The truth is that there is no requirement for nature to understand our definitions, our formulae, or even basic mathematics. We can fly because of how nature behaves, not because of how we describe it. We make up a bunch of words to describe what we have observed, then realize it is a bit wrong and fix it. Then repeat.
The descriptions that start with single molecules of air and Newtonian Law are the most accurate place to start. When the system is real-sized, this description becomes far too complex to solve and offers no intuition. The descriptions that deal with airflow shapes, multiple engineering terms, pressure fields, etc. are attempts to simplify the Newtonian calculations using assumptions and bounds with the caveat that the accuracy may reduce. and may in fact be completely wrong (especially true in earlier models). The descriptions that are given to pilots typically are lacking scientific accuracy, contain very few formulae, and don't yield useful results. However, they are the ones that are most intuitive and tend to be the easiest way to generate sufficient understanding to fly the airplane.
In the end, every explanation is inaccurate to some extent. The most accurate explanation is the Newtonian one. The complex explanation is just a derivation from Newtonian physics. Talking only about pressure gradients lies between these other two methods, and I think is just confusing.
This is how I like to think of it:
- First, think of just one molecule coming towards a wing. There is only one thing the wing can do to help the wing counter gravity, that is to deflect the molecule downwards.
- If you continue to deflect more molecules downwards, you will have more molecules below the level of the wing than you have above, so you will have greater pressure below.
- The molecules will move from highest pressure to lowest pressure. We've seen this, it seems intuitive and we've even added words to the physicist's vocabulary to explain why. Entropy, Brownian motion, etc.
- The move from high to low manifests itself in a number of ways, most of which are important for aerodynamicists to understand. Flow behind a wing can be upwards. Wing tip vortices will develop. There is a lot of flow disruption behind the wing, but in the production of lift, the wing only causes the initial effect. Everything else is a result of the disturbances to the air that have already been caused.
- The pressure gradient (created by moving air molecules downwards) will also change the flow in front of the wing. I think this is a key point to acknowledge, because this one seems to conflict with the starting point of considering just one molecule. It doesn't conflict, but does require that we now think of one molecule in front of the wing that already has some vertical velocity.
- If the single molecule starting point is still causing some concern, then consider a group of molecules, bumping into each other with a net vertical velocity. What can the wing do to that group to help the wing counter gravity? Would just compressing them help at all? Or would you have to change the net vertical velocity as well?
Sorry, no formulae to punch into your calculators. Just a description of what I believe is going on.
Capt Pit Bull, according to your understanding of physics, falling bodies don't accelerate, because otherwise momentum wouldn't be conserved. Include gravity into your consideration of downwash, and you will find that momentum and energy are conserved.