Global Stability Analysis of Blasius Boundary-Layer Flow over a Compliant Panel Accounting for Axial and Vertical Displacements

A state-space method is deployed in order to investigate the global stability of the Blasius base flow over a finite compliant panel embedded between rigid upstream and downstream wall sections accounting both for axial and vertical structural displacements. It is shown that global temporal instability can occur through the resonance between the Travelling-Wave Flutter (TWF) or Tollmien-Schlichting Wave (TSW) instability and the structural modes due to the vertical motion of the compliant section, while the axial structural modes remain stable in time. Local spatial stability of the least stable global temporal TSW mode reveals that a downstream amplified axial structural mode coexists with the downstream amplified TSW mode and it is stabilized by increasing the panel stiffness and destabilized as the Reynolds number decreases.