Unsteady plane flow past curved obstacles with infinite wakes

A theory of unsteady flow about obstacles behind which are wakes or cavities of infinite extent is developed for the case when the velocities and displacements of the unsteady perturbations about the mean steady motion are small. Unsteady Helmholtz flows (constant wake pressure) receive detailed attention both for general non-uniform motion and for the special case of harmonic motions of long duration. A number of possible applications of the theory to aerodynamic problems are indicated, the most important being the flutter of a stalled aerofoil. The classical theory of unsteady aerofoik motion is shown to be a special case of the theory given in this paper.