This part aims at check some relations on the velocity inside the rolls. It would confirm that the simulation made in the former paragraph is correct.
A study shows that the velocity could be expressed by:
We have lead some simulations on a 40x20 grid. The results have been plotted with the theoretical laws on the graph below:
The graph of the evolution of Vx max shows that the computations correspond to the experimental law. The two bents are quite confounded.
On the graph of Vy max, we could see that the two bents are quite confounded for epsilon<2. For epsilon>2, we don't obtain the same results. We could explain this differences: The law is right for small epsilon (<2 or 3). But we could notice that for big epsilon, so for big Ra, the computation are false too: we don't have anymore a laminar flow.
So the computation correspond to the experimental law.
To conclue this paragraph, we have plotted the velocity inside the box: