  Linear optimal gains are computed for the subcritical two-dimensional
separated boundary-layer flow past a bump. Very large optimal gain values are
found, making it possible for small-amplitude noise to be strongly amplified
and to destabilize the flow. The optimal forcing is located close to the summit
of the bump, while the optimal response is the largest in the shear layer. The
largest amplification occurs at frequencies corresponding to eigenvalues which
first become unstable at higher Reynolds number. Nonlinear direct numerical
simulations show that a low level of noise is indeed sufficient to trigger
random flow unsteadiness, characterized here by large-scale vortex shedding.
Next, a variational technique is used to compute efficiently the sensitivity of
optimal gains to steady control (through source of momentum in the flow, or
blowing/suction at the wall). A systematic analysis at several frequencies
identifies the bump summit as the most sensitive region for control with wall
actuation. Based on these results, a simple open-loop control strategy is
designed, with steady wall suction at the bump summit. Linear calculations on
controlled base flows confirm that optimal gains can be drastically reduced at
all frequencies. Nonlinear direct numerical simulations also show that this
control allows the flow to withstand a higher level of stochastic noise without
becoming nonlinearly unstable, thereby postponing bypass transition. In the
supercritical regime, sensitivity analysis of eigenvalues supports the choice
of this control design. Full restabilization of the flow is obtained, as
evidenced by direct numerical simulations and linear stability analysis.
