Updated Data

Found data which now covers the Sun's ambient conditions up to r = 0.983R. Because of this, I needed some new sexy graphs:

These are for the temperature, pressure, mass and density of the Sun.

This is a graph of the Sun's density against that of static cell's of various temperatures.

 

These two graphs plot the differences of temperature, density and pressure at the top and bottom of each cell, all over the actual value being used. One can see that at around r/R=0.95, the 1-d simulation just isn't sufficient. The rapidly decreasing pressure, temperature and density of the Sun means that the cell rapidly increases with volume, leading to greater differences between the top and bottom of the cell.

The rapidly expanding nature of the cell is illustrated above. Note the logarithmic y-axes.

The above graphs plot the motion and acceleration of two cells of different temperatures, assuming the only forces acting upon them are buoyancy and gravity.

This is the pressure scale height for the Sun.

Things to be done:

1. Work out the energy of the cell (thermal, internal, kinetic, gravitational) for each point to see which dominates. This can be done for different cell sizes/temperatures. This will give an idea of which processes govern the cell's behaviour.
2. Figure out heat loss/drag etc.