Structural and spectral analysis of varying-phase opposition control in turbulent channel flow

This study investigates the structural and spectral changes of a low Reynolds number turbulent channel flow due to varying-phase opposition control by means of direct numerical simulation. The focus is on three example controllers, each with a different phase shift in Fourier domain between sensor measurement and actuator response. Two of these controllers lead to drag reduction, while the third increases drag substantially. Based on snapshots of the flow structure and actuator response, as well as spatial spectra at various wall-normal planes, we show that drag reduced flows exhibit a strong imprint of the near-wall cycle in the control signal and that near-wall vortices are attenuated under these control schemes. In case of a drag increase, the control signal is much more multiscale and the most energetic scales are spanwise constant structures. In accordance with an increase in drag, these flows also show substantially more vortical activity, even far away from the wall. The present results suggest a range of spatial scales which may be used in the future to better understand the role of the phase and devise novel controllers with relaxed spatial resolution requirements.