Free and induced oscillations in Poiseuille flow

Characteristic features inherent in the small-disturbance propagation process in the fully-developed two-dimensional incompressible flow through an infinite channel are discussed. The disturbances are generated by two oscillators located on the opposite walls. The typical Reynolds number is supposed to be large. The asymptotic analysis is done within the framework of the theory describing the free interaction of the viscous wall layers with the fluid core. The first mode of free disturbances appears to be either stable or unstable depending upon the wave length. Therefore the induced oscillations decay far downstream only for sufficiently low frequencies. As the frequency approaches some critical value, the damping decrement becomes indefinitely small.