Sensitivity of plane Poiseuille flow to vibration of the channel walls (Q1317736)

The paper is devoted to a study of the sensitivity of plane Poiseuille flow to localized two-dimensional harmonic vibrations of the channel wall. With the basic flow being exactly parallel, the Fourier method is used to solve the linearized Navier-Stokes equations for a triangular shaped streamwise wall vibration intensity. Disturbances, symmetric with respect to the channel center, lead to flow rate oscillations, analogous to a fluctuating pressure gradient. Antisymmetric disturbances generate Tollmien-Schlichting instability waves, and the dependence of their amplitude is presented as function of the vibration frequency and Reynolds number.