Choosing Between Active and Passive Flow Control via Input-Output Analysis: Application to Couette Flow

Input-output analysis is utilized to determine between passive or active flow control strategies in transitional wall-bounded shear flows for a given streamwise and spanwise wave number pair $\text {(}k_{x},k_{z}\text {)}$ and to quantify the optimal temporal frequency in active flow control with constant actuation frequency that yields the strongest response to external forcing. Applying our methodology to plane Couette base flow reveals that for most actuation geometries and Reynolds numbers Re, the optimal actuation frequency is zero, corresponding to passive control devices or actuators that impose continuous forcing. We find that the scenarios in which active actuation is preferred are concentrated on a thin strip on the logarithmic $Re-k_{x}$ plane. Using our results, we obtain two equations: the first equation allows us to determine if active or passive actuation is preferred for a given streamwise and spanwise wave number pair and the Reynolds number. The second equation allows us to determine the optimal actuation frequency in the region where active actuation is preferred without the need for exhaustive experimentation or high-fidelity simulations. Our analysis shows that this optimal actuation frequency is inversely proportional to the Reynolds number.