Comparison of the Costs of Generating Tollmien–Schlichting Waves and Optimal Disturbances by Optimal Blowing–Suction

Abstract

The problem of generating Tollmien–Schlichting waves (leading eigenmodes) and optimal disturbances with a given accuracy using optimal blowing–suction is considered with the example of Poiseuille flow in a duct 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–suction is much more expensive than generating the leading modes.