On the roughness-induced effective boundary conditions for an incompressible viscous flow

We consider the laminar viscous channel flow with the lateral surface of th e channel containing surface irregularities. It is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channe l. After studying the corresponding boundary layers, we obtain rigorously t he Navier friction condition. It is valid when the size and amplitude of th e imperfections tend to zero. Furthermore, the coefficient in the law is de termined through an auxiliary boundary-layer type problem, and the tangenti al drag force and the effective mass flow are determined up to order O(epsi lon (3) (2)). The value of the effective coefficient is shown to be indepen dent with respect to the position of the mean surface in the region of O(ep silon). (C) 2001 Academic Press.