Start with a cube of still air, with zero mean velocity. Fly a plane through it, and that cube will have a mean downward velocity.
Start with a cube of still air, with zero mean velocity. Fly a plane through it, and that cube will have a mean downward velocity.
Fluid dynamics is really damn complex. Wikipedia is actually not that bad.
I'm not sure that's a real thing that happens in real life or theoretical physics.
If the airfoil isn't moving, is anything happening? Or are you talking about a non-moving airfoil with air moving around it? It's impossible to tell the difference between a non-moving airfoil with air moving around it and a moving airfoil with still air around it, given that they're equivalent provided you define the reference frame correctly.
But yes, the relative motion is what matters.
Are you saying if I have a cube suspended in space, and I put e.g. a drone inside it that just flies around in a circle inside the cube, the cube will start to move down? What then? Will the drone crash into the ceiling of the cube because it's independent from the cube itself?
My brain disagrees with this, but I'm a hacker, not a physicist.
But to your question, if it was a glass cube, I'm pretty sure the drone would hover in the middle of the cube while gravity pulls it down exactly like if the drone was turned off, based on conservation of momentum. Sure the drone is pushing the air down, but then the air hits the bottom, bounces up to the top, and then gets pushed by the drone again. It's (very literally) a closed system, so nothing happening inside is really noticeable outside, and vice-versa (steady state, if you smack the box the drone will notice).
A better analogy one of my favorite kids' shows (I think it was the German Wissen macht Ah) made was putting a heavy boat into a pot of water on a scale - of course the scale reflects the weight of the boat, it has to go somewhere.
It's like answering "how does a lightbulb work" by saying you put current in and it produces photons.