Forced oscillations of a viscous incompressible fluid in a semiinfinite channel

The linear theory of free interaction is used to examine the small forced perturbations of a viscous incompressible flow in a channel formed by two semiinfinite plates, assuming that the perturbations are induced by harmonic oscillators located on opposite walls of the channel. An analysis of flow stability with respect to symmetric and antisymmetric oscillations is presented, and a solution for the pressure function is obtained in the region of stable frequencies. It is shown that the solution to the external problem involving forced perturbations of a boundary layer on a plate is obtained from the solution of the internal problem if distance from the inlet (or the boundary layer thickness), is taken to be the similarity parameter.