Preventing transition to turbulence using streamwise traveling waves: direct numerical simulations

We use direct numerical simulations of the nonlinear Navier-Stokes (NS) equations to examine the effectiveness of streamwise traveling waves for controlling the onset of turbulence in a channel flow. We highlight the effect of a base flow induced by the streamwise traveling waves on the dynamics of velocity fluctuations and on the net efficiency of control. It is shown that properly designed downstream traveling waves are capable of reducing the fluctuations' kinetic energy and maintaining the laminar flow. In contrast, our results demonstrate that upstream traveling waves promote turbulence even when the uncontrolled flow stays laminar. Our numerical simulations elucidate the predictive power of the theoretical framework developed in a companion paper and suggest that the linearized NS equations with uncertainty serve as an effective control-oriented model for preventing transition.