Comparison of the costs for generating the Tollmien–Schlichting waves and optimal disturbances using optimal blowing-suction

The problem of generating the Tollmien–Schlichting waves (leading eigenmodes) and optimal disturbanceswith a given accuracy using optimal blowing–suction is considered with the example of Poiseuille flow in aduct of square cross-section and streamwise-harmonic blowing-suction through the duct walls. The problem is reduced to solving optimal control problems for the linearized governing equations of viscous incompressible media. It is shown for the first time that generating the optimal disturbances using blowing–suctionis much more expensive than generating the leading modes.