On the theory of unsteady shearing flow over a slot

Howe (1981) has proposed a linearized theory of unsteady shearing flow of a weakly compressible fluid over a two-dimensional slot in a thin rigid plate. The current investigation is concerned with an extension of this theory. The basic mean flow is generalized to include the possibility of there being parallel mean flows on both sides of the plate. An asymptotic theory is introduced to account for the influence of the ejected vorticity. This approach is based on a proposal due to Liepmann (1954) for calculating the aerodynamic noise generated by a turbulent boundary layer. A general formula is derived for the rate at which acoustic energy is extracted from the mean flow, and a study is conducted of the special case in which the mean flow velocities are the same on both sides of the plate.