The complaint wall is a relatively recent idea to reduce the drag by using flexible coatings on the aero- hydrodynamic surfaces. The idea of flexible skins comes from observations on swimming dolphins, and more generally on animal propulsion.
The compliant wall must interact with the boundary layer and influence its development, laminar or turbulent. If this has to be true, the wavelength of the skin flexibility must be of the same order of magnitude of the boundary layer thickness, while the amplitude must be of the same order as the viscous sublayer.
The idea is that, when the surface is affected by fluid flow around it, it will start an interaction surface-boundary layer such that the boundary layer remains attached for a longer length and the drag of the system will be reduced.
The problem, however, is not so easy. The properties of the compliant surface must be well understood, else the effect is … the opposite (that is a compliant surface that triggers boundary layer separation).
Some energy considerations are necessary: