The situation is as shown above. Now, to explain why the bottom disk rises, I applied Bernoulli's Equation at a point just below and just above the disk.The pressure difference hence obtained should push the disk up. Even though this is definitely incorrect, as these two points are not on a streamline, I have no clue as to the correct explanation.
The air between the 2 disks is moving faster than the air below the lower disc. Moving air has a lower pressure than stationary air (Bernoulli Principle). So the pressure above the lower disk is lower than the pressure above it. Therefore there is a net upward force on this disk.