Wave momentum and power balance in a boundary layer

The effects which a compliant surface have on wave momentum are examined analytically. The situation is that of high Re flows causing boundary layer turbulence and inducing vibration of the supporting structures. Previous studies have shown that compliant surfaces with irregularities of sufficient slope have drag reducing potential. Expressions are defined to describe an input of wave energy which is partially absorbed by the surface and partially converted into a horizontal force imparted by the fluid on the surface. The models show that compliant surfaces must be designed to react differently to upstream and downstream wave elements, i.e., there must be no symmetry in the upstream/downstream dispersion characteristics. The equations are extended to account for response of the turbulennce to wave absorption. Techniques are discussed for producing either drag or thrust by controlling the distorsions of the surface.