The effects of compliant walls on transition and turbulence

Two theoretical approaches to the phenomenon of drag reduction by a compliant wall are proposed. One is to study the limit cycle oscillations of the Navier-Stokes equations for a boundary layer flow over a compliant wall or a Poiseuille flow in a channel with a compliant wall. The other is a complementary study of a simpler, sequential model, which partially decouples the fluid and wall motions. In this approach, a 'Total Model' is constructed from suitable component models. While the first study is more rigorously based, it will be initially limited, by computational constraints, to relatively low Reynolds numbers. The second, more approximate approach, will allow consideration of a fully developed turbulent flow. The Total Model will predict the compliant wall motion accurately, but will not per se be sufficient to predict the skin friction drag. However, once the wall motion is known, the skin friction drag and the pressure drag can be computed separately, using one of the existing models.