The Generation of Disturbances in a Boundary Layer by Wall Perturbations: The Vibrating Ribbon Revisited Once More

Abstract

The creation of velocity fluctuations in a boundary layer by a time-periodic point source disturbance on the boundary wall is discussed. The boundary value problem models the flow created by a vibrating ribbon exciter originally employed by Schubauer & Skramtad in their historic experiment that demonstrated the existence of Tollmien-Schlichting waves. It will be shown here how the ensuing oscillatory motion in the flow can be split into two components. One describes the far field or asymptotic part downstream of the source, while the other provides the near field or local solution close to the source. The resultant flow disturbance is described by the convolution of these two components. Numerical integrations of the Orr-Sommerfeld equation have been obtained for a vibrating ribbon acting on a “parallel” boundary layer.