Linear instability and resonance effects in large-scale opposition flow control

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional set-up consists of measuring wall-normal velocity in the buffer layer and opposing it at the wall. This work explores the possibility of implementing this strategy with a detection plane in the logarithmic layer, where control could be feasible experimentally. We apply control on a channel flow at Re-tau = 932, only on the eddies with relatively large wavelengths (lambda/h > 0.1). Similarly to the buffer layer opposition control, our control strategy results in a virtual-wall effect for the wall-normal velocity, creating a minimum in its intensity. However, it also induces a large response in the streamwise velocity and Reynolds stresses near the wall, with a substantial drag increase. When the phase of the control lags with respect to the detection plane, spanwise-homogeneous rollers are observed near the channel wall. We show that they are a result of a linear instability. In contrast, when the control leads with respect to the detection plane, this instability is inactive and oblique waves are observed. Their wall-normal profiles can be predicted linearly as a response of the turbulent channel flow to a forcing with the advection velocity of the detection plane. The linearity, governing the flow, opens a possibility to affect large scales of the flow in a controlled manner, when enhanced turbulence intensity or mixing is desired.

Automated summary

Opposition flow control is an effective strategy for turbulent wall-bounded flows. This study investigates the implementation of this strategy in the logarithmic layer using a detection plane, and reveals the various responses it induces in a channel flow, such as virtual-wall effect, increased streamwise velocity, Reynolds stress, linear instability, and oblique waves.