Asymptotic theory of an oscillating wing section in weak ground effect

This study addresses unsteady aerodynamic forces acting on a wing section oscillating in a steady incompressible (and inviscid) uniform flow in presence of a distant flat ground. Three fundamental dimensionless parameters characterize the magnitude of those forces: the ratio δ of the wing transversal displacement to its chord, the ratio ε of the wing chord to its average distance from the ground, and the ratio k of the wing chord to the distance traveled by the flow during one oscillation period. With the first two serving as small parameters, asymptotic series of the form δf0(k)+δε2f1(k)+δε2g(k/ε)f2(k)+⋯ have been constructed for the wing lift and pitching moment. In the case of heave oscillations, three-terms-series for the lift fits nicely the available numerical data for wide range of δ,ε and k values.