The canonical derivation of Betz's law for wind turbines discusses pressure before and after a windmill actuator disk.
It's obvious that the wind resistance of the disk would cause a pressure increase before the windmill. But why is there a similar pressure drop behind the windmill (negative overshoot below ambient pressure)?
Note that this question is not about turbulence which is fully ignored in actuator disk momentum theory. This also does not depend on any aerodynamics like Bernoulli force on the wing of the turbine as again, all momentum actuator disk theory is independent of the implementation of the wind machine.
Indeed this question was controversial between 1865 and 1920 with many feeling a pressure drop was inconceivable despite Froude's assertion that it was there (Parsons' model was rejected).
But I can't find an intuitive or simple explanation in terms of momentum, energy or incompressible flow as to what causes the pressure drop.
Help?
Addendum: I note that there is a circular answer to this question that isn't helpful in explaining the phenomena. The circular answer is that if the wind speed through the actuator disk is higher than the final wake wind speed, then there has to be a pressure change. That answer is circular logic since the calculation of the higher wind speed presupposes a pressure drop!
As a counter proposition, suppose the wind speed through the actuator disk were the same as the wake wind speed. There still would be a pressure build up in front of the actuator disk to power the windmill. And you could then have ambient pressure behind the windmill. Why is this the wrong answer? I can't see what I'm missing.
