I was recently reading this very helpful string What is the physical meaning of circulation found in Kutta condition? and it explained very nicely potential flow around an airfoil. My question then is this: what happens to circulation around a cambered airfoil at a small, negative angle of attack which is producing lift, but is also producing upwash. How do we reconcile Kutta-Жуковский theorem with this observation?
Don't know if you're still on this, but I think that your doubt arises from a misunderstanding in terms: the angle of attack we are normally discussing about is the geometric one, i e. the AoA which is referred to the line connecting the leading edge with the trailing edge of the airfoil. This line has no real aerodynamic meaning (unless the airfoil is symmetrical: in that case it coincides with the line of zero lift). The AoA that separates positive lift and negative lift is the aerodynamic one and it's measured in respect to the line of zero lift.
For a not symmetrical airfoil (aka cambered airfoil) the line of zero lift is normally negative, just like in your example:
think about cambered airfoils, some of them have a zero lift angle at around -5°, so if you held one at -3°, you would have lift but negative AoA
Yes, you would have lift at negative geometric AoA but positive aerodynamic AoA.
The geometric AoA is normally used because the line connecting leading and trailing edge is easy to draw and not mistakable, even if that can lead to an airfoil producing positive lift at negative AoA: but that's not against physics, it's just a convention.
what happens to circulation around a cambered airfoil at a small, negative angle of attack which is producing lift, but is also producing upwash
Hopefully now it's clear that a positive lift is produced if and only if the circulation is positive too (and viceversa). That the (geometric) AoA is negative has nothing to do with the sign of the circulation and of the lift.
By the way, since we are dealing here with potential flow around a 2D airfoil, please note that the net downwash around the airfoil is always zero.
The forward top part of a cambered wing will always create upwash if it is lifting. Momentum (mass of air molecules) plays a key role in creating the lifting low pressure area above the wing.
Reynolds number also plays a key role, particularly velocity. "Top lift" can only be created if velocity is sufficient (literally) for the wing chord to pass before the low pressure area collapses$^1$. This tendency for the air to "bend" back towards the wing is the downwash.
if only the front top of the wing pushes air up, and the rest of the top is bending air down, the net effect is lift$^2$ $^3$
Lower Reynolds number wings cannot create top lift, and must rely on "surfing" the air (action/reaction) off the bottom of the wing. These wings will not create lift at negative angles of attack.
Top lift has a much lower drag penalty. This is why thin undercambered wings fell out of favor as airspeeds of early planes began to exceed 100 km/hr.
$^1$ angle of attack is also a critical factor
$^2$ this can happen even at a slightly negative AoA.
$^3$ similar to leverage, the longer distance/time, of downwash zone creates more lifting force than the upwash takes away
Thanks to everyone who has posted answers and comments on this over the years.
My question has an incorrect premise in it which was pointed out by some people and my responses reveal some sloppy use of terminology. ‘Upwash’ is probably better thought of as created by a wing, in that respect, in the wake of any airfoil producing lift there must be a downwash component, or else lift is not being produced.
However, in my mind I was considering that this component was not sufficient to turn the incident airflow from an upward to a downward direction. That the airflow is at such an angle should have been made clear in the question, but was not because I did not realise this at the time. As can be seen in some of the discussion, the reason this is of importance is that the only way this is possible is if some other effect is causing that updraft, perhaps a nearby body or another wing, or 3D effects from a different part of the same wing.
As a result, the question is no longer really a question.