A resolvent analysis of the effect of passive perforated surfaces on wall-bounded turbulence

This study investigates passive perforated surfaces that permit unsteady wall transpiration at specific frequencies in response to pressure fluctuations at the wall. These surfaces are described to interact with the wall-bounded turbulence through imposing an impedance boundary condition. A theoretical framework based on resolvent analysis was employed to evaluate the turbulent channel flow response to this impedance boundary condition which was determined from experimental measurements of sample fabricated passive perforated surfaces. Through this analysis, the relationship between pressure and wall-normal velocity fluctuations that can attenuate the near-wall turbulent activities was explored. It was found that the impedance angle had a key role on the flow response which led to either amplification or suppression of the turbulent structures associated with the near-wall turbulence cycle. The effective angle of impedance for suppressing the near-wall turbulence was found to be in the range of 0.4 pi and 1.4 pi. As the impedance angle dictated the phase difference between transpiration and pressure fluctuations at the wall, it was shown that an in-phase relationship between wall-normal velocity and pressure fields at the wall imposed by this favourable range of impedance angles led to suppression of the near-wall resolvent mode.