about the absolute humidity in the space? Would the absolute humidity at the ceiling be higher, the same or lower than the absolute humidity near the floor and would there be some way of calculating this?