We continue our study of Surface Cooling with the help of Circulating Cells, Version 5. We consider the transport of heat from a hot, sandy surface into the interior of a three-hundred meter cube of air. This three-hundred meter cube represents a single cell in the bottom row of our Rotating Greenhouse simulation. We refer to this cube as our super-cell. We are going to divide it into an array of sub-cells and heat the bottom row of sub-cells so as to induce convection within the super-cell.
We start by modifying our CC5 program. We set p_bottom to 100 kPa and p_top to 96.7 kPa. The total mass of our cell array is now 330 kg/m2, which is the mass of our super-cell. The program will create an array of sub-cells with 30 columns and 15 rows. Each sub-cell will have mass 20 kg/m2 and be 17 m high.
We set T_initial to 290 K, which is typical of a super-cell freshly-arrived at the surface our Rotating Greenhouse. We select Surface Heating, which warms the lowest sub-cells at a constant rate but allows no heat to escape from the array. According to our previous calculations, our super-cell will start to rise when it has warmed by a few degrees. Until then it will accumulate heat by convection of its own sub-cells.
When we start CC5, it calculates a value for the sub-cell impetus threshold using the procedure we describe in Impetus for Circulation. This value turns out to be 0.00003 K, a thousand times smaller than the value CC5 calculates for super-cells in our Rotating Greenhouse. As we showed in Simulation Time, each iteration of our simulation represents one second of planetary time. The heat arriving from the sun in the middle of the day can be as high as 1.4 kW/m2. Let us suppose our sandy planet surface is receiving 800 W/m2. The sub-cells have mass 20 kg/m2 and heat capacity 1 kJ/kgK. We set Q_heating to 0.04 K so that the bottom sub-cells warm at 0.04 K/s. We set our mixing fraction to 0.10. Each time a sub-cell circulates, it will exchange one tenth of its volume with its neighbors.
We reset the sub-cell array and start running. The Figure below shows the simulation after about an hour of simulated time (four thousand iterations).
We record the average temperature of our sub-cell rows and obtain the following plots.
After half an hour, the bottom row of sub-cells has warmed by 20 K and the row above has warmed by 15 K. Meanwhile, the average temperature of all the sub-cells taken together has risen by 5 K. Once it has warmed by 5 K, the super-cell is likely to rise away from the surface, so further warming will be prevented.
The sub-cells above the surface warms by ten or twenty degrees during the day. This warming provides the impetus for the local convection we proposed in our previous post. At the end of the day, sub-cell convection stops, and super-cell convection brings cool air down from above.
And so our simulation confirms the process we described in Surface Cooling, Part III. After sunset, the air temperature in a sandy desert will cool by twenty degrees within a couple of hours. Furthermore, the temperature we experience standing on the sand at mid-day will be twenty degrees warmer than the temperature of the air three hundred meters up.