The idea is that the rotation of the cylinder somehow by viscosity generates the circulating flow, which redirects both the incoming and outgoing flow and thus generates an upward reaction force on the cylinder as a lift force.
But the flow pattern in the right picture is not what observed. It is unphysical because
- It is symmetric in the flow direction. Reversing the flow will give the same picture. The real flow is not symmetric: the flow attachment and flow separation are different.
- The incoming attaching flow in the right picture has a different direction than that of the left picture. It is inconceivable that the mere rotation of the cylinder can cause such a major change of the incoming flow.
We see that the flow is unsymmetric in the flow direction both with and without rotation. We see that with rotation the separation is unsymmetric in the vertical direction, which is the true cause of the lift, not large scale circulation with symmetric attachment and separation, as in the unphysical right picture above.
It is instructive to compare with the following picture on Wikipedia which also shows an unsymmetric flow (now from right to left) with different separation and attachment:
See also Why a Topspin Tennis Ball Curves Down.
After this preparation circulation theory of lift of a wing is then typically pictured as follows suggesting the presence of a large scale circulation generating lift:
But this is again a picture of an unphysical mechanism which does not describe reality. The true mechanism is revealed in New Theory of Flight and as above results from different flow attachment and separation.
Watch the incorrect circulation theory: