Instabilities of a flexible surface in supersonic flow

The stability of a supersonic boundary layer above a flexiblesurface is considered in the limit of large Reynolds numberand for Mach numbers O(1). Asymptotic theory of viscous–inviscidinteraction has been used for this purpose. We found that fora simple elastic surface, for which deflections are proportionalto local pressure differences, the boundary-layer flow remainsstable as it is for a rigid wall. However, when either dampingor surface inertia is included the flow becomes unstable. Moreover,in a certain range of wave numbers the boundary layer developsmore then one unstable mode. It is interesting that these modesare connected to one another via saddle points in the complex-frequencyplane. A more complex Kramer-type surface is also analysed andin some parameter ranges is found to permit the evolution ofunstable Tollmien–Schlichting waves. The neutral curvesare found for a variety of situations related to the parametersassociated with the flexible surface.