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For a Mach 4.5 flat-plate adiabatic boundary layer, we study the sensitivityof the first, second Mack modes and streaks to steady wall-normalblowing/suction and wall heat flux. The global instabilities are characterisedin frequency space with resolvent gains and their gradients with respect towall-boundary conditions are derived through a Lagrangian-based method. Theimplementation is performed in the open-source high-order finite-volume codeBROADCAST and Algorithmic Differentiation is used to access the high-orderstate derivatives of the discretised governing equations. For the second Mackmode, the resolvent optimal gain decreases when suction is applied upstream ofFedorov's mode S/mode F synchronisation point leading to stabilisation andconversely when applied downstream. The largest suction gradient is in theregion of branch I of mode S neutral curve. For heat flux control, strongheating at the leading edge stabilises both the first and second Mack modes,the former being more sensitive to wall-temperature control. Streaks are lesssensitive to any boundary control in comparison with the Mack modes.Eventually, we show that an optimal actuator consisting of a single steadyheating strip located close to the leading edge manages to damp all theinstabilities together.

Adjoint-based linear sensitivity of a hypersonic boundary layer to steady wall blowing-suction/heating-cooling