Unsteady boundary layer due to an oscillating free stream vs. an oscillating model

The objective of this investigation is to calculate the unsteady boundary layer induced on a thin airfoil by two distinct mechanisms. First, a uniform upstream flow approaches an airfoil which is undergoing a periodic transverse oscillation of specified frequency and amplitude with respect to the wind tunnel. And secondly, a uniform upstream flow approaches the same airfoil which is fixed with respect to the wind tunnel but is now subjected to transverse oscillating flow. The transverse flow is produced at the walls of the wind tunnel test section and will contain a spatial distribution at the test section centerline. The method employed in this analysis uses the classical potential flow/boundary layer interaction. The mathematical model assumes a laminar incompressible flow over a two-dimensional thin airfoil. In addition, the amplitude of the transverse oscillation is assumed to be small with respect to the chord of the airfoil. This restriction is also equivalent to small transverse velocities relative to the upstream flow, if the frequencies are moderate. This assumption produces a set of linear disturbance equations for the unsteady flow. No other restrictions are placed upon the spatial distribution of the transverse flow, although results are presented only for cosine distribution which represents the worst possible case.