  We study the boundary layer theory for slightly viscous stationary flows
forced by an imposed slip velocity at the boundary. According to the theory of
Prandtl (1904) and Batchelor (1956), any Euler solution arising in this limit
and consisting of a single ``eddy" must have constant vorticity. Feynman and
Lagerstrom (1956) gave a procedure to select the value of this vorticity by
demanding a \textit{necessary} condition for the existence of a periodic
Prandtl boundary layer description. In the case of the disc, the choice --
known to Batchelor (1956) and Wood (1957) -- is explicit in terms of the slip
forcing. For domains with non-constant curvature, Feynman and Lagerstrom give
an approximate formula for the choice which is in fact only implicitly defined
and must be determined together with the boundary layer profile. We show that
this condition is also sufficient for the existence of a periodic boundary
layer described by the Prandtl equations. Due to the quasilinear coupling
between the solution and the selected vorticity, we devise a delicate iteration
scheme coupled with a high-order energy method that captures and controls the
implicit selection mechanism.
