Transitional boundary-layer response to wall vibrations

The effects of wall vibration on the development of Tollmien-Schlichting (T-S) waves in a transitional flat-plate boundary layer are considered. Theoretically, the dynamic interaction between T-S waves and velocity perturbations induced by the vibrating wall is demonstrated through the kinetic energy balance of velocity perturbations. For a compliant wall, the response of T-S waves to velocity perturbations induced by the vibrating wall has been studied for various phase angles between the T-S wave velocity and the wall velocity, and for various amplitudes of the wall vibration. Experimentally, T-S waves are induced by a vibrating wire located in the upstream portion of the wall. The downstream portion is vibrated at the same frequency as that of the wire and the phase between the two oscillations can be varied. Depending on the phase angle, the T-S waves may be either amplified or attenuated, even if the wavelengths do not coincide.