A global stability analysis of a thin-airfoil wake

In this paper we review the problem of the wake-flow stability for a thin airfoil by using both a locally plane-wave analysis, based on a WKBJ approximation, and a global numerical stability analysis. The core of the instability is further localized by performing a structural sensitivity analysis of the linearized Navier-Stokes operator as outlined in [7]. In particular the sensitivity of the eigenvalue to a spatially-localized feedback from velocity to force is evaluated by using the product of the direct and adjoint global mode. It is shown, using a plane wave analysis, that the flow at the trailing edge is absolutely unstable for any Reynolds number for values of the parameter m corresponding to separation of the base flow. The analysis further shows that the base flow at the trailing edge is not absolutely unstable as the value of m tends to zero. The global eigenvalue analysis shows that the frequency and growth rate are very similar to what is found with the local plane wave analysis at the trailing edge. Finally, the structural sensitivity analysis indicates that the wavemaker is situated just downstream of the trailing edge.