You need to read up a bit more on the physical principles of flight. One of the best books I know on that topic is John Denker’s See How It Flies. Your question is dealt with in Chapter 3.
@hanski you seem to start with a mistake.
In a wind tunnel the object eg a plane is static and the wind or air flow is created by fans.
In reality the plane creates (shall we say) its own wind by the shape of the wings and the fact that the aircraft is driven forward by its engine or in the case of a glider by its movement into the air.
This is where the lift is generated (well actually its pressure differential between the air travelling below and that travelling above the wing.
The wings themselves are designed to suit a particular purpose. Winglets or the Jodel cranked wing along with tapering of the wing allows the air flow to be less (draggy) towards its tips. The idea being that this improves slow flight. The air also flows along the wing from its widest to its skinniest part.
Delta wings are more slabby. These aircraft are usually carrying a great deal of power. This power allows for a certain amount of slowish flight with no necessity for wingtips. Their biggest problem is in fact slowing especially in the case of military jets.
Before everyone jumps on me I have deliberately tried to be as general and simple as possible by avoiding engineering and physics terms.
If you want fun, think about how and why aeroplanes can fly upside-down… 
Ultranomad wrote:
One of the best books I know on that topic is John Denker’s See How It Flies.
I second that. A very good book!
You can also read through the wikipedia about lift
However, I wouldn’t care much about this unimportant “higher velocity above than below” stuff and so on. That’s a bit too sophisticated for most GA motor-powered planes, like we use them all.
The airfoils we use are symmetric or near-symmetric. At least for a physical observation of the major forces involved in lift and thrust and drag, it’s negligible. They generate lift just the same way as does your hand that you put out a window when driving a car. It’s for the absolute most part just the angle of attack with regards to airflow that decides over lift. If the wing has a high angle of attack and sufficient power is applied, the airflow hits the wing on its underside and is reflected to below. As a result, the plane goes up. That’s it. End of the story.
You can even have a perfectly laminar airflow with a symmetric airfoil. And that is what is pushed further for our general aviation stuff. Because in the end we do not want too much lift, because lift equals drag. Lift is just designed to be enough to be sufficient in cruise, to have a convenient angle of attack.
If you go into glider profiles or some special purposes then you’ll see some cambered airfoils and even adjustable airfoils. But for us, that is a side-effect only.
Now before anyone starts to shout at me: look into the numbers! The effect produced by different speeds of airflow just due to the airfoil design are magnitudes smaller than what we set with engine power settings and angle of attack, that is: deflecting air masses.
Thanks for all your good comments. But I do not refer to lift this time – only to speed of air around airplanes. The link from Ultranomad is REALLY good. I have read some of those pages before but did not remember them. They seem to confirm my thoughts as long as the wing is creating lift:
https://www.av8n.com/how/htm/airfoils.html right before 3.6.2 says
“As we saw in the bottom panel of figure 3.9, at high angles of attack a wing is extremely effective at speeding up the air above the wing and retarding the air below the wing. The maximum local velocity above the wing can be more than twice the free-stream velocity. This creates a negative pressure (suction) of more than 3 Q.”
Picture 3.20/3.23/3.24 explain about the circulation which gives more speed above the wing (towards the tail of the plane) and slows it down below.
wikipedia tells like this: “The actual critical Mach number varies from wing to wing. In general, a thicker wing will have a lower critical Mach number, because a thicker wing deflects the airflow passing around it more than a thinner wing does, and thus accelerates the airflow to a faster speed. For instance, the fairly-thick wing on the P-38 Lightning has a critical Mach number of about .69.”
So when Lightning flies at 0.7, the air around reaches 1 mach somewhere – I can not see any other way than that the speed above wing runs to the opposite direction of the airplane at speed of 0.3 mach.
But the ‘critical mach number’ is not limited to the wing and can appear to wing even without lift formation. Air around fuselage may also reach speed of sound before the plane reaches it. Can that be explained with some circulation or how? Not a critical question but interesting. Anyway to me it looks magical that the plane actually makes the air run to the opposite direction even twice the plane speed (see the quote from av8n).
hanski wrote:
Anyway to me it looks magical that the plane actually makes the air run to the opposite direction even twice the plane speed (see the quote from av8n).
When you consider the average speed of the air molecules is near 1000knots, moving in every direction already, it is perhaps not so hard to consider an extra 200knots as nothing… It is quite difficult to apply newtons laws to fluids, and those laws break down at the atomic level anyway.
It is much easier to measure and model changes in dynamic pressure, which you can also see as an integration of the velocities in a particular region. When a light aircraft flies at 100knots there is still a pressure wave travelling at the speed of sound very slightly disturbing the airflow in front of the aircraft. You know this because you can hear a plane approach.
It’s all been written before but it is all Newtonian mechanics really. All the other stuff e.g. Bernoulli or Navier Stokes are simplifications to make it all practical for fluids 
There is no “circulation” either in a physical sense. It is only when you integrate the airflow around a wing that you get a negative reverse flow. The air doesn’t actually flow backwards.
hanski wrote:
In my opinion the wing moving to left must give the still air some speed towards right, which sounds ridiculous
It’s not ridiculous, it’s exactly what is happening. IMO most misconceptions about how a wing works stems from the (mostly) mathematically correct, and to a slightly lesser degree physically correct assumption that a wing in a wind tunnel “is the same as” a real wing moving in still air. From a conceptional point of view it gives the wrong message, because it doesn’t really pick up the main point: circulation.
In still air, the velocity of the air is, well zero. If you subtract the “wind tunnel velocity” from the typical diagram and videos, all you are left with is circulation. This is what still air observes, and ONLY that. Circulation around a wing IS lift. Lift IS circulation. Zero circulation = zero lift. This is true no matter what airspeed you have (the speed of the wing through the air). To create lift you need something moving through the air at a velocity relative to the (still) air. The shape of that ting has to be specific for it to create circulation in the air. If you measure the (still) air in a region when an airplane passes by, the only thing you will measure is circulation and the effects (+ some drag effects etc).
Circulation can be a hard nut to understand, but if you don’t, you have no clue whatsoever what lift is all about. It’s only recently that a first principle theory has been made for the ad hoc Kutta condition.
But is there really such a thing a still air outside space and a vacuum?
