Airflow Across a Persistent Cold Air Pool in a Basin

[skyfridge]

This question is regarding the general fluid dynamics involving warm air advection aloft a persistent cold air pool in a small basin that is recessed in a horizontal planar surface. For scale, the basin has a compound parabolic shape, with a 30° viewing angle, a .146m radius at the base, a .292m radius at the aperture and a height of .759m. It has a temperature inversion at the base, with a temperature at the base that is up to 40°C below the ambient temperature aloft.

Angus[1] compares a simpler enclosure uncovered and covered with a polyethylene mesh, under mild winds.

In attempting to answer the questions, I have researched multiple disciplines, including general science, fluid dynamics, meteorology, greenhouse ventilation, building wind loads and agriculture, but I haven't found any specific information to answer the questions.

(1) How would airflow aloft the uncovered basin mix with the cold air pool in the basin under different wind speeds? Specifically, would the temperature inversion minimize mixing? What equations model this case?

(2) To what degree would a screen covering the aperture or recessed in the basin affect mixing of the advection with the cold air pool? What equations would model this case?

[1] Performance comparison of sky window spectral selective and high emittance radiant cooling systems under varying atmospheric conditions, Dr Angus Gentle, Prof Geoff Smith

 

[skyfridge]

Also, the dynamic pressure of the advection across the aperture would be

q=1/2*ρ*t^2

so the advection would be at a lower pressure than the volume in the basin. What does that do to the volume of air in the basin?

I'm picturing a vertical pipe filled with water with an inverted temperature gradient and water moving across the top of the pipe. Since the temperature decreases and thus the density increases from top to bottom in the vertical pipe, I might assume that would lessen the mixing. Does the volume of air act like a surface, preventing or minimizing the advection from circulating into the basin?

The flow across the horizontal surface would probably be laminar to transitional, but I'm guessing. How would that affect the mixing?

A screen atop the basin would probably make it turbulent. Would the advection across the uncovered (or basin with a recessed screen) basin also be laminar to transitional? How does that affect the mixing?