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Linear optimal gains are computed for the subcritical two-dimensionalseparated boundary-layer flow past a bump. Very large optimal gain values arefound, making it possible for small-amplitude noise to be strongly amplifiedand to destabilize the flow. The optimal forcing is located close to the summitof the bump, while the optimal response is the largest in the shear layer. Thelargest amplification occurs at frequencies corresponding to eigenvalues whichfirst become unstable at higher Reynolds number. Nonlinear direct numericalsimulations show that a low level of noise is indeed sufficient to triggerrandom flow unsteadiness, characterized here by large-scale vortex shedding.Next, a variational technique is used to compute efficiently the sensitivity ofoptimal gains to steady control (through source of momentum in the flow, orblowing/suction at the wall). A systematic analysis at several frequenciesidentifies the bump summit as the most sensitive region for control with wallactuation. Based on these results, a simple open-loop control strategy isdesigned, with steady wall suction at the bump summit. Linear calculations oncontrolled base flows confirm that optimal gains can be drastically reduced atall frequencies. Nonlinear direct numerical simulations also show that thiscontrol allows the flow to withstand a higher level of stochastic noise withoutbecoming nonlinearly unstable, thereby postponing bypass transition. In thesupercritical regime, sensitivity analysis of eigenvalues supports the choiceof this control design. Full restabilization of the flow is obtained, asevidenced by direct numerical simulations and linear stability analysis.

Open-loop control of noise amplification in a separated boundary layer flow