Why does the air at the top of the wing move down? I think it's because of a negative pressure field. Some people think it's the viscosity of the fluid. Why does the air at the bottom of the wing move down? I think it's because of a positive pressure field. But others don't think so. What is the reason?

  • $\begingroup$ Do you mean - since the air approaching the wing has been split into two streams and the upper one has been directed upward, then why does the stream curve down again after passing the crest of the wing? $\endgroup$ – Ponder Stibbons Dec 18 '19 at 0:18
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    $\begingroup$ There is no negative pressure here. Did you mean positive the first time? you said positive the second time. In which case, I would guess that you have a viable way of looking at it. The stream of air is, in a sense, pressed to the wing by the ambient pressure. $\endgroup$ – Ponder Stibbons Dec 18 '19 at 0:20
  • $\begingroup$ @PonderStibbons Generally speaking, air moves downward through the wing. Why? $\endgroup$ – enbin zheng Dec 18 '19 at 0:22
  • $\begingroup$ "Through"? What type of wing? An aircraft wing is not usually permeable to the atmosphere to any significant degree, so the air moves around the wing, not through it. Do you mean that the air moves downward from the wing (which in a momentum balance sense is the nature of lift). $\endgroup$ – Ponder Stibbons Dec 18 '19 at 0:25
  • $\begingroup$ @PonderStibbons Oh, I'm sorry. I mean the air flow around the wing, not through the wing. $\endgroup$ – enbin zheng Dec 18 '19 at 0:29

Lift is generated by conservation of momentum. The wing causes air to be directed more downward, to gain momentum downward, and that is balanced by the upward momentum of the aircraft.

It is a classic theorem that no lift is generated from a non viscous fluid. And so in this sense, the viscosity is required to get this additional downward motion. But, on the other hand - even if lift is not being generated, the air has to split, some of it being pushed upward to go over the wing, and that has to be pushed back again. This push back down is effectively due to the pressure gradient. It is an important thing that in a non viscous fluid all these pushes and pulls do really add to zero.

But, also ...

One can get a good approximation to the performance of the wing by using the equations for non viscous fluid plus boundary layer theory. That is, it is only in the interaction of the wing with the air right on the wings surface that viscosity comes into play. So, in this sense - the viscosity cannot be significant in the overall flow and bending of the stream of air around the wing. Viscosity is a bit like tripping someone up to make them fall down the stairs.

The bulk motion is not affected by viscosity, it is driven by the pressure gradient, but the boundary conditions implicitly give the viscosity a big impact.

  • $\begingroup$ What causes the fluid to flow down the wing when there is no viscosity? $\endgroup$ – enbin zheng Dec 18 '19 at 7:55
  • $\begingroup$ The pressure gradient. Consider an object submerged in stationary water. This object is pushed down by the pressure above it and pushed up by the pressure below it. The upward push less the downward push is the net push up. If this is greater than the weight then the object moves up. If it is less, the object moved down. That object can be a blob of water and the same thing applies. Similarly in air, except that it is complicated by the air being compressible. $\endgroup$ – Ponder Stibbons Dec 18 '19 at 23:04
  • $\begingroup$ Positive viscosity on the other hand is only ever a drag, causing an object to lose energy, it is not the motive cause of motion. Viscosity is not the same thing as, for example, a stickiness that would cause the fluid to somehow hug the surface of a solid. The fluid only curves around the wing because it is pushed by the pressure gradient. If the rest of the air was not there, it would fly off into space and not hug the wing. $\endgroup$ – Ponder Stibbons Dec 18 '19 at 23:09
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    $\begingroup$ You mean was causes downwash? Are you asking, effectively, what causes the lift? You might get something from iopscience.iop.org/article/10.1088/1757-899X/50/1/012025/pdf showing that a spinning cylinder can generate lift and so the angle of attack is a detail of the flat wing approach. $\endgroup$ – Ponder Stibbons Dec 19 '19 at 2:46
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    $\begingroup$ For a flat wing, consider squirting water at a surface at an angle. Then water bounces off at a different angle. The change in velocity means a change in momentum. So, taking the Newtonian principle of conservation of momentum, the surface has to absorb the momentum. The deflection of the air under the wing happens for essentially the same reason (despite differences of detail) and keeps the aircraft in the air likewise. There are other ways to explain this - such as vortex shedding using the vorticity equation, but the basic linear momentum change due to atoms bouncing off the wing covers it. $\endgroup$ – Ponder Stibbons Dec 19 '19 at 2:52

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