I've been thinking about the downwash / momentum issue some more. I guess I'm retreating a little from some (but not all!) aspects of my earlier thoughts...
Some key points:
1) If the air is exerting an upward force on the wing, the wing is exerting an equal and opposite downward force on the air. That is certain.
2) If we were in outer space, accelerating our spacecraft by shooting BB's or isolated gas molecules or whatever, out the end of a rocket nozzle, we could be sure that the momentum imparted to the BB's or gas molecules was just as large as the momentum imparted to the space craft.
3) However, when we create lift by pushing down on the air, there are forces that act against the air accelerating freely. NOT the mass of the air molecules (that's not a "force")-- -- rather, the inter-molecular forces created by shearing the airmass, etc. So just because we exert force X on the air, doesn't mean that we see a commensurate acceleration of the air molecules. And the wing doesn't care how much the air is accelerating. As long as the wing is pushing on the air it is happy regardless of whether the air is accelerating or not. Just as the lift force does not actually end up accelerating the aircraft upwards, (most of the time), because it is all used up opposing gravity. The air doesn't care whether the aircraft actually accelerates upward or not. As long as the air exerts an upward force on the aircraft it is happy, regardless of whether the aircraft actually accelerates upwards or not. The force on the air equals the force on the aircraft, no matter how much or how little either actually accelerates, and the happiness is mutual all around and Newton is happy too.
4) Example: if we were swimming in honey, we could hold ourselves up while imparting very little downward acceleration to the honey molecules, because the downward force we exert on the honey would be opposed so strongly by the viscosity (resistance to shearing) of the honey. F=ma, a = F/m, but the net acceleration of the honey is reduced by the fact that other forces arise that act in opposition to the force from our hands as we swim in the honey. That doesn't matter to us as we swim--as long as we are pushing on the honey, the honey is pushing on us the other way too, no matter how much the honey is actually accelerating in response to our push..
5) For a given lift force, just as the amount of momentum imparted to the fluid is less if the fluid is highly viscous, so too is the distance that the momentum will propagate before being dissipated into heat.
6) -- IMPORTANT-- The dissipation of the downwash momentum by shear forces etc does not violate the laws of physics, nor does it contradict the idea that a scale under a box (in which an aircraft or bird is flying) will "feel" the weight of the aircraft in a way that is varies according to the vertical component of the G-load (lift force) that the aircraft is creating,
7) Regardless of whether we are flying in honey or water, if we do some maneuver that makes us weightless, a scale under the pool will no longer detect our weight, and if we do some maneuver that involves a 2-G pullout from a dive, the scale under the pool will detect twice our normal weight. (Assume we are very heavy and very skinny, so buoyancy is negligible, for simplicity.)
8) The extreme ("most viscous") case is when we are standing on dry land. Again, the scale beneath us registers more weight when we are doing a high-G maneuver (e.g. accelerating upwards by un-bending our legs as we jump up). The other extreme case is when viscosity is zero-- we are floating in outer space, accelerating ourselves by shooting bb's out of a gun. If a scale happens to be in our line of fire, the scale will register more weight (force) when we are shooting a lot of BB's to accelerate rapidly, than when we are shooting only a few BB"s to accelerate slowly. So I'm still convinced that a scale under the box of air containing an aircraft does "feel" the aircraft's weight in a way that varies according to the vertical component of the G-load (lift force) that the aircraft is creating.
9) So, it's not appropriate to think of the aerodynamic creation of lift as being exactly equivalent to say, shooting BB's out of a gun in a vacuum. Here are some other ways that the air is different than
BB's-- see this link
section 3.6 here
By the way this is a very good website
Especially the section on airfoils and airflow
10) Key points in summary-- the earth does "feel" the downward push or shove that the aircraft exerts on the air molecules. This downward push or shove in turn pushes or shoves on the earth and makes the earth "feel" the weight of the aircraft. Put a gigantic box 5 miles per side and open to space on top, under the aircraft, and a scale under the box, and the scale WILL register the weight of the aircraft, and doubly so during a 2G pullout, and not at all during a 0G ballistic maneuver. However this downward push or shove exerted by the aircraft on the medium (air), and transmitted in turn to the earth, need not be expressed as a large downward momentum of the medium (air), especially if the viscosity if the medium (air or whatever other fluid we are flying in) is very high.
11) In the real world of course we do see a downwash behind a wing-- it has a huge and well-known effect on the stability and control of the aircraft-- it exerts a downward push or shove on the horizontal tail surface (if there is one). The downwash is also visible in smoke trails. Wake vortices are known to sink downward. Under the right conditions the tip vortices (containing the entrained downwash) can be seen to sink away from the main body of a jet contrail. Etc etc etc.In the real world it is easy to see that a downwash exists behind a wing.
12) Questioning the magnitude of the downwash is not the same as questioning that wing is exerting a downward push or shove on the air-- that is beyond any doubt, downwash or no. Newton's laws and all that.
13) One way to look at the downwash is to see it as kind of a failure of efficiency of the wing-- if we could eliminate tip vortices, etc, the wing would act as if it had infinite span and no downwash-- which is also the same as saying the air would behave as if it had infinite resistance to shearing, and thus did not permit the formation of a downwash? I'm a little hazy on how this all comes together but I think it does somehow.
14) I saw the downwash behind the wing of a hang glider this very morning.