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

Abstract

In this paper we develop a uniformly valid, second-order theory for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulae 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.