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 necessary condition for the existence of a periodic Prandtl boundary layer description. We will show that this condition is also sufficient for the existence of a periodic boundary layer described by the Prandtl equations. 

This is joint work with S. Iyer and T. Nguyen.