Sensitivity and forcing response in separated boundary-layer flow

The stability of separating boundary-layer flow on a flat plate is numerically investigated by means of three-dimensional eigenmodes of the linearized Navier-Stokes equations obtained by linearization about the steady state. The disturbance variables are approximated using a Chebyshev-Chebyshev collocation technique in inhomogeneous directions. Due to the large size of the generalized eigenvalue problem, an Arnoldi iterations method using ARPACK routines is employed. By expanding the flow disturbance variables in the basis of eigenmodes the growth potential is revealed by the computation of the optimal initial condition. This yields a low-dimensional model of the flow and a unified view on its stability characteristics. Furthermore, a general formalism is developed to assess how harmonic forcing may alter the stability properties of flows studied by a global approach of the linear stability theory. This formalism is based on the sensitivity analysis performed by the pseudo-spectrum calculation and the resolution of the forced problem. These results are compared and extended with direct numerical simulations