Oscillations of laminar flow velocity in a channel induced by harmonic perturbation of mass injection velocity through the permeable wall

Transient Navies–Stokes equations for laminar flow of incompressible fluid in a channel with permeable wall are reduced to a single equation for the transversal profile of longitudinal flow velocity. Small–amplitude harmonic perturbation of injection velocity induces oscillations of longitudinal velocity with the peak at the walls. The oscillations amplitude in peaks dramatically increases with the distance along the channel; with the frequency growth peaks come closer to the walls.