Ok, a lot to break down here... Vortices, vorticity and turbulence are all different things:
Vorticity:
The rotation of a fluid parcel. Take a fluid parcel (= a tiny bit of fluid) and ask if it rotates: yes, then this fluid has vorticity. Vorticity is a vector field, just like velocity, and therefore defined at every point in the flow. Note that a laminar boundary layer also contains vorticity. This is a mathematically well defined quantity. Further more, in 2D, if you take the integral around a closed line of the flow velocity tangent to that line, the result will be non-zero if the fluid captured in this closed line has vorticity.
Vortex:
This is a flow feature where fluid is rotating around a central point (or line in 3D, called a vortex filament, which is actually a potential flow concept). It is less well defined. In the book of Green called 'Fluid Vortices' I remember him (don't have the book with me right now...) saying something along the lines of "A vortex is defined as such when most fluid dynamicists agree it is a vortex!", although he said this a bit with tongue in cheek.
Turbulence:
Even harder to really pin down. But generally speaking it is a random-ish fluctuation of velocities on top of a mean flow. It often starts from an instability in the flow, meaning that a small perturbation grows into large flow features. I'm actually not sure if a vortex is inherently instable such that it will always generate turbulence, or that laminar vortices exist...? But a shear layer (two layers of flow on top of each other with each a different direction) I believe is inherently instable and thus transitions to turbulence rather quickly (but I'm not a genius in stability theory...). Let's not bother with the question about what happens if the fluctuations become as large or larger than the mean flow.
So, is turbulence required for lift? Hmm, turbulence in the boundary layer is not necessary since fully laminar flow around a wing can also generate lift, albeit (much?) less efficient. But, directly behind the wing, at its trailing edge there is a shear layer generating turbulence. This is however not needed for lift I guess.
Is vorticity needed for lift? Yes it is. I see a wing more as an 'air-bender'. Imagine in 2D a strip of air hitting a wing. After it has passed, the strip is 'bend' or rotated downward. This is only possible if you have vorticity in the flow. Try generating a flow field where part of it is 'bend'when there is no vorticity anywhere in the flow, it is not possible. It is captured in 2D in the Kutta-Joukowski theorem stating that lift is equal to the density times free stream velocity times circulation (circulation and vorticity are directly related). No circulation, no lift.
Are vortices needed for lift? Well, Helmholtz second theorem states that a vortex filament cannot end in a fluid. It needs to either end on a surface or form a closed loop. Along the span of a wing there are these 'bound vortices' (as
@russ_watters already showed with a picture) since the line integral around an airfoil of the flow tangential to this airfoil
*) is not equal to zero (thus there must be vorticity). These bound vortices cannot end in the fluid and thus continue downstream, roll up in two trailing vortices (see picture) and connect through the starting vortex. At least, in potential flow theory where there is no viscosity dissipating these flow features. So I guess vortices are inherently coupled to wings...
Just a few extra remarks about things I have an opinion on:
- A 'partial vacuum' above the wing is not necessary for the wing to function, and in fact does not really exist for airplanes going below mach 0.3-ish. Or, even more relevant, wings work absolutely fine in water and water is incompressible for all intents and purposes here (think of these hydrofoil boats).
- Also, the 'greater speed on top of the wing' is misleading with regards to lift generation. Although true, many then continue to say: 'well, speed is higher, Bernoulli says that pressure is thus lower, and hence lift!'. But why then! Why is the pressure lower if speed is higher... This doesn't really explain anything in my opinion.
- A wing generates lift because air (or water) is 'pushed' downwards, for which a force is needed according to Newtons (real**)) second law: the change in (vertical) momentum is equal to a force. Newtons third law states that an equal but opposite force is thus necessary, which is the lift on the airfoil.
- Bernoulli, although absolutely correct and useful, is the most misleading and misused law there is in fluid dynamics, certainly for the laymen. It does not generate any intuition to understand flow. Pressure decreases if velocity increases... I've wondered very long about why this would be true, maybe that's why I studied fluid dynamics later on :).
- An airplane making use of the 'ground effect' still generates downwash, and in fact this downwash makes the ground effect a thing. The downwash 'hits' the ground generating an extra pressure which gives kind of an extra push upward to the plane (the post already too long for more explanation).
- The more interesting question about wings is this: why would the flow not separate from the upper side? Why would it follow the surface at all? This has more to do with the Coanda effect. So a plane doesn't fly because of Bernoulli, but because of Coanda! :)
*) ón the airfoil the flow has zero speed due to no-slip. So take the flow just outside of the boundary layer.
**) Newton's second law is often quoted as ##F = ma## or force is equal to mass times acceleration. But this is only true if ##m## is constant. The 'real' law is ## F = d (mv) / dt##, or force is equal to the change in momentum. If you apply the chain rule this can be written as ## F = vd(m)/dt + md(v)/dt = v\dot{m} + ma## if ##\dot{m}##, or the mass flux is zero only ##ma## remains. But in fluid dynamics the first term is usually more important.
