Turbulent drag characteristic of small amplitude rigid surface waves

The paper discusses an experimental and theoretical investigation of low speed turbulent flow over transverse rigid wavy surfaces having a wavelength on the order of the boundary layer thickness. In addition the results of theoretical investigations of laminar flow over short wavelength waves and turbulent flow over long wavelength (wavelength much greater than the boundary layer thickness) wavy walls are presented. Surface pressure and net drag measurements obtained for the short wavelength symmetric and asymmetric waves in a turbulent flow agreed with the results obtained with a Navier-Stokes spectral code and indicated no significant drag reduction. Several asymmetric wave configurations did significantly reduce the pressure drag compared to sine wave geometries, but these waves still did not produce a net drag reduction. The Navier-Stokes calculations for laminar flow indicated a drag reduction of up to 17 percent for certain short wavelength waves. Boundary layer calculations for turbulent flow over long wavelength surface waves indicated that net drag reductions on the order of 10 percent may be possible for large-radius waisted bodies.