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For channel flow at subcritical Reynolds numbers ($Re<5772$), alaminar-to-turbulent transition can emerge due to a large transientamplification in the kinetic energy of small perturbations, resulting in anincrease in drag at the walls. The objectives of the present study arethree-fold: (1) to study the nonlinear effects on transient energy growth, (2)to design a feedback control strategy to prevent this subcritical transition,and (3) to examine the control mechanisms that enable transition suppression.We investigate transient energy growth of linear optimal disturbance in planePoiseuille flow at a subcritical Reynolds number of $Re=3000$ using linearanalysis and nonlinear simulation. We find that the amplification of the giveninitial perturbation is reduced when the nonlinear effect is substantial, withlarger perturbations being less amplified in general. Moreover, we designlinear quadratic optimal controllers to delay transition via wall-normalblowing and suction actuation at the channel walls. We demonstrate that thesefeedback controllers are capable of reducing transient energy growth in thelinear setting. The performance of the same controllers is evaluated fornonlinear flows where a laminar-to-turbulent transition emerges withoutcontrol. Nonlinear simulations reveal that the controllers can reduce transientenergy growth and suppress transition. Further, we identify and characterizethe underlying physical mechanisms that enable feedback control to suppress anddelay laminar-to-turbulent transition.

Feedback control for transition suppression in direct numerical simulations of channel flow