Instability of the Flow in a Plane Channel with Compliant Walls of Finite Thickness

Abstract The model of the stability of viscous incompressible flow in a channel with thick compliant walls is developed and studied under the assumption of small disturbances. The eigenvalue problem thus obtained is solved numerically using the collocation method. The computations are carried out for several viscoelastic materials. Some new results concerning the effect of the wall thickness and the characteristic flow velocity on the flow stability are obtained. The effect of viscoelastic properties of the channel wall material on the suppression of the Tollmien–Schlichting instability is estimated.