Originally Posted by ciurpita
is the angular momentum of the air changing?
When you talk about an object's linear momentum, you're talking about something that's unambiguous (as long as you pick one reference frame and stick to it). When you talk about an object's angular momentum, there's some ambiguity introduced because you have to specify the point you're measuring the angular momentum about. A logical point in many instances is the object's center of mass.
In the case of a lifting wing moving through the air, you could measure the air's angular momentum in the wing's reference frame using a point on the wing's centerline. If the wing is left/right symmetric, the air's angular momentum around both the axis that points in the wing's direction of motion, and the vertical axis (assuming wings-level flight) won't change. The left-right symmetry says that it can't.
The air's angular momentum about the "wing line" axis can change (the flow around a 3D lifting wing cannot be front-back symmetric). In fact, you can show that if the linear downward momentum in the wing's wake is increasing, the air's angular momentum about the wing line axis has to be changing (which raises the question of where the torque is coming from to cause this change in angular momentum).