Suppressing subcritical transition in plane Poiseuille flow

Abstract

For channel flow at subcritical Reynolds numbers (Re<5772), a laminar-to-turbulent transition can emerge due to a large transient amplification in the kinetic energy of small perturbations, resulting in an increase in drag at the walls. The objectives of the present study are twofold: (1) to design a feedback control strategy to prevent this subcritical laminar-toturbulent transition, and (2) to examine the control mechanisms that enable transition suppression. In this paper, we investigate transient energy growth of linear optimal disturbance of plane Poiseuille flow at a subcritical Reynolds number of Re = 3000 using linear analysis and nonlinear simulation. We find that the amplification of the given initial perturbation revealed from linear analysis is suppressed by the presence of the nonlinearity in the direct numerical simulations, with larger initial perturbations being less amplified in general. Moreover, we design linear quadratic optimal controllers to delay transition via wall-normal blowing and suction actuation at the channel walls. We demonstrate that these feedback controllers are capable of reducing transient energy growth in the linear setting. Next, the performance of the same controllers is evaluated for nonlinear flows where a laminar-to-turbulent transition emerges without control. Nonlinear simulations reveal that the controllers can reduce transient energy growth of optimal disturbances and suppress transition. Further, we identify and characterize the underlying physical mechanisms that enable feedback control to suppress and delay laminar-to-turbulent transition. These findings can provide valuable insights and guidance for developing actuation strategies in future investigations.