A complete second-order theory for the unsteady flow about an airfoil due to a periodic gust

A uniformly valid second-order theory is developed for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulas for the airfoil response functions (i.e., fluctuating lift) are given. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. A number of results relevant to the general theory of the scattering of vorticity waves by solid objects are also presented.