How can the Magnus effect be explained with Bernoulli?

Hi folks,

According to Bernoulli’s principle, an increase of speed will be
accompanied by a decrease in static pressure. However, Bernoulli’s law
only pertains to flows without any external energy being added (or
removed).
That’s why I do not understand why Bernoulli can be used to explain
the Magnus effect.
If a clockwise rotating cylinder (Flettner-Rotor) is moved through the
air from right to left (i.e. free stream direction is from left to
right), this will cause the flow on the upper site (free stream
velocity + rotation) to be faster than on the lower site (free stream
velocity - rotation). More importantly, an upward lifting force acting
on the turning cylinder can be observed.
All books / internet sites I checked so far explain the lifting effect
by Bernoulli’s law (faster flow on the upper site of the cylinder
causes a drop in static pressure and hence lift).
However, I don’t see why Bernoulli applies here as the rotation of the
cylinder means to add additional energy to the free stream and thus
should not lead to a reduced static pressure, should it?
Therefore, I would be very grateful for any advice why the Magnus
effect can be explained with Bernoulli’s law.

Thank you
Mikki