Influence of inertia of a compliant surface on viscous instability of an incompressible boundary layer

An incompressible boundary layer on a compliant plate is considered. The influence exerted by the inertia of the plate on the stability of the boundary layer is studied in the limit of high Reynolds numbers on the basis of triple-deck theory. The flow is found to have two additional oscillation eigenmodes, one of which is always unstable, but grows more slowly than classical modes corresponding to Tollmien–Schlichting waves. It is shown that, with decreasing inertia of the plate, the perturbations first split into two wave packets, which later merge in a single one that grows progressively more quickly.