This paper evaluates and modifies the so-called suboptimal control technique for turbulent skin friction reduction through a combination of low-order modelling and direct numerical simulation (DNS). In a previous study, Nakashima et al. (J. Fluid Mech., vol. 828, 2017, pp. 496–526) employed resolvent analysis to show that the efficacy of suboptimal control was mixed across spectral space when the streamwise wall shear stress (case ST) was used as a sensor signal, i.e. specific regions of spectral space showed drag increment. This observation suggests that drag reduction may be attained if control is applied selectively in spectral space. DNS results presented in the present study, however, do not show a significant effect on the flow with selective control. A posteriori analyses attribute this lack of efficacy to a much lower actuation amplitude in the simulations compared to model assumptions. Building on these observations, resolvent analysis is used to design and provide a preliminary assessment of modified control laws that also rely on sensing the streamwise wall shear stress. Control performance is then assessed by means of DNS. The proposed control laws generate as much as $10\,\%$ drag reduction, and these results are broadly consistent with resolvent-based predictions. The physical mechanisms leading to drag reduction are assessed via conditional sampling. It is shown that the new control laws effectively suppress the near-wall quasi-streamwise vortices. A physically intuitive explanation is proposed based on a separate evaluation of clockwise and anticlockwise vortices.
Piecewise suboptimal control laws for differential games
