On the asymptotic limit of flows past a ribbed boundary

Several physical as well as numerical experiments have shown that a fluid flowing between two parallel plates can be significantly influenced by the shape of the boundary. In particular, the presence of microscopic asperities parallel to the flow (riblets) can considerably reduce the drag experienced by the fluid (see Chu and Karniadakis [7], Savill et al. [11]). The main objective of the present paper is to discuss mathematical aspects of this phenomenon. For the sake of simplicity, we consider a flow confined to a domain Ω ⊂ R, periodic with respect to the first two spatial coordinates y = (x1, x2):