my understanding is that Bernoulli's principle also involves equal transit times. Meaning that the same two positions need to rejoin later.
When the sail has no thickness the outer flow cannot go faster and still be a valid Bernoulli effect, because the outer and inner paths have the same distance.
That being said, there might still be another similar principle at work, though technically speaking it should not be called Bernoulli.
It isn't at all. Bernoulli never asserted that particles are bound in any way, he just discovered a relationship between static and dynamic pressure. I don't know why people apply his name to the equal transit time theory of lift; there is no real association.
Perhaps because it is always drawn that way, that the same streamline gets separated then goes over the wing, then goes back together. Then in big letters it says Bernoulli principle.
Now that I read about it more, it looks like Bernoulli's principle is just conservation of energy - and as you say, there are no other requirements.
If you don't assume equal transit, then there's no reason to expect the particles above the wing to move faster than those below. And without that, there's no reason Bernoulli's principle would come into play at all.
There are other ways to expect differences in velocity. A bit like the venturi effect in a pipe constriction, a constant flow rate will have to involve faster velocity when the area of flow reduces.
If you trace a line on the wing cross section between the stagnation point and the trailing edge you will see the upper surface restricts/squeezes the flow more than the lower surface. So with a constant flow rate, the upper velocity will be higher even without equal transit.
Yes there is. Suction on upper surface to maintain attached flow -> lower pressure -> increased speed to conserve momentum. Bernoulli's relationship holds true along a streamline, equal transit time doesn't.
I disagree that bernoulli's principle demands equal transit times, but I think it is an irrelevant point.
I believe the key fact is instead that the outer flow is forced into a curve, even though the straight path is technically free (no sail to stop it), because a vacuum (low pressure zone, anyone?) would be generated between the outer flow and the sail.
Hence, the sail needs no thickness to generate its lift, but only to separate the inner and outer flow.
Moreover, due to the viscosity of air, the area of influence of the sails goes well past the immediate layer of outer flow, but rather the layers of outer air closest to the sail have a similar "sail" effect, to a lesser degree, to adjacent layers of air.
The "Equal transit time" is one of the "lie to children" explanations of lift. In fact, classic wings depend on inequal speed caused by a vortex behind the wing - which is also an oversimplified model. Such "bootstrap" vortex causes an opposite vortex to form around the wing, giving difference in speed of air on both sides. Once you have the airflow in the right way, Bernoulli's principle gives you lift.
That's the very simplified version of a simplified explanation used in aviation teaching materials :)
When the sail has no thickness the outer flow cannot go faster and still be a valid Bernoulli effect, because the outer and inner paths have the same distance.
That being said, there might still be another similar principle at work, though technically speaking it should not be called Bernoulli.