The attenuation of three-dimensional wavepackets of streaks and Tollmien-Schlichting (TS) waves in a transitional boundary layer using feedback control is investigated numerically. Arrays of localized sensors and actuators (about 10-20) with compact spatial support are distributed near the rigid wall equidistantly along the spanwise direction and connected to a low-dimensional (r = 60) linear quadratic Gaussian controller. The control objective is to minimize the disturbance energy in a domain spanned by a number of proper orthogonal decomposition modes. The feedback controller is based on a reduced-order model of the linearized Navier-Stokes equations including the inputs and outputs, computed using a snapshot-based balanced truncation method. To account for the different temporal and spatial behaviour of the two main instabilities of boundary-layer flows, we design two controllers. We demonstrate that the two controllers reduce the energy growth of both TS wavepackets and streak packets substantially and efficiently, using relatively few sensors and actuators. The robustness of the controller is investigated by varying the number of actuators and sensors, the Reynolds number and the pressure gradient. This work constitutes the first experimentally feasible simulation-based control design using localized sensing and acting devices in conjunction with linear control theory in a three-dimensional setting.

Modal analysis by proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) of experimental data from a fully turbulent flow is presented. The flow case is a turbulent confined jet with co-flow, with Reynolds number based on the jet thickness of Re=10700. Experiments are performed with time-resolved Particle Image Velocimetry (PIV). The jet is created in a square channel with the confinement ratio is 1:5. Statistics of the flow are presented in terms of mean and fluctuating fields. Analysis of spatial spectra and temporal spectra reveal the presence of dominant wavelengths and frequenciesembedded in broad-band turbulent spectrum. Frequencies in the shearlayer migrate from St ≈ 1 near the jet inlet to St < 0.1 at 18 jet thickness downstream.

This flow case provides an interesting and challenging benchmark for testing POD and DMD and discussing their efficacy in describing a fully turbulent case. At first, issues related to convergence and physical interpretation of the modes are discussed, then the results are analyzed and compared. POD analysis reveals the most energetic spatial structures that are related to the flapping of the jet; a low frequency peak (St = 0.02) is found when the associated temporalmode is analyzed. Higher order modes revealed the presence of fasteroscillating shear flow modes combined to a recirculation zone near the inner jet. The flapping of the inner jet is sustained by this region. A good agreement is found between DMD and POD; however, DMD is able to rank the modes by frequencies, isolating structures associated to harmonics of the flow.