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

TL;DR

This study investigates large-scale opposition flow control in turbulent channel flows, revealing linear instability effects and resonance phenomena when controlling at the logarithmic layer, with implications for flow manipulation.

Contribution

It demonstrates the feasibility of opposition control at the logarithmic layer and uncovers linear instability mechanisms influencing flow response and large-scale flow manipulation.

Findings

Control creates a virtual-wall effect reducing wall-normal velocity.

Phase lag in control induces spanwise rollers due to linear instability.

Control response can be predicted linearly based on advection velocity.

Abstract

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional setup 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.