The form of the loss of stability of a boundary layer on a flexible surface at high Reynolds numbers

The linear problem of the stability of a boundary layer on a flexible surface with respect to small two-dimensional perturbations in the form of travelling waves is considered. A boundary-layer model with self-induced pressure (a three-layer model) is used to describe the fluid flow. The flexible surface is modelled by a thin plate lying on an elastic base. It is shown that, in the system in question two forms of loss of stability are possible: Tollmien-Schlichting instability and instability caused by the action of hydrodynamic pressure on the surface around which the flow occurs. A special feature of the latter form of instability is that there is no neutral system of perturbations or a sudden onset of instability. The solutions obtained are analysed and the conditions leading to the appearance of such instability are established. (C) 2003 Elsevier Science Ltd. All rights reserved.