Asymptotic Approximation of the Solution of Stokes Equations in a Domain with Highly Oscillating Boundary

We consider a viscous incompressible flow in an infinite horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities which size depends on a small parameter, and with a fixed height. We assume that the flow is governed by the stationary Stokes equations. Using a boundary layer corrector we derive and analyze a first order asymptotic approximation of the flow. © 2007 Università degli Studi di Ferrara.