Assessment of suboptimal control for turbulent skin friction reduction via resolvent analysis

This paper extends the resolvent analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336-382) to elucidate the drag reduction mechanisms for the suboptimal control laws proposed by Lee, Kim & Choi (J. Fluid Mech., vol. 358, 1998, pp. 245-258). Under the resolvent formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes identified via a gain-based decomposition of the Navier-Stokes equations. This decomposition enables targeted analyses of the effects of suboptimal control on high-gain modes that serve as useful low-order models for dynamically important coherent structures such as the near-wall (NW) cycle or very-large-scale motions. The control laws generate blowing and suction at the wall that is proportional to the fluctuating streamwise (Case ST) or spanwise (Case SP) wall shear stress, with the magnitude of blowing and suction being a design parameter. It is shown that both Case ST and SP can suppress resolvent modes resembling the NW cycle. However, for Case ST, the analysis reveals that control leads to substantial amplification of flow structures that are long in the spanwise direction. Quantitative comparisons show that these predictions are broadly consistent with results obtained in previous direct numerical simulations. Further, the predicted changes in mode structure suggest that suboptimal control can be considered a modified version of opposition control. In addition to the study of modes resembling the NW cycle, this paper also considers modes of varying speed and wavelength to provide insight into the effects of suboptimal control across spectral space.