Stability and sensitivity analysis for flow control

Wakes, jets and boundary layers are examples of open flows, where fluid particles are convected downstream outside the physical domain of interest. These flows can exhibit several types of instabilities, depending on the considered geometry and flow conditions. A common classification in open flows is made according to the features of their instabilities. Flows are called noise amplifiers, or amplifiers, when the instabilities are the result of strong amplifications of external disturbances, that also define their characteristics. Conversely, oscillators are flows that show an intrinsic dynamics and, under specific conditions, synchronised self-sustained oscillations occur. The characterization of the instability mechanisms is the fundamental stage to design effective and efficient control strategies. In this thesis, the study of amplifiers and oscillators is carried out in the framework of the linear stability analysis. Concerning the amplifiers, the study is here addressed to investigate passive methods for transition delay in a Blasius boundary layer, aimed at a reduction of the friction drag. All the control strategies here considered are based on the methods of the spanwise mean velocity gradient, where the laminar-turbulent transition is delayed through a modulation of the velocity inside the boundary layer in spanwise direction. Different control devices are investigated in detail through the use of direct numerical simulations and local stability analyses. The results of the stability problem are summarized in neutral stability curves, that allow to identify promising configurations in terms of stabilization of the Blasius unstable mode. The study of oscillators is here conducted characterizing the leading global unstable modes that define the flow behaviours. The flow in micromixers is first of all investigated using global stability analysis. In particular, starting from the well documented T-junction configuration, variations in geometry and fluid properties are here considered to assess their effects on the onset of different flow regimes. Moreover, the global stability approach is also applied to the flow past a sphere, in order to characterize its second bifurcation that drives the system from a steady asymmetric solution towards an unsteady flow state. Finally, a theoretical work is presented, in which an accurate estimation of the global stability modes and of the characteristics of wakes, under assumption of slowly non-parallel flow, is obtained by a higher-order correction term in the WKBJ asymptotic approximation.