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We will present a formal asymptotic solution of the incompressible Navier-Stokes equations that describes the interaction of a rapidly oscillating shear flow with a mean flow. The mean flow satisfies the incompressible Euler equations, with a Reynolds averaged stress from the shear flow, while the shear flow satisfies unsteady Prandtl boundary layer equations, forced by gradients of the mean flow. The linearization of these equations has been used by Friedlander, Vishik, Lifschitz, and others to study the instability of solutions of the incompressible Euler equations.